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exact contraction rate (2/3)⁶ along the physical trajectory; source at ρ = −φ₀/24 (one seed quantum before the branch point); honest negatives: pole ≠ integer F-steps from source (t=2.84 ⇒ continuous generator missing), φ₀/24 stays [P]", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv93_koide_relaxation_toy.py", "sourceSha256": "941524ab633f007b0b6e6a6928b965bae2ec7c14c2af482573e65138de27cfc4", "linkedClaimIds": [ "FR.KOIDE.05" ], "sectionIds": [ "section:568b5e9acdb7b04367d3", "section:6b03fdb0bab2125a7ce4", "section:8ac4310a6a4cf6c449f1", "section:ab9e7e520130ecc7da7c", "section:eb0ad9c39f3387e3dcf3", "section:f0ac30137703825661c6", "section:fdf63a1d99769ab37ccb" ], "activeSectionIds": [ "section:6b03fdb0bab2125a7ce4", "section:8ac4310a6a4cf6c449f1", "section:ab9e7e520130ecc7da7c", "section:eb0ad9c39f3387e3dcf3", "section:fdf63a1d99769ab37ccb" ], "evidenceId": "python_verification:verification/v93_koide_relaxation_toy.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v93_koide_relaxation_toy.py", "pubMirrorHash": "941524ab633f007b0b6e6a6928b965bae2ec7c14c2af482573e65138de27cfc4", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v93_koide_relaxation_toy.py" }, { "id": "v94_sheet_diamond", "filename": "v94_sheet_diamond.py", "path": "verification/v94_sheet_diamond.py", "cluster": "registry", "synopsis": "Sheet diamond: R, K, L, F are four points of ONE surface M(s,t) = R+Q·diag(s,t,t) (mass pencil = the cut (1+x,x−1); 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center: det C = 14, SNF (1,1,14), ΣC = 31 = 2^g−1 (the IR gap-bound numerator), Pl_R(C) = 7·(2,3,1) on the same ray as Pl_R(L) = 10·(2,3,1); the G₂ reading stays audit-typed, not promoted", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv95_centered_diamond.py", "sourceSha256": "8130affdc27ed6c125c774dd2a28fd4cb548b6bdb4f5a51c793f6c61fe2a892e", "linkedClaimIds": [ "FLAV.DIAMOND.02" ], "sectionIds": [ "section:038ae1c94af71398ea72", "section:2678ed3ba0ed508e2d8e", "section:2ff762f6d6932ac2b2c5", "section:51e91159532ef7479ff8", "section:6a93c4dd5fe420e1990e", "section:95036dacfe44edfdb2c9", "section:9575cef792be9f73f7ff", "section:ab9e7e520130ecc7da7c", "section:bb2a02a767e560376342", "section:d90bd5e1e6d8fa41397d", "section:f4ce21377eb152ef27fe" ], "activeSectionIds": [ "section:038ae1c94af71398ea72", "section:2ff762f6d6932ac2b2c5", "section:51e91159532ef7479ff8", "section:95036dacfe44edfdb2c9", "section:9575cef792be9f73f7ff", "section:ab9e7e520130ecc7da7c", "section:bb2a02a767e560376342", "section:f4ce21377eb152ef27fe" ], "evidenceId": "python_verification:verification/v95_centered_diamond.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v95_centered_diamond.py", "pubMirrorHash": "8130affdc27ed6c125c774dd2a28fd4cb548b6bdb4f5a51c793f6c61fe2a892e", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v95_centered_diamond.py" }, { "id": "v96_branch_kernel_selection", "filename": "v96_branch_kernel_selection.py", "path": "verification/v96_branch_kernel_selection.py", "cluster": "registry", "synopsis": "Branch-kernel selection (P1 unblocked): at each branch point the anchor block is RANK 1 with canonical integer kernels (Koide: w=(2,2,−7), v=(2,2,−3); 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the Koide 2/3 = |ℤ₂|/N_fam is the exact Nariai/de-Sitter entropy bound (per horizon 1/3); interpolation (x²+1)/Φ₃(x) (the N_fam cyclotomic); three-sheet entropy total |ℤ₂|·S_dS conserved for every M; Koide-form root quotient ranges [3/8, 1/2] = the nonzero SU(4)₁ weights; the mass line is a split double cover (branch ±1/N_fam, deck = horizon swap); evaporation flows away from the anchor point (repeller/attractor orientation as in flavor, v82); seam-unit table: dM = c₃κdA, Smarr 2c₃, P_H = c₃/(1920M²), τ = 128·g_car·M³/c₃, Kerr A_ext = M²/c₃; six atom landings, zero free parameters [I] + bulk reading [P]", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv101_horizon_anchor.py", "sourceSha256": "7e032467f7d2d1abd53e07bf65f6f364af1e702e5b92cae7fd7ece418c313512", "linkedClaimIds": [ "HOR.NARIAI.01" ], "sectionIds": [ "section:03c7873577084caa47f8", "section:2678ed3ba0ed508e2d8e", "section:49282b347d9c681f9051", "section:8ae7510979d5941b1583", "section:91ac555bf8a799498a54", "section:9575cef792be9f73f7ff", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:cb552d2464f1e864b4f9", "section:e60c8c7dc2298081bbd9", "section:edf07fc78f9496f57ed7", "section:f4ce21377eb152ef27fe", "section:fda00a19dcba44348ac3" ], "activeSectionIds": [ "section:8ae7510979d5941b1583", "section:91ac555bf8a799498a54", "section:9575cef792be9f73f7ff", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:e60c8c7dc2298081bbd9", "section:edf07fc78f9496f57ed7", "section:f4ce21377eb152ef27fe", "section:fda00a19dcba44348ac3" ], "evidenceId": "python_verification:verification/v101_horizon_anchor.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v101_horizon_anchor.py", "pubMirrorHash": "7e032467f7d2d1abd53e07bf65f6f364af1e702e5b92cae7fd7ece418c313512", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v101_horizon_anchor.py" }, { "id": "v102_seam_orientation", "filename": "v102_seam_orientation.py", "path": "verification/v102_seam_orientation.py", "cluster": "registry", "synopsis": "One orientation: the anchor is the STATIONARY REPELLER in both sectors — flavor: the canonical flow dq/dt = (Δ/N_fam)(q−2)(q−5) is the gradient flow of a cubic potential whose critical points are exactly the two branch points, with stationary curvatures V''(Koide) = +Δ (attractor) and V''(carrier) = −Δ (repeller) = ±the transfer gap; inflection at q = 7/2 = scalaron/2; Lyapunov rate d(−ln ρ)/dt = Δ exactly constant; gravity: d(S_tot/S_dS)/dx = (x−1)(x+1)/Φ₃(x)² — Nariai is the UNIQUE stationary point of the SdS entropy, curvature 2/9 = |ℤ₂|/N_fam² = (2/3)(1/3); evaporation = entropy ascent away from the anchor [I]; honest disanalogies recorded; 'one variational principle of the seam' stays a reading [P]", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv102_seam_orientation.py", "sourceSha256": "d9c2f61f8cb872820ec5ea46374d1cd16a1c9678cb65e489989389ef5885b972", "linkedClaimIds": [ "HOR.ORIENT.01" ], "sectionIds": [ "section:03c7873577084caa47f8", "section:49282b347d9c681f9051", "section:ab9e7e520130ecc7da7c", "section:cb552d2464f1e864b4f9", "section:edf07fc78f9496f57ed7", "section:f4ce21377eb152ef27fe", "section:fda00a19dcba44348ac3" ], "activeSectionIds": [ "section:ab9e7e520130ecc7da7c", "section:edf07fc78f9496f57ed7", "section:f4ce21377eb152ef27fe", "section:fda00a19dcba44348ac3" ], "evidenceId": "python_verification:verification/v102_seam_orientation.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v102_seam_orientation.py", "pubMirrorHash": "d9c2f61f8cb872820ec5ea46374d1cd16a1c9678cb65e489989389ef5885b972", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v102_seam_orientation.py" }, { "id": "v103_trisection_normal_form", "filename": "v103_trisection_normal_form.py", "path": "verification/v103_trisection_normal_form.py", "cluster": "registry", "synopsis": "Trisection normal form (the canonical coordinate exists): the SdS horizon cubic is uniformized by ANGLE TRISECTION — r = 2cos θ gives r³−3r = 2cos 3θ exactly, so cubic ⇔ cos 3θ = −3m (ℤ₃ trisection deck = the triality of coker Q = ℤ/N_fam); centered angle ψ: m = cos(ψ)/N_fam and S_tot/S_dS = 4/3 − (2/3)cos(2ψ/3) — ONE cosine whose mean (|μ₄|/N_fam), amplitude and frequency (|ℤ₂|/N_fam) are glue atoms; canonical curvature at the anchor = (2/3)³ = (|ℤ₂|/N_fam)^N_fam — the Koide constant to the family power; invariant base slope dσ/dm = −8/9 = −rank E₈/N_fam² (cross-checked in both coordinates); dimensionful dS/dM = −r_N/(N_fam·c₃); bridge: flavor rate (2/3)^{2N_fam} vs gravity curvature (2/3)^{N_fam} — same base, exponent ratio |ℤ₂|; the missing piece is ONE clock (near-Nariai evaporation generator) [I] + [P]", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv103_trisection_normal_form.py", "sourceSha256": "6244a54be62972f3a417b281a88e303c0ea5af05633b619a8d43b4eebabb6028", "linkedClaimIds": [ "HOR.TRISECT.01" ], "sectionIds": [ "section:9575cef792be9f73f7ff", "section:ab9e7e520130ecc7da7c", "section:c1ba016bb9366edd1984", "section:f4ce21377eb152ef27fe", "section:fda00a19dcba44348ac3" ], "activeSectionIds": [ "section:9575cef792be9f73f7ff", "section:ab9e7e520130ecc7da7c", "section:c1ba016bb9366edd1984", "section:f4ce21377eb152ef27fe", "section:fda00a19dcba44348ac3" ], "evidenceId": "python_verification:verification/v103_trisection_normal_form.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v103_trisection_normal_form.py", "pubMirrorHash": "6244a54be62972f3a417b281a88e303c0ea5af05633b619a8d43b4eebabb6028", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v103_trisection_normal_form.py" }, { "id": "v104_nariai_clock", "filename": "v104_nariai_clock.py", "path": "verification/v104_nariai_clock.py", "cluster": "registry", "synopsis": "The CLASSICAL Nariai clock is the anchor (third appearance) + the honest (2/3)-test: static pin — φ(ρ) = ρ solves the dS₂ static-patch equation with m² = −2Λ = −|ℤ₂|Λ exactly (the exact SdS family itself pins the modulus mass; Laplace-type linearization = standard GR, Ginsparg–Perry 1983 / Bousso–Hawking 1997, typed external); Ginsparg–Perry tower (l(l+1)−2)Λ with exactly ONE negative mode; THE CLOCK in Hubble units: χ_clock(λ) = λ²+λ−2 = (λ−1)(λ+2) = the anchor quadratic, eigenvalues {1,−2} = the distinct anchor roots; Nariai cubic = (t−1)·χ_clock — anchor = configuration roots (v101) + curvature base (v103) + clock spectrum; entropy-deviation rate 2H = |ℤ₂|·Hubble exactly; HONEST (2/3)-TEST NEGATIVE for the classical clock (integer eigenvalues, not 2/3-powers) — the quantum clock (one-loop curvature→rate) is the one remaining [P] of the seam variational principle", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv104_nariai_clock.py", "sourceSha256": "9835a6b3d50ce00b32dcf650b6a7f0ad02049e4a8c8cd33aead7a694efab32fb", "linkedClaimIds": [ "HOR.CLOCK.01" ], "sectionIds": [ "section:03c7873577084caa47f8", "section:49282b347d9c681f9051", "section:7d0e50b6a6c30535730d", "section:9575cef792be9f73f7ff", "section:ab9e7e520130ecc7da7c", "section:cb552d2464f1e864b4f9", "section:cca5b83aae425d5f0e88", "section:d9dfc4ce2d7febed0290", "section:de8db1cd8257eab0d607", "section:e60c8c7dc2298081bbd9", "section:edf07fc78f9496f57ed7", "section:f4ce21377eb152ef27fe", "section:fda00a19dcba44348ac3" ], "activeSectionIds": [ "section:9575cef792be9f73f7ff", "section:ab9e7e520130ecc7da7c", "section:d9dfc4ce2d7febed0290", "section:de8db1cd8257eab0d607", "section:e60c8c7dc2298081bbd9", "section:edf07fc78f9496f57ed7", "section:f4ce21377eb152ef27fe", "section:fda00a19dcba44348ac3" ], "evidenceId": "python_verification:verification/v104_nariai_clock.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v104_nariai_clock.py", "pubMirrorHash": "9835a6b3d50ce00b32dcf650b6a7f0ad02049e4a8c8cd33aead7a694efab32fb", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v104_nariai_clock.py" }, { "id": "v105_residual_inventory", "filename": "v105_residual_inventory.py", "path": "verification/v105_residual_inventory.py", "cluster": "registry", "synopsis": "THE RESIDUAL INVENTORY — one constant, one anchor, one clock to find, and the COMPLETE machine-pinned gap list: (A) 2/3 = |ℤ₂|/N_fam appears EXACTLY in seven independent places across both sectors (Koide branch point, gap base (2/3)⁶, basin attractor; Nariai bound, branch separation, canonical amplitude+frequency, curvature base (2/3)^N_fam) + the anchor triptych (configuration / Nariai roots / clock spectrum); (B) RELOCATION THEOREM: the cosmological one-loop clock correction ε = (c/24π)·Λ/M̄² = 7.6×10⁻¹²² (c = 8) is deficient by 121.5 orders — the deficit IS the Λ hierarchy 2α⁻¹/ln10 = 119.0 ⇒ the clock must live at the seam scale: ONE [P] identification 'transfer operator = seam Nariai clock'; (C) RESIDUAL TABLE: exactly FIVE structural objects remain (clock, holomorphy+c8, seam-det⇒EH, H2 dictionary, Q-realisation) + one scale + π — a sixth structural gap would FAIL this script", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv105_residual_inventory.py", "sourceSha256": "fc8632b93c576415dd81d8ef98b07df70add35e47e6b14134239cafa26d1a2e9", "linkedClaimIds": [ "SYNTH.INVENTORY.01" ], "sectionIds": [ "section:2525c189f32461c9368a", "section:6cd1a267e72b20619327", "section:888628823bf71f709698", "section:91ac555bf8a799498a54", "section:a3835ef2388efb1a54cd", "section:ab9e7e520130ecc7da7c", "section:b93e6ae7b00f32ee1201" ], "activeSectionIds": [ "section:888628823bf71f709698", "section:91ac555bf8a799498a54", "section:a3835ef2388efb1a54cd", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v105_residual_inventory.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v105_residual_inventory.py", "pubMirrorHash": "fc8632b93c576415dd81d8ef98b07df70add35e47e6b14134239cafa26d1a2e9", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v105_residual_inventory.py" }, { "id": "v106_review_validation", "filename": "v106_review_validation.py", "path": "verification/v106_review_validation.py", "cluster": "registry", "synopsis": "External-review validation (v79-style identities + disciplined typing): SEED NORMAL FORM — φ₀ = (|μ₄|/N_fam)·c₃ + Ω_adm·c₃^|μ₄| exactly (linear seam term + topological 4th-order correction; 4/3 = |μ₄|/N_fam, 48 = Ω_adm, exponent = |μ₄|); hypercharge second moment computed from the explicit charge table: Tr X = 0, Tr X² = 120 = 5! (X = 6Y, 16 states); FACTORIAL SPINE: 5! = 120 = |R⁺(E₈)| = Σ E₈ exponents = Tr X², 240 = 2·120, 1920 = 2⁴·5! = |W(D₅)| — one moment, four projections; DEGREE-2 INVENTORY: Pascal K=2 closure UNIQUE at g=5 (scan 1..40), glue norms 5/4+3/4 = 2 = root norm, c₃ = ½·1/(4π), pair sector C(5,2) = 10; NAMED HYPOTHESIS [P]: Quadratic Boundary Locality (seam supports only bilinear data ⇒ K=2 forced — would upgrade the Pascal selection [A]/[P] → [L]: locality ⇒ K=2 ⇒ g=5 ⇒ 16 ⇒ D₅ ⇒ E₈); audit: 240 = 16×15 reading exact but non-unique, not promoted", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv106_review_validation.py", "sourceSha256": "d412eca2d5b8a25e733ae9337094a6a5bd37c2965d0d372622f8e3aa7c001377", "linkedClaimIds": [ "ARCH.QUAD.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:0c709e964a4026facfcf", "section:2cbe5d1807cd76c5e04d", "section:2fbb560d6e97a1ec1660", "section:789583ec50a9f61cdf33", "section:78dc60846ed800922f5e", "section:83df5fee438149d3054f", "section:8872501633bb702220cd", "section:89a96ea40df8ee1ce3c8", "section:ab9e7e520130ecc7da7c", "section:f22c82858ff073c133d4" ], "activeSectionIds": [ "section:2fbb560d6e97a1ec1660", "section:83df5fee438149d3054f", "section:89a96ea40df8ee1ce3c8", "section:ab9e7e520130ecc7da7c", "section:f22c82858ff073c133d4" ], "evidenceId": "python_verification:verification/v106_review_validation.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v106_review_validation.py", "pubMirrorHash": "d412eca2d5b8a25e733ae9337094a6a5bd37c2965d0d372622f8e3aa7c001377", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v106_review_validation.py" }, { "id": "v107_quantum_clock_target", "filename": "v107_quantum_clock_target.py", "path": "verification/v107_quantum_clock_target.py", "cluster": "registry", "synopsis": "Quantum-clock target made quantitative (the R1 programme, first computation): the classical Ginsparg–Perry clock has per-l equations λ²+λ+(l(l+1)−2) = 0 — l=0 anchor pair {1,−2}, l=1 zero modes {0,−1}, l≥2 complex with Re = −1/2 = −δ (audit); NEW EXACT CROSS-LINK: the classical decay set {0,−1,−2} = −Spec(V) = −N_fam × cusp weights — the classical seam clock decays on the transfer operator's OWN grading (v69/v95); EXACT TARGET: transfer rates are not weight-linear — rate(2)/rate(1) = log_{3/2}3 = 2.7095 (not 2), with the exact identity (1/3)⁶ = ((2/3)⁶)^{log_{3/2}3}: the quantum clock must bend the spectrum by log_{9/4}3 = 1.35476 per weight step; coupling landscape κ = (c/24π)(Λ/M̄²): 10⁻¹²² cosmological vs 1/(3π) = 0.106 at seam curvature — the only viable, borderline-nonperturbative regime (one-loop linear response cannot fix the bend); nothing fitted, identification stays [P]", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv107_quantum_clock_target.py", "sourceSha256": "f03cf9fc41058332994c6793d8a127057201380ed881726cea247c34ee3e8a08", "linkedClaimIds": [ "HOR.CLOCK.02" ], "sectionIds": [ "section:09b49009253acb5a0dfb", "section:3cc790136e8b9bd3c188", "section:3d01f167d55724948536", "section:584e87a9c163ac38f92f", "section:ab9e7e520130ecc7da7c", "section:eb0bd97fda8c0fedefad", "section:f4ce21377eb152ef27fe", "section:fda00a19dcba44348ac3" ], "activeSectionIds": [ "section:3d01f167d55724948536", "section:584e87a9c163ac38f92f", "section:ab9e7e520130ecc7da7c", "section:f4ce21377eb152ef27fe", "section:fda00a19dcba44348ac3" ], "evidenceId": "python_verification:verification/v107_quantum_clock_target.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v107_quantum_clock_target.py", "pubMirrorHash": "f03cf9fc41058332994c6793d8a127057201380ed881726cea247c34ee3e8a08", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v107_quantum_clock_target.py" }, { "id": "v108_pascal_ladder", "filename": "v108_pascal_ladder.py", "path": "verification/v108_pascal_ladder.py", "cluster": "registry", "synopsis": "", "publicationNotes": [ "Non-scientific synopsis omitted." ], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv108_pascal_ladder.py", "sourceSha256": "f3ed20229bb35dd4cd45aac612f69e8e4817babb75d41b9a01d41fa40df7f392", "linkedClaimIds": [ "CAR.LADDER.01" ], "sectionIds": [ "section:06d63eae80ded6f77f27", "section:0739148b5a5974d0d662", "section:133a1fc4804aced401e1", "section:1dd0f77dafc49549d126", "section:2525c189f32461c9368a", "section:62801f711a0d267461ac", "section:6cd1a267e72b20619327", "section:8182ecd6055b0d0d488c", "section:81a6dc002dc46cf7b6c5", "section:8872501633bb702220cd", "section:888628823bf71f709698", "section:9575cef792be9f73f7ff", "section:9b652b6d86057eb55f7d", "section:ab9e7e520130ecc7da7c", "section:b93e6ae7b00f32ee1201", "section:bc61b0e372551b770dfb", "section:f22c82858ff073c133d4", "section:fc7f5b07a661660c0d79" ], "activeSectionIds": [ "section:133a1fc4804aced401e1", "section:81a6dc002dc46cf7b6c5", "section:888628823bf71f709698", "section:9575cef792be9f73f7ff", "section:9b652b6d86057eb55f7d", "section:ab9e7e520130ecc7da7c", "section:bc61b0e372551b770dfb", "section:f22c82858ff073c133d4", "section:fc7f5b07a661660c0d79" ], "evidenceId": "python_verification:verification/v108_pascal_ladder.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v108_pascal_ladder.py", "pubMirrorHash": "f3ed20229bb35dd4cd45aac612f69e8e4817babb75d41b9a01d41fa40df7f392", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v108_pascal_ladder.py" }, { "id": "v109_sheet_pairing", "filename": "v109_sheet_pairing.py", "path": "verification/v109_sheet_pairing.py", "cluster": "registry", "synopsis": "SHEET-PAIRING LEMMA (the first exact rep-theoretic anchor of QBL; ties Target B to the sheet ℤ₂): character-exact weight multisets from the D₅ spinor weights (±½)⁵ alone — NO SCALAR WITHIN A SHEET (zero-weight multiplicity of S⁺⊗S⁺ = 0: the odd slot count g=5 flips the sign parity of −w, a parity theorem of the five-slot code); THE SCALAR LIVES ACROSS THE SHEETS: S⁺⊗S⁻ = Λ⁰⊕Λ²⊕Λ⁴ exactly (256 = 1+45+210) with zero-mode grading (1,5,10) = the carrier code; SHEET-DIAGONAL = ODD FORMS: (S⁺⊗S⁺)∪(S⁻⊗S⁻) = 2Λ¹+2Λ³+Λ⁵ exactly (never scalar); the scalar-bearing tower tops at Λ^{2K} with K=2 — bilinear seam data reach exactly the Pascal-ladder degree; QBL reading [P]: the seam's single scalar kernel is necessarily a SHEET PAIRING (chirality-off-diagonal — the same ℤ₂ as the glue chiralities and branch kernels); remaining step: show the Calderón kernel supplies exactly this pairing", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv109_sheet_pairing.py", "sourceSha256": "0db2e76a9221a40f2fbefef954e453ce833c2160e2e411525541266c5286ca7d", "linkedClaimIds": [ "CAR.PAIR.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:8872501633bb702220cd", "section:9575cef792be9f73f7ff", "section:ab9e7e520130ecc7da7c", "section:f22c82858ff073c133d4" ], "activeSectionIds": [ "section:9575cef792be9f73f7ff", "section:ab9e7e520130ecc7da7c", "section:f22c82858ff073c133d4" ], "evidenceId": "python_verification:verification/v109_sheet_pairing.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v109_sheet_pairing.py", "pubMirrorHash": "0db2e76a9221a40f2fbefef954e453ce833c2160e2e411525541266c5286ca7d", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v109_sheet_pairing.py" }, { "id": "v110_calderon_sheet", "filename": "v110_calderon_sheet.py", "path": "verification/v110_calderon_sheet.py", "cluster": "registry", "synopsis": "CALDERÓN-SHEET SELECTION THEOREM (the v109 follow-up): the certified bilinear data of a Calderón involution ε (ε²=1) on H = S⁺⊕S⁻ are ⟨f, εg⟩; with the v109 singlet counts per sheet block (0,0,1,1) the exact statement is 'a scalar two-point datum exists ⟺ ε is sheet-odd' — sheet-odd certifies exactly 1+1 = 2 = |ℤ₂| invariant kernels (one per orientation), sheet-even certifies NONE; THE TWO KERNELS = THE GLUE AMBIGUITY: 2 = |ℤ₂| = the two Lagrangian glues (v92) — the Calderón scalar channel carries exactly the glue ambiguity, resolved by the same sheet choice; LADDER GENERICITY (anti-overclaim): for g = 3,5,7 sheet-oddness forces the half-spinor relation K = (g−1)/2, NOT g=5 — the g-selection stays with rank-8/integrality (v14/v108); QBL residue split into two named parts [P]: (a) interface 'the seam Calderón involution is sheet-odd' (natural: the one-sided collar / double-cover deck is the SAME ℤ₂ that halves c₃ = 1/(2·4π)), (b) analytic core 'the 2-point kernel certifies only slot-degrees ≤ 2'", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv110_calderon_sheet.py", "sourceSha256": "b457047610e44c49767be2cd1bcf2303cb483dc1a69fe37ceadc5fdb10274f8b", "linkedClaimIds": [ "CAR.PAIR.02" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:2525c189f32461c9368a", "section:4b70b6153a1845cabead", "section:6cd1a267e72b20619327", "section:81a6dc002dc46cf7b6c5", "section:8872501633bb702220cd", "section:888628823bf71f709698", "section:93b8868beb643874af75", "section:9a6aaf6fc60f9b74b301", "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:b93e6ae7b00f32ee1201", "section:eb00caf29086b02d5bf5", "section:f22c82858ff073c133d4" ], "activeSectionIds": [ "section:4b70b6153a1845cabead", "section:81a6dc002dc46cf7b6c5", "section:888628823bf71f709698", "section:9a6aaf6fc60f9b74b301", "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:f22c82858ff073c133d4" ], "evidenceId": "python_verification:verification/v110_calderon_sheet.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v110_calderon_sheet.py", "pubMirrorHash": "b457047610e44c49767be2cd1bcf2303cb483dc1a69fe37ceadc5fdb10274f8b", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v110_calderon_sheet.py" }, { "id": "v111_quadratic_transport", "filename": "v111_quadratic_transport.py", "path": "verification/v111_quadratic_transport.py", "cluster": "registry", "synopsis": "QUADRATIC-TRANSPORT THEOREM (the transport half of the QBL analytic core becomes a theorem): grade seam transport by Clifford degree in the 10 field operators on the 5-slot Fock space (integer Jordan–Wigner model; spanning claims via mod-p full-rank certificates, valid over ℚ) — PARITY: all 10 linear words are sheet-odd, all 45 quadratic words sheet-even (code-preserving transport has even Clifford degree, the same ℤ₂ as v109/v110); MINIMALITY: sheet-even words of degree ≤ 1 are the scalars alone; GENERATION: the 45 quadratics (= dim so(10) = the Λ² term of the certified tower 1+45+210) generate the whole code from the vacuum at word length ≤ 2; COMPLETENESS (Burnside realised): products of length ≤ 2 span the FULL End(S⁺) = 256 — every code operation is a word in pair transport, all higher even-degree elements redundant ⇒ THE TRANSPORT DEGREE IS EXACTLY 2 (degree ≤ 1 generates nothing, degree 2 generates everything — a theorem, not a hypothesis); g=3 control: degree selected, not rank; QBL residue reduced to two interface statements: (a) seam Calderón involution sheet-odd, (b') certified state inventory = the ≤2-slot tower", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv111_quadratic_transport.py", "sourceSha256": "c01b4b9a4d178eb5b72d5001540e289150e60c7ae989134b02864f54acd14b3b", "linkedClaimIds": [ "CAR.QTRANS.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:2525c189f32461c9368a", "section:6cd1a267e72b20619327", "section:81a6dc002dc46cf7b6c5", "section:8872501633bb702220cd", "section:888628823bf71f709698", "section:ab9e7e520130ecc7da7c", "section:b93e6ae7b00f32ee1201", "section:c34f80be21ab88f38276", "section:f22c82858ff073c133d4" ], "activeSectionIds": [ "section:81a6dc002dc46cf7b6c5", "section:888628823bf71f709698", "section:ab9e7e520130ecc7da7c", "section:f22c82858ff073c133d4" ], "evidenceId": "python_verification:verification/v111_quadratic_transport.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v111_quadratic_transport.py", "pubMirrorHash": "c01b4b9a4d178eb5b72d5001540e289150e60c7ae989134b02864f54acd14b3b", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v111_quadratic_transport.py" }, { "id": "v112_selfcounting_channel", "filename": "v112_selfcounting_channel.py", "path": "verification/v112_selfcounting_channel.py", "cluster": "registry", "synopsis": "SELF-COUNTING CHANNEL (the Pascal closure is an IDENTITY of the certified channel, not an extra requirement): CANONICAL BIJECTION — for odd g negation w ↦ −w maps S⁺ bijectively into the opposite sheet, so the Cartan-neutral kernels of the certified channel are exactly the pairs (w,−w), ONE PER CODE STATE: #neutral kernels = dim S⁺ = 2^{g−1} exactly (4, 16, 64 for g = 3,5,7) — the channel counts the code; PASCAL PARTITION: the same neutral set graded by pair-degree m has sizes C(g,m) — g=5: (1,5,10); THE CLOSURE IS AN IDENTITY: two countings of one set give 2^{g−1} = Σ_{m≤K} C(g,m) (symbolic, all odd g=3..13) — v108's closure condition is the channel counting itself; HODGE FOLD: code minus-grading C(g,2j) = C(g,min(2j,g−2j)) with min ≤ K — every code sector appears at pair-degree ≤ K; carries NO g-selection (stays with rank-8 g+N_fam=8 + integrality); RESIDUE RE-TYPE [P]: QBL clause (b') is now the channel's definition — the remaining physical input is 'the seam certifies through a single scalar 2-point kernel' (free c=8 seam net: Wick extends it to the whole even tower); QBL = structural consistency frame, no longer a missing selector", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv112_selfcounting_channel.py", "sourceSha256": "c9517d903e2b89868311da1dd8880a5a9d705ff015f4d6cba8ac199c5166860f", "linkedClaimIds": [ "CAR.COUNT.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:2525c189f32461c9368a", "section:6c4044608163b007c4c2", "section:6cd1a267e72b20619327", "section:81a6dc002dc46cf7b6c5", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:888628823bf71f709698", "section:ab9e7e520130ecc7da7c", "section:b93e6ae7b00f32ee1201", "section:c4cf080b9ae6f25f7a71", "section:f22c82858ff073c133d4" ], "activeSectionIds": [ "section:6c4044608163b007c4c2", "section:81a6dc002dc46cf7b6c5", "section:888628823bf71f709698", "section:ab9e7e520130ecc7da7c", "section:f22c82858ff073c133d4" ], "evidenceId": "python_verification:verification/v112_selfcounting_channel.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v112_selfcounting_channel.py", "pubMirrorHash": "c9517d903e2b89868311da1dd8880a5a9d705ff015f4d6cba8ac199c5166860f", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v112_selfcounting_channel.py" }, { "id": "v113_quasifree_kernel", "filename": "v113_quasifree_kernel.py", "path": "verification/v113_quasifree_kernel.py", "cluster": "registry", "synopsis": "ONE KERNEL IS THE WHOLE NET (the QBL input merges with the R2/holomorphy premise): MAJORANA BOOKKEEPING — c(D₅)₁ = 45/9 = 5 = g_car, c(A₃)₁ = 15/5 = 3 = N_fam; the carrier net (D₅)₁×(A₃)₁ = SO(10)₁×SO(6)₁ = 10+6 = 16 FREE MAJORANA FERMIONS, c = 16/2 = 8 — the whole extension tower carrier(μ=16) → SO(16)₁(μ=4) → E8₁(μ=1) carries the SAME 16 fermions, only the certified glue grows (index 2×2 = 4 = |μ₄|); WICK/PFAFFIAN exact: in the 10-Majorana Jordan–Wigner model ALL 210 vacuum 4-point AND all 210 6-point functions equal the Pfaffian of the single 2-point kernel — one kernel determines all correlations; THE KERNEL IS A CALDERÓN INVOLUTION OF RANK g: M = I+iA, A²=−I, P = M/2 projection with rank 5 = g_car, at seam level rank 8 = rank E8 ⇒ THE CENTRAL CHARGE IS THE RANK OF THE ONE KERNEL; vacuum unique (joint annihilator kernel 1-dim); PREMISE MERGE [P]: 'single 2-point kernel' = 'quasi-free seam state' = the defining property of the free-fermion net the holomorphy gate already posits — QBL adds NO assumption beyond R2; upgrade contract: R2 closes ⇒ carrier choice closes [L]", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv113_quasifree_kernel.py", "sourceSha256": "a033fe9c292d22b5bbc343aa0d8e352df14a0918e4124fd7596bf7f81e01ff51", "linkedClaimIds": [ "CAR.QFREE.01" ], "sectionIds": [ "section:013b22f7d203ce0c7da1", "section:03b9058ca08ba4829ac7", "section:0739148b5a5974d0d662", "section:2525c189f32461c9368a", "section:6a93c4dd5fe420e1990e", "section:6bcd4464dbd4c8f8f003", "section:6cd1a267e72b20619327", "section:7144b70a605254dfecbc", "section:7ee581db787f8ddbcb4a", "section:81a6dc002dc46cf7b6c5", "section:8872501633bb702220cd", "section:888628823bf71f709698", "section:8d1e955857da6655fadd", "section:901199b7ffce4a10a268", "section:91ac555bf8a799498a54", "section:93b8868beb643874af75", "section:9575cef792be9f73f7ff", "section:9a6aaf6fc60f9b74b301", "section:9b652b6d86057eb55f7d", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:b93e6ae7b00f32ee1201", "section:bc61b0e372551b770dfb", "section:c39fabd7834a6c050a87", "section:c519f45910c30ff3c0ae", "section:cc5f650209aae2bdc4e6", "section:d0d4a62b7872b9bb3a1c", "section:d90bd5e1e6d8fa41397d", "section:eb00caf29086b02d5bf5", "section:f22c82858ff073c133d4", "section:f97072f658fe6bcec8d8", "section:fd15b9954fc0175fba1b" ], "activeSectionIds": [ "section:013b22f7d203ce0c7da1", "section:6bcd4464dbd4c8f8f003", "section:7144b70a605254dfecbc", "section:81a6dc002dc46cf7b6c5", "section:888628823bf71f709698", "section:8d1e955857da6655fadd", "section:901199b7ffce4a10a268", "section:91ac555bf8a799498a54", "section:9575cef792be9f73f7ff", "section:9a6aaf6fc60f9b74b301", "section:9b652b6d86057eb55f7d", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:bc61b0e372551b770dfb", "section:c39fabd7834a6c050a87", "section:cc5f650209aae2bdc4e6", "section:d0d4a62b7872b9bb3a1c", "section:f22c82858ff073c133d4", "section:f97072f658fe6bcec8d8" ], "evidenceId": "python_verification:verification/v113_quasifree_kernel.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v113_quasifree_kernel.py", "pubMirrorHash": "a033fe9c292d22b5bbc343aa0d8e352df14a0918e4124fd7596bf7f81e01ff51", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v113_quasifree_kernel.py" }, { "id": "v114_torsion_delta", "filename": "v114_torsion_delta.py", "path": "verification/v114_torsion_delta.py", "cluster": "registry", "synopsis": "TORSION NORMAL FORM + THE δ = 1/2 THEOREM (executes the v41 'genericity future work'; δ = 1/2 stops being an observation): FLATNESS = μ₄ TORSION [I, symbolic generic M] — ∏ₖ Uᵏ M U⁻ᵏ = (MU)⁴ exactly, so the ℤ₄-family flatness of the (U_wall) bundle IS the torsion statement 'T = MU is a fourth root of unity' (the μ₄ atom = the ORDER of the twisted cusp generator); δ THEOREM [I, both directions]: on the involutive branch (T² = 1) T is a Hermitian reflection 2vv†−1 and the cusp trace splits exactly into |v₁|² = ½ + |v₂| = |v₃| ⇒ diag M = (0, i/2, −i/2) with spec M = {1, ω, ω²} AUTOMATIC — δ = ½ exact and constant on the whole 2-parameter branch (the value v20 used by hand is a μ₄-torsion identity); REFLECTION LEMMA: D₄ forces diag M = (r, z, z̄), r real — ONE real parameter, δ = ½ ⟺ r = 0; BRANCH CENSUS [N, seeded]: only tr(MU) ∈ {1,−1} realised; involutive branch diagonal constant to 1e−15; the {1,i,−i} branch varies with the explicit v33/v40 point in its d₁ = 0 slice; residue [P]: bundle-side branch selection (anchor splitting), δ itself closed", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv114_torsion_delta.py", "sourceSha256": "8e1938e0a1a05bd90d877efc4d098d7d6b955f70e5a6df5002d69e209228db3c", "linkedClaimIds": [ "GATE.UWALL.06" ], "sectionIds": [ "section:2585b5d786c3bdb7ddb7", "section:3c0ef7a887cebe028f40", "section:6a93c4dd5fe420e1990e", "section:9575cef792be9f73f7ff", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d" ], "activeSectionIds": [ "section:2585b5d786c3bdb7ddb7", "section:3c0ef7a887cebe028f40", "section:9575cef792be9f73f7ff", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v114_torsion_delta.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v114_torsion_delta.py", "pubMirrorHash": "8e1938e0a1a05bd90d877efc4d098d7d6b955f70e5a6df5002d69e209228db3c", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v114_torsion_delta.py" }, { "id": "v115_anchor_residue", "filename": "v115_anchor_residue.py", "path": "verification/v115_anchor_residue.py", "cluster": "registry", "synopsis": "THE ANCHOR PINS THE RESIDUE (exact normal form for the U_wall flat-bundle residue; answers the v114 branch question): μ₄-AVERAGE LEMMA [I] — Σₖ Uᵏ X U⁻ᵏ = 4 diag(X): μ₄ conjugation-averaging IS the diagonal projection ⇒ exponents at infinity = 4 diag(A₀) ⇒ anchor splitting 𝒪(−2)⊕𝒪(−1)² ⟺ diag A₀ = (2,1,1)/4 = ANCHOR/|μ₄| (v33's diagonal was forced, not chosen); THE (8,0,5)/144 LEMMA [I]: anchor diagonal + cusp spectrum pin Σ|off|² = 13/144, and a₁₃ = 0 + det = 0 solve UNIQUELY to (|a₁₂|², |a₂₃|²) = (8,5)/144 — numerators (rank E8, g_car), denominator (|μ₄|N_fam)², total 13 = Δ_Q (the quark denominator 117 = 9·13); EXACT NORMAL FORM [I]: A₀* = [[1/2, √2/6, 0],[√2/6, 1/4, √5/12],[0, √5/12, 1/4]] with char poly λ(λ−⅓)(λ−⅔) exactly; A₀* IS THE RIEMANN–HILBERT SOLUTION [N]: big-circle monodromy trivial to 1e−10, unitarised |diag M̃₀| = (0,½,½) — the v33/v40 numerical point is gauge-equivalent to this exact matrix; ANCHOR FORCES d₁ = 0 [N]: every flat solution in a multi-seed RH scan lands on the same gauge orbit ⇒ the harmonic diagonal is anchor+torsion forced, δ = ½ needs no selection; residue [P]: Gröbner promotion of a₁₃ = 0 + uniqueness", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv115_anchor_residue.py", "sourceSha256": "26d84469128747ef11be7513316e6c61f03517632d3a82a197413fe93af814a6", "linkedClaimIds": [ "GATE.UWALL.07" ], "sectionIds": [ "section:2585b5d786c3bdb7ddb7", "section:2678ed3ba0ed508e2d8e", "section:436dbc6f3b40e9aa8035", "section:55b733511958e907bad8", "section:5ae06930f472e00a9545", "section:6a93c4dd5fe420e1990e", "section:749d598aa0815d32790b", "section:93b8868beb643874af75", "section:9a6aaf6fc60f9b74b301", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:cc5f650209aae2bdc4e6", "section:d90bd5e1e6d8fa41397d", "section:e1f5b724a85f51ec5624", "section:eb00caf29086b02d5bf5", "section:f1cb1505fb0d067d8745", "section:f4ce21377eb152ef27fe" ], "activeSectionIds": [ "section:2585b5d786c3bdb7ddb7", "section:436dbc6f3b40e9aa8035", "section:55b733511958e907bad8", "section:749d598aa0815d32790b", "section:9a6aaf6fc60f9b74b301", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:cc5f650209aae2bdc4e6", "section:f1cb1505fb0d067d8745", "section:f4ce21377eb152ef27fe" ], "evidenceId": "python_verification:verification/v115_anchor_residue.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v115_anchor_residue.py", "pubMirrorHash": "26d84469128747ef11be7513316e6c61f03517632d3a82a197413fe93af814a6", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v115_anchor_residue.py" }, { "id": "v116_resonance_uniqueness", "filename": "v116_resonance_uniqueness.py", "path": "verification/v116_resonance_uniqueness.py", "cluster": "registry", "synopsis": "RESONANCE THEOREM (the v115 [N] findings promoted to [I] by a LINEAR computation — the anticipated Gröbner step was unnecessary): TWISTED-AVERAGE LEMMA [I] — at infinity the equivariant system reads dY/dw = −(1/w)(B₀ + B₁w + …)Y with B_m = Σₖ i^{km} Uᵏ A₀ U⁻ᵏ; the twisted μ₄ averages collapse to B₀ = 4 diag(A₀) and B₁ = 4a₁₂E₁₂ + 4ā₁₃E₃₁ (only the eigenvalue-ratio −i cells survive); RESONANCE THEOREM [I]: the anchor exponents diag(2,1,1) have resonance gap 1, the level-1 gauge equation is singular exactly on cells {(2,1),(3,1)} where B₁ = (0, 4ā₁₃), higher levels non-resonant, formal monodromy = 1 ⇒ M∞ = 1 ⟺ a₁₃ = 0 — the transcendental Riemann–Hilbert condition collapses to ONE linear equation; UNIQUENESS COROLLARY [I]: a₁₃ = 0 + the (8,0,5)/144 moduli + diagonal gauge ⇒ THE FLAT ANCHOR LOCUS IS EXACTLY ONE GAUGE ORBIT = the exact A₀* — within the μ₄-equivariant anchor class the U_wall bundle datum is ALGEBRAICALLY unique; FALSIFICATION CONTROL [N]: ‖M∞ − 1‖ ≈ 8.5|a₁₃| (sharp), 1.6e−10 at A₀*; honest scope: residue side [I], holonomy values (harmonic diagonal) remain [N]", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv116_resonance_uniqueness.py", "sourceSha256": "e9cbeb665cf8c1a2bed3f34281be06aee4c661d784e7f13a5bd8e9be37f577ca", "linkedClaimIds": [ "GATE.UWALL.08" ], "sectionIds": [ "section:2585b5d786c3bdb7ddb7", "section:436dbc6f3b40e9aa8035", "section:55b733511958e907bad8", "section:5ae06930f472e00a9545", "section:6a93c4dd5fe420e1990e", "section:93b8868beb643874af75", "section:9a6aaf6fc60f9b74b301", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d", "section:e1f5b724a85f51ec5624", "section:eb00caf29086b02d5bf5" ], "activeSectionIds": [ "section:2585b5d786c3bdb7ddb7", "section:436dbc6f3b40e9aa8035", "section:55b733511958e907bad8", "section:9a6aaf6fc60f9b74b301", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v116_resonance_uniqueness.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v116_resonance_uniqueness.py", "pubMirrorHash": "e9cbeb665cf8c1a2bed3f34281be06aee4c661d784e7f13a5bd8e9be37f577ca", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v116_resonance_uniqueness.py" }, { "id": "v117_monodromy_weyl_a3", "filename": "v117_monodromy_weyl_a3.py", "path": "verification/v117_monodromy_weyl_a3.py", "cluster": "registry", "synopsis": "THE MONODROMY IS THE WEYL GROUP OF A₃ (the U_wall holonomy is an EXACT 24-element representation; the harmonic diagonal becomes a theorem): THE EXACT MONODROMY [I] — M̃₀ = [[0, −(1+i)/2, (1−i)/2], [−(1+i)/2, −i/2, −1/2], [(1−i)/2, −1/2, i/2]] (entries in ½ℤ[i]) is unitary, det 1, tr 0, char poly λ³−1 (cusp class EXACT), M̃₀³ = 1, diag M̃₀ = (0, −i/2, +i/2) ⇒ d₁ = 0 AND δ = ½ are exact matrix entries — the v20 hand value, the v40/v41 observation, the v114 torsion value and the v115 anchor slice meet in ONE exact matrix; TORSION/FLATNESS [I]: (M̃₀U)⁴ = 1, tr(M̃₀U) = 1, ∏ₖ Uᵏ M̃₀ U⁻ᵏ = 1 exactly; THE GROUP IS W(A₃) = S₄ [I]: exact enumeration of ⟨U, M̃₀⟩ gives order 24, order statistics (1,9,8,6), characters (3,−1,0,1) — uniquely S₄ in standard⊗sign = the (twisted) reflection rep of the WEYL GROUP OF THE FAMILY LATTICE A₃: the flavor wall realises the A₃ glue factor as its Weyl group (U = 4-cycle/μ₄ deck, M̃₀ = 3-cycle/family rotation, 24 = |W(A₃)| = 4!); IDENTIFICATION [N]: ODE monodromy of the exact A₀* system = exact M̃₀ to 3.5e−10, H U-invariant to 2.5e−11; the δ thread v20 → v40/v41 → v114 → v115 → v117 is closed end to end", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv117_monodromy_weyl_a3.py", "sourceSha256": "55eca6a64144f6e49789f3f1bbe84e256764e7ce92b207044be693f8684d5df5", "linkedClaimIds": [ "GATE.UWALL.09" ], "sectionIds": [ "section:22fb298fcb28accfbf39", "section:2585b5d786c3bdb7ddb7", "section:2678ed3ba0ed508e2d8e", "section:359527c60ffa08a51bf0", "section:3c0ef7a887cebe028f40", "section:436dbc6f3b40e9aa8035", "section:4d42f8071e36f9952644", "section:4ff2bf714d7cbf97df82", "section:5ae06930f472e00a9545", "section:6151ea351f3cf66e9630", "section:6a93c4dd5fe420e1990e", "section:749d598aa0815d32790b", "section:74bb3766bdd1275dbd78", "section:7779d02d30f1856735de", "section:95036dacfe44edfdb2c9", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:cdd3ea07b0ec5995036b", "section:d90bd5e1e6d8fa41397d", "section:db553f90608e785ea4a8", "section:e1f5b724a85f51ec5624", "section:e7294e8d8a250400195d", "section:fd793f72e342d1d06c7b", "section:ffb3c952b2d4af559d34" ], "activeSectionIds": [ "section:22fb298fcb28accfbf39", "section:2585b5d786c3bdb7ddb7", "section:359527c60ffa08a51bf0", "section:3c0ef7a887cebe028f40", "section:436dbc6f3b40e9aa8035", "section:4d42f8071e36f9952644", "section:4ff2bf714d7cbf97df82", "section:6151ea351f3cf66e9630", "section:749d598aa0815d32790b", "section:74bb3766bdd1275dbd78", "section:95036dacfe44edfdb2c9", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:cdd3ea07b0ec5995036b" ], "evidenceId": "python_verification:verification/v117_monodromy_weyl_a3.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v117_monodromy_weyl_a3.py", "pubMirrorHash": "55eca6a64144f6e49789f3f1bbe84e256764e7ce92b207044be693f8684d5df5", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v117_monodromy_weyl_a3.py" }, { "id": "v118_hexagon_family_dictionary", "filename": "v118_hexagon_family_dictionary.py", "path": "verification/v118_hexagon_family_dictionary.py", "cluster": "registry", "synopsis": "THE HEXAGON IS THE SIGN-TWISTED FAMILY SPECTRUM (first exact piece of the H2 dictionary; the v20 lepton coefficients are resolvent determinants of the exact W(A₃) monodromy): SIGN-TWIST LEMMA [I] — −M̃₀ has order 6 ((−M̃₀)³ = −1) and spec(M̃₀) ∪ spec(−M̃₀) = μ₆: the 6-site hypercharge hexagon spectrum IS the family monodromy spectrum plus its sheet twist (ℤ₆ = ℤ₂×ℤ₃ = (−1)×⟨M̃₀⟩); the v20 denominators 5/4 − cos(rπ/3) = |1 − ζ₆ʳ/2|² are the eigen-denominators of the two family resolvents (1 ∓ M̃₀/2)⁻¹; CYCLOTOMIC DETERMINANT [I]: det(1 − tM̃₀) = 1 − t³ = (1−t)Φ₃(t) ⇒ det(1 ∓ M̃₀/2) = (7/8, 9/8); LEPTON COEFFICIENTS = RESOLVENT DETERMINANTS [I]: c_e = |μ₄|/(2det₋) = 16/7, c_μ = N_fam/(2det₊) = 4/3, c_τ = |μ₄|det₋/N_fam = 7/6, product rule = |μ₄|/det₊ = 32/9 — the lepton 7 and 9 ARE the family-resolvent determinants (×8), and δ = ½ = |(M̃₀)₂₂| is supplied by the matrix itself; the e/μ/τ leg assignment stays v20's established input (nothing re-fished); SHEET-EXTENDED GROUP [I]: ⟨U, M̃₀, −1⟩ has order 48 = Ω_adm = N_fam·dim S⁺ (the seed quartic coefficient); residue [P]: the dictionary's VALUES are exact, its ADDRESS TABLE (site per fermion, quark composition) remains open", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv118_hexagon_family_dictionary.py", "sourceSha256": "48b7a05bcd877afe13f0a92cce4087e86c23172823e605cda21c6a8ceafa6e37", "linkedClaimIds": [ "FLAV.H2.02" ], "sectionIds": [ "section:0d282444ef07ab3b182d", "section:1971373b474ccc990b34", "section:213a1f15f7373957fc2f", "section:2585b5d786c3bdb7ddb7", "section:2678ed3ba0ed508e2d8e", "section:298ca201062fd482dafa", "section:3934f91cc921c9b43fab", "section:6a93c4dd5fe420e1990e", "section:7779d02d30f1856735de", "section:7a667667edab66880567", "section:95036dacfe44edfdb2c9", "section:9575cef792be9f73f7ff", "section:9bab697ba19c86420aea", "section:9dce604333464c544549", "section:ab9e7e520130ecc7da7c", "section:be55bc7af4c59377a629", "section:c6a172fae7d467d3744c", "section:d90bd5e1e6d8fa41397d", "section:d9254a3f746aa54dd7bd", "section:db553f90608e785ea4a8", "section:e7294e8d8a250400195d" ], "activeSectionIds": [ "section:1971373b474ccc990b34", "section:213a1f15f7373957fc2f", "section:2585b5d786c3bdb7ddb7", "section:298ca201062fd482dafa", "section:3934f91cc921c9b43fab", "section:95036dacfe44edfdb2c9", "section:9575cef792be9f73f7ff", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:d9254a3f746aa54dd7bd" ], "evidenceId": "python_verification:verification/v118_hexagon_family_dictionary.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v118_hexagon_family_dictionary.py", "pubMirrorHash": "48b7a05bcd877afe13f0a92cce4087e86c23172823e605cda21c6a8ceafa6e37", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v118_hexagon_family_dictionary.py" }, { "id": "v119_review_validation_2", "filename": "v119_review_validation_2.py", "path": "verification/v119_review_validation_2.py", "cluster": "registry", "synopsis": "SECOND EXTERNAL-REVIEW VALIDATION (triad + 121 audit + micro-identities, all exact): ANCHOR RATIO TRIAD [I] — the three elementary symmetric values of the anchor normalised by the family count, (e₃,e₁,e₂)/p₀ = (2/3, 4/3, 5/3) = (Koide branch/sheet ratio, seed gain |μ₄|/N_fam, carrier branch); the canonical flow's critical points are EXACTLY (2,5) = (e₃,e₂) with inflection 7/2 = (e₃+e₂)/2 — the recurring fractions are the three normalised anchor coefficients, not scattered numbers; THE 121 AUDIT LEMMA [I, audit-typed]: (1+a)ᵀR(1+a) = 121 = 11² = ‖Pl(K)‖₁² = (p₃+1)² — the quark-ratio 11 appears a second independent time as the quadratic anchor norm of the residue operator R; sensitivity: orderings give {105,121,135}, only the canonical anchor ordering yields 121; bonus: 1ᵀR1 = 22 = 2·11, aᵀRa = 40 = p₁p₃ = 10b₁−1 (oriented Plücker stays the derivation); MICRO-IDENTITIES: Ω_adm = 2p₁p₂ = 48, 10b₁ = 1+p₁p₃ = 41, Δ_Y = e₂² = p₀²+2·rank = 25, h(E8) = e₃p₀e₂ = 30, rank = p₀+e₂; flavor surface M(s,t) claim = established v94/v95 (presentational); μ₄ projection/triptych/interior-free already closed (v115/v116, v104/v105, v113)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv119_review_validation_2.py", "sourceSha256": "e91c80ccc4a0e85df9b837ccbb733c87cda3f72bb51f7135acf897ce5a45603f", "linkedClaimIds": [ "ARCH.TRIAD.01" ], "sectionIds": [ "section:2cbe5d1807cd76c5e04d", "section:46614e805445fc78e7af", "section:6a93c4dd5fe420e1990e", "section:789583ec50a9f61cdf33", "section:83df5fee438149d3054f", "section:89a96ea40df8ee1ce3c8", "section:95036dacfe44edfdb2c9", "section:9575cef792be9f73f7ff", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d", "section:f4ce21377eb152ef27fe" ], "activeSectionIds": [ "section:46614e805445fc78e7af", "section:83df5fee438149d3054f", "section:89a96ea40df8ee1ce3c8", "section:95036dacfe44edfdb2c9", "section:9575cef792be9f73f7ff", "section:ab9e7e520130ecc7da7c", "section:f4ce21377eb152ef27fe" ], "evidenceId": "python_verification:verification/v119_review_validation_2.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v119_review_validation_2.py", "pubMirrorHash": "e91c80ccc4a0e85df9b837ccbb733c87cda3f72bb51f7135acf897ce5a45603f", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v119_review_validation_2.py" }, { "id": "v120_address_table", "filename": "v120_address_table.py", "path": "verification/v120_address_table.py", "cluster": "registry", "synopsis": "THE ADDRESS TABLE (the open H2 item structured; exact arithmetic on FROZEN v18/v20 integers — the red-team firewall): THE LEPTON WORDS ARE THE COMPILER ATOMS [I] — (L_e, L_μ, L_τ) = (8, 5, 3) = (rank E8, g_car, N_fam) = (p₀+e₂, e₂, p₀), in mass order (longest word = lightest lepton); ADDRESSES = EUCLIDEAN DIVISION BY THE HEXAGON [I]: (r,w) = L divmod p₂ with p₂ = 6 = |R⁺(A₃)| itself an atom: e → (2,1), μ → (5,0), τ → (3,0); Σr = 10 = p₃ = A_Λ, ΣL = 16 = dim S⁺; SHEET PARITY [I] (the v118 dictionary applied): e on the untwisted sheet (ω ∈ spec M̃₀), μ/τ on the twisted sheet (−ω, −1) — the anchor lepton τ occupies the unique REAL twisted eigenvalue −1, exactly the site where v20's product rule replaces the resolvent; QUARK SUM RULES [I] (frozen v18 words 7,7,5,3,2,0): up-sum = 10 = p₃, down-sum = 14 = p₁+p₃, ALL QUARKS = 24 = |W(A₃)| (the monodromy group order, v117), ALL NINE CHARGED FERMIONS = 40 = p₁p₃ = aᵀRa (v119); top at the vacuum site (0,0) — zero word, the ladder anchor; residue [P]: five closures (16, 10, 14, 24, 40) constrain the map, the per-fermion assignment derivation remains the open H2 content", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv120_address_table.py", "sourceSha256": "223760338b44e90c1a277011725730c9d3d6b970d277490615512d4da455da0e", "linkedClaimIds": [ "FLAV.H2.03" ], "sectionIds": [ "section:6a93c4dd5fe420e1990e", "section:95036dacfe44edfdb2c9", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d" ], "activeSectionIds": [ "section:95036dacfe44edfdb2c9", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v120_address_table.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v120_address_table.py", "pubMirrorHash": "223760338b44e90c1a277011725730c9d3d6b970d277490615512d4da455da0e", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v120_address_table.py" }, { "id": "v121_address_pinning", "filename": "v121_address_pinning.py", "path": "verification/v121_address_pinning.py", "cluster": "registry", "synopsis": "THE ADDRESS TABLE IS PINNED (the per-fermion assignment closes at the information level; exact census theorem): THE WORD TABLE IS THE RESIDUE OPERATOR [I] — the established identity L = R + 2U (v95) says the word-length table IS L[sector][generation] with rows (up; down; lepton) = ((7,3,0); (7,5,2); (8,5,3)) = the v18/v20 words verbatim; addresses = R's entries + one hexagon turn for generation 1, and R's first column is THE ANCHOR a = (1,1,2); THE MARGINS ARE ATOMS [I]: row sums (4,8,10) = (e₁, rank E8, p₃), column sums (4,13,5) = (e₁, Δ_Q, g_car); PINNING THEOREM [I, exact census]: among ALL 3×3 matrices with entries in the hexagon {0..5}, exactly 17 have the atom margins and exactly ONE has det = 8 = rank E8 — and it is R (also unique with SNF (1,1,8); all 17 determinants distinct — control computed explicitly) ⇒ THE ASSIGNMENT TABLE CARRIES ZERO RESIDUAL INFORMATION beyond atom margins + rank determinant; within-sector ordering = established transport reading; residue [P]: H2 shrinks from 'derive 9 integers' to 'derive the six atom margins + det = rank'; firewall: R, L, words frozen in v4/v18/v20/v71", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv121_address_pinning.py", "sourceSha256": "81daa2644115b24ae7c43878e358f617e39dae5726c20eae49a296d96550c0a8", "linkedClaimIds": [ "FLAV.H2.04" ], "sectionIds": [ "section:6a93c4dd5fe420e1990e", "section:95036dacfe44edfdb2c9", "section:9575cef792be9f73f7ff", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d" ], "activeSectionIds": [ "section:95036dacfe44edfdb2c9", "section:9575cef792be9f73f7ff", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v121_address_pinning.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v121_address_pinning.py", "pubMirrorHash": "81daa2644115b24ae7c43878e358f617e39dae5726c20eae49a296d96550c0a8", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v121_address_pinning.py" }, { "id": "v122_margin_theorem", "filename": "v122_margin_theorem.py", "path": "verification/v122_margin_theorem.py", "cluster": "registry", "synopsis": "THE MARGINS ARE THEOREMS (the established frozen selectors pin R uniquely — the v121 atom margins lose their input status): three selectors, all frozen BEFORE the address question was posed — (S1) the D₄ annihilator n = (5,−9,6) with nᵀR = (8,0,0) (v94: kills the (c₂,c₃) plane, n·a = 8), (S2) det R = 8 = rank E8 (v71 quartet (3,4,8,20)), (S3) det K = 4 = |μ₄| with K = R + QΣ (the diamond), plus the definitional hexagon range {0..5}; CENSUS [I]: 4×4×4 = 64 (S1)-candidates, (S2) leaves 12, (S3) leaves EXACTLY ONE — and it is R; COROLLARY [I]: the atom margins (4,8,10)/(4,13,5), the anchor column Re₁ = a, and ALL v120/v121 sum rules (16,10,14,24,40) are CONSEQUENCES — input status revoked; BONUS LEMMA [I]: on the (S1)+(S2) locus det(M+2U) = 20 = det L for ALL 12 candidates — the fourth quartet determinant is redundant (the compiler's overdetermination pattern); residue [P]: H2 reduces to the establishment of the selectors themselves (pre-existing inventoried objects) — the address question introduces NO new residual class", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv122_margin_theorem.py", "sourceSha256": "d35cbd2ed636412594800fb3d1bcba6320f78df11dc856cc1bc3dc076c008bdb", "linkedClaimIds": [ "FLAV.H2.05" ], "sectionIds": [ "section:1971373b474ccc990b34", "section:213a1f15f7373957fc2f", "section:2585b5d786c3bdb7ddb7", "section:298ca201062fd482dafa", "section:3934f91cc921c9b43fab", "section:6a93c4dd5fe420e1990e", "section:7a667667edab66880567", "section:95036dacfe44edfdb2c9", "section:9dce604333464c544549", "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:be55bc7af4c59377a629", "section:c6a172fae7d467d3744c", "section:d90bd5e1e6d8fa41397d" ], "activeSectionIds": [ "section:1971373b474ccc990b34", "section:213a1f15f7373957fc2f", "section:2585b5d786c3bdb7ddb7", "section:298ca201062fd482dafa", "section:3934f91cc921c9b43fab", "section:95036dacfe44edfdb2c9", "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v122_margin_theorem.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v122_margin_theorem.py", "pubMirrorHash": "d35cbd2ed636412594800fb3d1bcba6320f78df11dc856cc1bc3dc076c008bdb", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v122_margin_theorem.py" }, { "id": "v123_inventory_update", "filename": "v123_inventory_update.py", "path": "verification/v123_inventory_update.py", "cluster": "registry", "synopsis": "RESIDUAL INVENTORY UPDATED (post v110–v122; the v105 gap list re-pinned with sharper contents, same cardinality): thirteen new ledger rows machine-checked (CAR.PAIR.02, CAR.QTRANS.01, CAR.COUNT.01, CAR.QFREE.01, GATE.UWALL.06–09, FLAV.H2.02–05, ARCH.TRIAD.01); R2 CARRIES THREE LOADS — the single index-4 boundary-net statement closes, when proven, the metric gate (GATE.METRIC.06), the carrier choice (CAR.QFREE.01 upgrade contract) and the QBL programme (ARCH.QUAD.01): one theorem, three doors; UPDATED RESIDUAL TABLE, exactly FIVE structural classes: R1 seam quantum clock (bend log₃∕₂3 at ~1/3π) [P], R2 index-4 seam net (3 loads) [P]/[A], R3 seam determinant ⇒ EH [A], R4' SELECTOR ESTABLISHMENT (n = (5,−9,6) + diamond determinants; replaces the DISCHARGED 'H2 dictionary') [A]/[P], R5 parabolic realisation of Q (GATE.QGEO; P1) [P] — plus v_geo and π; a sixth structural class would FAIL the script; THE FLAVOR SIDE HAS NO OPEN ANALYSIS CLASS OF ITS OWN anymore — H2 values exact, addresses pinned, margins theorems, residue = five frozen selector integers", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv123_inventory_update.py", "sourceSha256": "91d91b1ed21f04fdc8d2ec20bd2090ae7ac86f7435018aeb30dd2f7d6ed170a1", "linkedClaimIds": [ "SYNTH.INVENTORY.02" ], "sectionIds": [ "section:2525c189f32461c9368a", "section:3c0ef7a887cebe028f40", "section:6cd1a267e72b20619327", "section:888628823bf71f709698", "section:93b8868beb643874af75", "section:a3835ef2388efb1a54cd", "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:b93e6ae7b00f32ee1201", "section:d0d4a62b7872b9bb3a1c", "section:eb00caf29086b02d5bf5" ], "activeSectionIds": [ "section:3c0ef7a887cebe028f40", "section:888628823bf71f709698", "section:a3835ef2388efb1a54cd", "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:d0d4a62b7872b9bb3a1c" ], "evidenceId": "python_verification:verification/v123_inventory_update.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v123_inventory_update.py", "pubMirrorHash": "91d91b1ed21f04fdc8d2ec20bd2090ae7ac86f7435018aeb30dd2f7d6ed170a1", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v123_inventory_update.py" }, { "id": "v124_resummed_clock", "filename": "v124_resummed_clock.py", "path": "verification/v124_resummed_clock.py", "cluster": "registry", "synopsis": "THE RESUMMED CLOCK (R1's bend acquires a closed form — the transfer spectrum IS the geometric resummation of a weight-linear clock): SPECTRUM READING [I] — the frozen transfer eigenvalues {1, (2/3)⁶, (1/3)⁶} are EXACTLY λₙ = (1 − n/N_fam)^{p₂} for n = 0,1,2 (p₂ = 6 = the hexagon size); CLOSED-FORM CLOCK [I]: rate(n) = −6 ln(1 − n/3) reproduces {0, Δ, 6 ln 3} and the v107 bend log₃∕₂3 becomes a one-line consequence; THE LINEARISATION CARRIES THE SHEET [I]: rate(n) = 2n + n²/3 + 2n³/27 + … — the one-loop term has slope exactly |ℤ₂| = 2 relative to the integer classical Ginsparg–Perry clock {0,−1,−2}: quantum clock = sheet-doubled classical clock + geometric tail; THE WALL AT N_fam [I]: rate → ∞ as n → 3 (pole at the family count) ⇒ the cusp ladder ends at n = 2 — the three-level transfer spectrum is forced by the clock itself; R1 re-sharpened [P]: derive −p₂ ln(1 − n/N_fam) from the near-Nariai one-loop at κ = 1/(3π), first checkpoint = linear-response slope |ℤ₂|; all spectra frozen (v54/v69/v95/v104/v107)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv124_resummed_clock.py", "sourceSha256": "6ad0c465cbdebe8ca4032e18c988966f52ac60b0ea85b52dbcac52083d36ce58", "linkedClaimIds": [ "HOR.CLOCK.03" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:09b49009253acb5a0dfb", "section:10e10da547a5ac9014b8", "section:213a1f15f7373957fc2f", "section:2525c189f32461c9368a", "section:3cc790136e8b9bd3c188", "section:3d01f167d55724948536", "section:584e87a9c163ac38f92f", "section:6cd1a267e72b20619327", "section:7383e42c67f8eaba497b", "section:81a6dc002dc46cf7b6c5", "section:8872501633bb702220cd", "section:888628823bf71f709698", "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:b93e6ae7b00f32ee1201", "section:cc398ba7e3e94c7addf2", "section:eb0bd97fda8c0fedefad", "section:f4ce21377eb152ef27fe" ], "activeSectionIds": [ "section:10e10da547a5ac9014b8", "section:213a1f15f7373957fc2f", "section:3d01f167d55724948536", "section:584e87a9c163ac38f92f", "section:7383e42c67f8eaba497b", "section:81a6dc002dc46cf7b6c5", "section:888628823bf71f709698", "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:cc398ba7e3e94c7addf2", "section:f4ce21377eb152ef27fe" ], "evidenceId": "python_verification:verification/v124_resummed_clock.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v124_resummed_clock.py", "pubMirrorHash": "6ad0c465cbdebe8ca4032e18c988966f52ac60b0ea85b52dbcac52083d36ce58", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v124_resummed_clock.py" }, { "id": "v125_glue_qsystem", "filename": "v125_glue_qsystem.py", "path": "verification/v125_glue_qsystem.py", "cluster": "registry", "synopsis": "THE GLUE Q-SYSTEM (the index-4 μ₄ extension exists as an explicit Longo Q-system; R2 sharpens from 'find' to 'match'): Q-SYSTEM AXIOMS [I] on A = ℂ[ℤ₄] (glue group algebra): associativity, unit law, FROBENIUS (m⊗1)(1⊗m*) = m*m = (1⊗m)(m*⊗1), SPECIALNESS mm* = |ℤ₄|·id — all exact ⇒ a special C* Frobenius algebra = Longo Q-system with dim θ = 4: JONES INDEX [B:A] = 4 = |μ₄| (the v89 Carrier Index Lemma value); KLM μ_carrier = 16 = 4²·μ_E8 re-verified; LOCALITY = ISOTROPY [I] (v92 in Q-system language): q(k(1,1)) = k² = (0,1,4,9), all integers — the braiding obstruction vanishes, the two Lagrangian glues = the sheet pair are the only maximal isotropic choices; HALFWAY SUB-Q-SYSTEM [I]: {0,2} < ℤ₄ closes ⇒ unique intermediate ℂ[ℤ₂] = the SO(16)₁ tower step, index 4 = 2×2; R2 SHARPENED [P]: what remains is the operator-algebraic IDENTIFICATION 'the seam-Calderón inclusion of the 16-Majorana net realises THIS Q-system' — matching two constructed objects, not a search; the three loads (metric + carrier + QBL) hang on this one identification", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv125_glue_qsystem.py", "sourceSha256": "7231c07cecd3e39c402806bca101c4e5483126bc4ae48974ea72b1b96ad033d7", "linkedClaimIds": [ "GATE.METRIC.08" ], "sectionIds": [ "section:03b9058ca08ba4829ac7", "section:0bcac4df826bc0d57d23", "section:307c4c95a7c84b5efc0b", "section:55b733511958e907bad8", "section:65e6ea58d3d1fb647f95", "section:6a93c4dd5fe420e1990e", "section:701d23928f8e38ea7d4b", "section:7144b70a605254dfecbc", "section:73dd631de817637ce12d", "section:7a7de20f53ed3e69fb6f", "section:93b8868beb643874af75", "section:9a6aaf6fc60f9b74b301", "section:a153934887244824336d", "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:aeb16d254373e2e88a13", "section:b3146d55cec712d485d5", "section:c9d9fdab1f8620914792", "section:ce5afee193d0ce1ea07e", "section:d0d4a62b7872b9bb3a1c", "section:d90bd5e1e6d8fa41397d", "section:daecafc150c9651ad391", "section:dccf3e7f3250c009523d", "section:e09bf94c77ca8cb235a1", "section:e16d657ff22e85d37e54", "section:eb00caf29086b02d5bf5", "section:f97072f658fe6bcec8d8", "section:fbf67a6377a333f71dff", "section:fd15b9954fc0175fba1b" ], "activeSectionIds": [ "section:0bcac4df826bc0d57d23", "section:55b733511958e907bad8", "section:65e6ea58d3d1fb647f95", "section:7144b70a605254dfecbc", "section:7a7de20f53ed3e69fb6f", "section:9a6aaf6fc60f9b74b301", "section:a153934887244824336d", "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:aeb16d254373e2e88a13", "section:b3146d55cec712d485d5", "section:ce5afee193d0ce1ea07e", "section:d0d4a62b7872b9bb3a1c", "section:dccf3e7f3250c009523d", "section:e09bf94c77ca8cb235a1", "section:e16d657ff22e85d37e54", "section:f97072f658fe6bcec8d8" ], "evidenceId": "python_verification:verification/v125_glue_qsystem.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v125_glue_qsystem.py", "pubMirrorHash": "7231c07cecd3e39c402806bca101c4e5483126bc4ae48974ea72b1b96ad033d7", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v125_glue_qsystem.py" }, { "id": "v126_clock_wall_bridge", "filename": "v126_clock_wall_bridge.py", "path": "verification/v126_clock_wall_bridge.py", "cluster": "registry", "synopsis": "THE CLOCK AND THE WALL SHARE A SPECTRUM (the v124 resummed-clock weights ARE the Mehta–Seshadri parabolic weights; R1's first checkpoint passes classically): THE WEIGHTS ARE THE PARABOLIC WEIGHTS [I] — the arguments n/N_fam = {0, 1/3, 2/3} of the resummed logarithm are EXACTLY spec A₀* (the exact U_wall residue, v115); spectral bridge λₙ = (1 − αₙ)^{p₂} over α ∈ spec A₀* reproduces the frozen transfer spectrum {1, (2/3)⁶, (1/3)⁶} — the horizon clock and the flavor wall share their spectrum through α ↦ 1−α; CHECKPOINT 1 PASSES CLASSICALLY [I]: the linear coefficient p₂/N_fam = 2 = |ℤ₂| equals the established classical entropy-deviation rate 2H = |ℤ₂|×Hubble (v104) — the slope-2 linear response is already the classical entropy rate, so the genuinely QUANTUM content of R1 isolates to the geometric tail Σ_{k≥2} αᵏ/k; THE DETERMINANT IS THE ENTROPY CURVATURE [I]: det(1 − A₀*) = 2/9 = |ℤ₂|/N_fam² — exactly the v102 gravity entropy curvature at the anchor (fourth independent appearance); tr(1 − A₀*) = 2 = |ℤ₂|, det A₀* = 0; R1 re-targeted [P]: derive 'rate = −p₂ ln(1 − α)' with α the parabolic weight — first order classical, tail quantum: ONE SPECTRUM, TWO GATES, ONE OBJECT A₀*", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv126_clock_wall_bridge.py", "sourceSha256": "ca81230ce9ba5d72404c5198345bc328c5c6c6e18b68f94b03a2571d8f81beb2", "linkedClaimIds": [ "HOR.CLOCK.04" ], "sectionIds": [ "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:f4ce21377eb152ef27fe", "section:fda00a19dcba44348ac3" ], "activeSectionIds": [ "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:f4ce21377eb152ef27fe", "section:fda00a19dcba44348ac3" ], "evidenceId": "python_verification:verification/v126_clock_wall_bridge.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v126_clock_wall_bridge.py", "pubMirrorHash": "ca81230ce9ba5d72404c5198345bc328c5c6c6e18b68f94b03a2571d8f81beb2", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v126_clock_wall_bridge.py" }, { "id": "v127_ring_resummation", "filename": "v127_ring_resummation.py", "path": "verification/v127_ring_resummation.py", "cluster": "registry", "synopsis": "THE CLOCK IS A LOG-DETERMINANT (the geometric tail is the standard ring/RPA resummation; the 'O(1) resummation' demanded by v107 is now TYPED): LOG-DET IDENTITY [I] — for a rank-1 insertion P (tr Pᵏ = 1): −ln det(1 − αP) = −ln(1 − α) = Σₖ αᵏ/k, so the resummed clock is EXACTLY rate = −p₂ Tr ln(1 − αP): p₂ = 6 identical one-loop ring towers, ONE PER HEXAGON SITE (= positive root of A₃), coupling α = the Mehta–Seshadri parabolic weight; RING LADDER [I]: the k = 1 ring is the CLASSICAL term (6α = |ℤ₂|n = the v104/v126 entropy rate), the k = 2 ring is the first quantum correction (1/3 at weight 1); partial sums converge to {Δ, 6 ln 3} monotonically from below; COUPLING CROSS-LINK [I, audit]: κ_seam = 8/(24π) = 1/(3π) = α₁/π — the seam coupling is the first parabolic weight over π; THE WALL = RING DIVERGENCE [I]: radius of convergence |α| < 1, divergence at α → 1 (n → N_fam) — the v124 wall is the standard RPA instability; R1 FINAL FORM [P]: 'the seam clock is the RPA determinant of one mode on six sites' — resummation type identified, derivation open", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv127_ring_resummation.py", "sourceSha256": "5de0295475ccf05e27817ac7ec3fd93bfec01acdea0327794ab45f75d78b0f60", "linkedClaimIds": [ "HOR.CLOCK.05" ], "sectionIds": [ "section:4d3487ca2d27735cbff3", "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:f4ce21377eb152ef27fe" ], "activeSectionIds": [ "section:4d3487ca2d27735cbff3", "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:f4ce21377eb152ef27fe" ], "evidenceId": "python_verification:verification/v127_ring_resummation.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v127_ring_resummation.py", "pubMirrorHash": "5de0295475ccf05e27817ac7ec3fd93bfec01acdea0327794ab45f75d78b0f60", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v127_ring_resummation.py" }, { "id": "v128_graded_hull", "filename": "v128_graded_hull.py", "path": "verification/v128_graded_hull.py", "cluster": "registry", "synopsis": "THE GRADED HULL + THE ZERO-MODE MULTIPLICITY (both named computations R1/R2 gain their structural anchors): R2 HALF — EXPLICIT COSET CONSTRUCTION [I]: the 240 E8 roots built as explicit norm-2 vectors in D₅⊕A₃+glue coordinates decompose over the glue ℤ₄ as 240 = 52 + 64 + 60 + 64 (C₀ = carrier 40+12, C₁ = (16,4̄), C₂ = (10,6), C₃ = (16̄,4)) — the v89 branching as vectors; THE GRADING IS EXACT [I]: for ALL 6720 root pairs whose sum is again a root, coset(r₁+r₂) = coset(r₁)+coset(r₂) mod 4 — E8 IS A ℤ₄-GRADED LIE ALGEBRA over the carrier, and the grading group IS the glue = the v125 Q-system: the checksum hull is the Q-system's graded module realised in 248 dimensions; R1 HALF — THE MULTIPLICITY IS THE ZERO-MODE COUNT [I]: the Ginsparg–Perry l=1 sector (the zero modes λ ∈ {0,−1}) has 2l+1 = 3 modes, sheet doubling gives 2×3 = 6 = p₂ = |R⁺(A₃)| — the ring multiplicity of the v127 clock equals the sheet-doubled zero-mode count ([P]: zero modes are exactly the modes forcing nonperturbative resummation in dS one-loop physics — the natural home of the six RPA towers); residue [P]: R1 = compute the RPA determinant on the six sheet-doubled zero modes, R2 = identify the seam-Calderón inclusion with the ℤ₄-graded structure now exhibited inside E8 itself", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv128_graded_hull.py", "sourceSha256": "27de4db51eaecb32799f034d6f2dc0bdd4e9a9e59139cad42846200095a302dc", "linkedClaimIds": [ "E8.GRADE.01" ], "sectionIds": [ "section:0bcac4df826bc0d57d23", "section:2678ed3ba0ed508e2d8e", "section:307c4c95a7c84b5efc0b", "section:51e91159532ef7479ff8", "section:701d23928f8e38ea7d4b", "section:7d0e50b6a6c30535730d", "section:93b8868beb643874af75", "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b63f8484d81bde8026ec", "section:cca5b83aae425d5f0e88", "section:d0d4a62b7872b9bb3a1c", "section:eb00caf29086b02d5bf5", "section:f4ce21377eb152ef27fe" ], "activeSectionIds": [ "section:0bcac4df826bc0d57d23", "section:51e91159532ef7479ff8", "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b63f8484d81bde8026ec", "section:d0d4a62b7872b9bb3a1c", "section:f4ce21377eb152ef27fe" ], "evidenceId": "python_verification:verification/v128_graded_hull.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v128_graded_hull.py", "pubMirrorHash": "27de4db51eaecb32799f034d6f2dc0bdd4e9a9e59139cad42846200095a302dc", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v128_graded_hull.py" }, { "id": "v129_entropy_power_law", "filename": "v129_entropy_power_law.py", "path": "verification/v129_entropy_power_law.py", "cluster": "registry", "synopsis": "THE CLOCK IS AN ENTROPY POWER LAW (what the resummation argument 1 − n/N_fam IS physically): THE THREE ENTROPY LEVELS [I] — the established Nariai bookkeeping (v101) has S/S_dS ∈ {1, 2/3, 1/3} (pure dS; two-horizon total; single horizon — deficit S_dS/3 per step): EXACTLY the complementary cusp weights; THE CLOCK IS AN ENTROPY POWER LAW [I]: λₙ = (Sₙ/S_dS)^{p₂} = the frozen transfer spectrum, rate(n) = p₂ ln(S_dS/Sₙ) — hexagon-weighted log-entropy deficits (audit: exponent p₂ = 6 = 2h reads as the two-point form of a weight h = 3 = N_fam operator); THE COUPLING IS THE ENTROPY DEFICIT [I] (triple identity): α = n/N_fam = MS parabolic weight (v115/v126) = 1 − Sₙ/S_dS = ΔSₙ/S_dS — the RPA insertion strength is the fractional entropy deficit, not a free parameter in ANY of its three readings; ORIENTATION CONSISTENT [I]: weight 0 ↔ pure dS (max entropy, stationary attractor), weight 2 ↔ single horizon (fastest decay) — the established repeller → attractor flow; R1 THERMODYNAMIC FORM [P]: derive Γₙ ∝ (Sₙ/S_dS)^{p₂} from the near-Nariai one-loop — a Gibbons–Hawking-type entropy power law with exponent = the hexagon size", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv129_entropy_power_law.py", "sourceSha256": "9f41ea31db064c8a63879bced40e588161f2961a8beb2b8690914130d67b6507", "linkedClaimIds": [ "HOR.CLOCK.06" ], "sectionIds": [ "section:03c7873577084caa47f8", "section:49282b347d9c681f9051", "section:7d0e50b6a6c30535730d", "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:cb552d2464f1e864b4f9", "section:cca5b83aae425d5f0e88", "section:de8db1cd8257eab0d607", "section:edf07fc78f9496f57ed7", "section:f4ce21377eb152ef27fe", "section:fda00a19dcba44348ac3" ], "activeSectionIds": [ "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:de8db1cd8257eab0d607", "section:edf07fc78f9496f57ed7", "section:f4ce21377eb152ef27fe", "section:fda00a19dcba44348ac3" ], "evidenceId": "python_verification:verification/v129_entropy_power_law.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v129_entropy_power_law.py", "pubMirrorHash": "9f41ea31db064c8a63879bced40e588161f2961a8beb2b8690914130d67b6507", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v129_entropy_power_law.py" }, { "id": "v130_born_square", "filename": "v130_born_square.py", "path": "verification/v130_born_square.py", "cluster": "registry", "synopsis": "THE BORN SQUARE (the amplitude weight is h = N_fam = half the zero-mode count; the clock exponent p₂ = 2h is its Born square — the v128 multiplicity and the v129 weight are ONE object): EXPONENT BOOKKEEPING [I] — each zero mode trades a Gaussian integral for a moduli factor ∝ S^{1/2} (standard collective coordinates); with n_zero = 6 the transition AMPLITUDE scales as A ∼ (S/S_dS)^{n_zero/2} = (S/S_dS)³ and the PROBABILITY is its Born square Γ = |A|² = (S/S_dS)⁶ = the v129 entropy power law ⇒ h = n_zero/2 = 3 = N_fam, p₂ = 2h: the weight audit is DERIVED from mode counting, the factor 2 is the Born rule; THE THREE ARE THE SPHERE'S CONFORMAL DIRECTIONS [I]: dim of the l=1 eigenspace on S² = 2l+1 = 3 = the number of proper conformal Killing vectors of the sphere (the classic near-Nariai zero modes, Ginsparg–Perry/Bousso–Hawking class); the ×2 is the HORIZON PAIR = the SdS mass-line deck (v101): n_zero = |ℤ₂|×3 = 6 = p₂ — every factor an established object; CONSISTENCY [I]: the same 3 counts generations and the sphere's conformal directions; residue [P]: justify the per-zero-mode S^{1/2} normalisation on the Nariai instanton — textbook-class, no exotic object remains in R1", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv130_born_square.py", "sourceSha256": "3efb6b755e57a0e338dd03ddfceafea81a0663668ce7e3d3f7c236c9a4822d79", "linkedClaimIds": [ "HOR.CLOCK.07" ], "sectionIds": [ "section:37e45eedbaaf285f97f5", "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:f4ce21377eb152ef27fe" ], "activeSectionIds": [ "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:f4ce21377eb152ef27fe" ], "evidenceId": "python_verification:verification/v130_born_square.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v130_born_square.py", "pubMirrorHash": "3efb6b755e57a0e338dd03ddfceafea81a0663668ce7e3d3f7c236c9a4822d79", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v130_born_square.py" }, { "id": "v131_measure_is_area", "filename": "v131_measure_is_area.py", "path": "verification/v131_measure_is_area.py", "cluster": "registry", "synopsis": "THE MEASURE IS THE AREA (the per-mode S^{1/2} of the Born square is the zero-mode NORM, computed exactly; the R1 residue narrows to one determinant-ratio cancellation): ZERO-MODE NORM = AREA [I] — on S²(r) the L² norm² of each of the three normalised l=1 harmonics is EXACTLY r² = A/(4π) (all three integrated exactly): the norm of every zero mode IS the horizon area, hence the entropy; JACOBIAN BOOKKEEPING [I]: the collective-coordinate Jacobian per mode is the mode norm ∼ S^{1/2} (standard change of variables, no model input); six sheet-doubled modes ⇒ amplitude ratio (Sₙ/S_dS)³, Born square ⇒ Γ ratio (Sₙ/S_dS)⁶ = the v129 power law — every exponent factor now has a derivation-level origin: norm = area → Jacobian = S^{1/2} → six modes → amplitude S³ → Born → S⁶; UNIT CONSISTENCY [I]: the 4π in norm² = A/(4π) is the same Gauss–Bonnet primitive that builds c₃ = 1/(2·4π), and it CANCELS in all ratios — exactly why the clock sees only entropy FRACTIONS; THE LAST STEP [P]: show det'ₙ/det'_dS = 1 + O(deficit) (non-zero-mode determinant cancellation, same local near-Nariai geometry) — the one remaining computation: R1 = norm (exact, done) + Jacobian (standard) + Born (rule) + det-ratio (open) (the cancellation since derived within the family, v144)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv131_measure_is_area.py", "sourceSha256": "6cc5cad3be8af18a7c49f76da4d89dbf44da4be50b727dfffa3cdcce2d1f6e33", "linkedClaimIds": [ "HOR.CLOCK.08" ], "sectionIds": [ "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:e09bf94c77ca8cb235a1", "section:f4ce21377eb152ef27fe" ], "activeSectionIds": [ "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:e09bf94c77ca8cb235a1", "section:f4ce21377eb152ef27fe" ], "evidenceId": "python_verification:verification/v131_measure_is_area.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v131_measure_is_area.py", "pubMirrorHash": "6cc5cad3be8af18a7c49f76da4d89dbf44da4be50b727dfffa3cdcce2d1f6e33", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v131_measure_is_area.py" }, { "id": "v132_detratio_anomaly", "filename": "v132_detratio_anomaly.py", "path": "verification/v132_detratio_anomaly.py", "cluster": "registry", "synopsis": "THE DET-RATIO ANOMALY IS THE KOIDE CONSTANT (the v131 'last step' acquires its first exact invariant): SPECTRAL SETUP — the Ginsparg–Perry sphere operator on unit S² is L = −Δ − 2 (the −2 = −|ℤ₂| = the v104 modulus mass), eigenvalues (l+2)(l−1), kernel = 3 zero modes (l=1); THE HEAT COEFFICIENT IS MADE OF ATOMS [I]: a₁ = R/6 − E = 1/3 + 2 = 1/N_fam + |ℤ₂| = 7/3; THE ANOMALY IS THE KOIDE CONSTANT [I]: ζ(0)|det′ = a₁ − dim ker = 7/3 − 3 = −2/3 = −|ℤ₂|/N_fam, independently confirmed by numerical continuation of the heat trace (~1e−7) — the EIGHTH appearance of 2/3 and the first as a SPECTRAL anomaly; CONSEQUENCE [I]: det′(cL) = c^{ζ(0)} det′(L) — the determinant ratio between configurations is NOT automatically 1: the S²-sector share of the scaling budget is exactly −2/3 per Hubble-unit conversion, while the dimensionless GP tower is configuration-independent; BUDGET STATEMENT [P]: show the FULL 4d ζ(0) budget (dS₂ + gauge/ghost + S² sectors) vanishes or is absorbed — the S² share is pinned exactly, nothing claimed about the total", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv132_detratio_anomaly.py", "sourceSha256": "959ffe6dadf34e8d59a51d59eba60d10f6771d730cf6ca2d84486bfa663058e0", "linkedClaimIds": [ "HOR.CLOCK.09" ], "sectionIds": [ "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:e09bf94c77ca8cb235a1", "section:f4ce21377eb152ef27fe" ], "activeSectionIds": [ "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:e09bf94c77ca8cb235a1", "section:f4ce21377eb152ef27fe" ], "evidenceId": "python_verification:verification/v132_detratio_anomaly.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v132_detratio_anomaly.py", "pubMirrorHash": "959ffe6dadf34e8d59a51d59eba60d10f6771d730cf6ca2d84486bfa663058e0", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v132_detratio_anomaly.py" }, { "id": "v133_zeta_budget", "filename": "v133_zeta_budget.py", "path": "verification/v133_zeta_budget.py", "cluster": "registry", "synopsis": "THE ZETA BUDGET, BOTH ROUTES COMPUTED EXACTLY (the reduced seam route carries pure anchor-ratio anomalies; the naive 4d route does not — the budget computation structurally selects the reduced seam reading): Euclidean Nariai = S²×S², so the temporal dS₂ sector continues to the SAME unit sphere; THE REDUCED ROUTE [I]: each 2d sector carries the v132 operator with ζ(0)|det′ = −2/3; two sectors give budget = −4/3 = −e₁/p₀ = MINUS THE SEED GAIN (the second v119 triad ratio; the first, −2/3, is the per-sector share); the six zero modes split 3+3 across the two spheres — the sheet doubling IS the two-sphere structure of Euclidean Nariai (= the horizon pair, v101); THE NAIVE 4D ROUTE [I]: standard unit-S² heat expansion 1/t + 1/3 + t/15 (verified numerically), symmetric split ⇒ a₂(4d) = (4/3)² + 2·(9/10) = 161/45, six zero modes, ζ(0)|det′,4d = 161/45 − 6 = −109/45 (continuation ~1e−8) — NO anchor-atom reading; ROUTE DISCRIMINATION [I+P]: reduced-route anomalies = pure anchor ratios (two of the three triad values), 4d-route anomaly is not an atom ⇒ the ζ budget structurally favours the REDUCED seam reading, consistent with the 2d-seam architecture (route-selection evidence, not proof); remaining [P]: graviton/ghost shares on S²×S² (Volkov–Wipf class) — a finite list of known heat coefficients", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv133_zeta_budget.py", "sourceSha256": "ae7c481fa74df7510e91858a3c1288ca21fc62cade93c353205778a8795a6645", "linkedClaimIds": [ "HOR.CLOCK.10" ], "sectionIds": [ "section:213a1f15f7373957fc2f", "section:2525c189f32461c9368a", "section:6cd1a267e72b20619327", "section:81a6dc002dc46cf7b6c5", "section:888628823bf71f709698", "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:b93e6ae7b00f32ee1201", "section:f4ce21377eb152ef27fe" ], "activeSectionIds": [ "section:213a1f15f7373957fc2f", "section:81a6dc002dc46cf7b6c5", "section:888628823bf71f709698", "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:f4ce21377eb152ef27fe" ], "evidenceId": "python_verification:verification/v133_zeta_budget.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v133_zeta_budget.py", "pubMirrorHash": "ae7c481fa74df7510e91858a3c1288ca21fc62cade93c353205778a8795a6645", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v133_zeta_budget.py" }, { "id": "v134_dual_anchor", "filename": "v134_dual_anchor.py", "path": "verification/v134_dual_anchor.py", "cluster": "registry", "synopsis": "THE DUAL ANCHOR LEMMA (the inverse flavor response of the anchor IS the Nariai root — the third purely algebraic leg of the flavor↔horizon bridge): d := aᵀR⁻¹ = aᵀL⁻¹ = (−1/2, −1/2, 1) with d·1 = 0, d·a = 1 and d = (3/2)(a − (4/3)1) — the normalised TRACELESS anchor — and (1,1,−2) = −2d: the inverse flavor response stores exactly the Nariai double-root structure (v101) up to sign and scale, so the horizon is not glued on afterwards — it sits inside the flavor compiler as a dual invariant [I]; WHY INVARIANT (Sherman–Morrison, exact): L = R + 6·1e₁ᵀ makes a covector winding-invariant iff it annihilates R⁻¹1 = (1,1,−1)/4, and the anchor does — the winding deformation lives in the democratic direction, which d kills [I]; CONTROL: 1, e₁ and n = (5,−9,6) do NOT lie on the invariance plane (1/4, 1/4, −5/2) — the membership is special, not generic [I]; THE DUAL NORMAL PAIR: d (sheet normal: kills 1, dual to a, ∝ Nariai root) and n (torsion normal: nᵀR = (8,0,0), nᵀL = (20,0,0), n·a = 8, n·1 = 2 = |Z₂|) form the dual basis of the flavor boundary [I]; consequence [P]: third algebraic bridge leg beside the shared clock spectrum (v126) and the entropy power law (v129); the R4′ selector programme acquires a geometric target — derive the PAIR (d, n), not n alone", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv134_dual_anchor.py", "sourceSha256": "702b4a2a4394c89bc3af3a021eb599ba7b50322aa93b4522d1193cda59959e99", "linkedClaimIds": [ "FLAV.DUAL.01" ], "sectionIds": [ "section:2585b5d786c3bdb7ddb7", "section:2678ed3ba0ed508e2d8e", "section:51e91159532ef7479ff8", "section:6a93c4dd5fe420e1990e", "section:95036dacfe44edfdb2c9", "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d", "section:fda00a19dcba44348ac3" ], "activeSectionIds": [ "section:2585b5d786c3bdb7ddb7", "section:51e91159532ef7479ff8", "section:95036dacfe44edfdb2c9", "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:fda00a19dcba44348ac3" ], "evidenceId": "python_verification:verification/v134_dual_anchor.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v134_dual_anchor.py", "pubMirrorHash": "702b4a2a4394c89bc3af3a021eb599ba7b50322aa93b4522d1193cda59959e99", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v134_dual_anchor.py" }, { "id": "v135_det_surface", "filename": "v135_det_surface.py", "path": "verification/v135_det_surface.py", "cluster": "registry", "synopsis": "THE DETERMINANT SURFACE (the sheet diamond is a 2d surface with iso-volume WALLS at the discrete atoms): det M(s,t) = 3s(t+1)(t+2) + t² + 5t + 8 on the established diamond M(s,t) = R + Q·diag(s,t,t) (v94/v95) — two iso-volume walls INDEPENDENT of s: t = −2 ⇒ det = 2 = |Z₂| (the Z₂ wall) and t = −1 ⇒ det = 4 = |μ₄| (the μ₄ wall; K = M(1,−1) lies on it, so det K = 4 is a LAYER, not an isolated hit); the winding line t = 0 carries det = 6s + 8 ⇒ (det R, det C, det L) = (8, 14, 20), and det F = det M(1,1) = 32 = 2^g_car closes the four canonical points [I]; ANCHOR BLOCK: det B = 6s(t+2) + 3t² + 15t + 16 with det B(s,0) = 2·det M(s,0) EXACTLY on the winding line, its own Z₂ wall det B(s,−2) = −2, and t = −1 is NOT a B-wall (6s+4, recorded honestly) [I]; ROW-BUDGET AXES: rowsum(C) = (7,11,13), rowsum(U) = (3,3,3) (democratic winding), rowsum(V) = (1,2,3) = Spec(Q₊) verbatim; audit: the centre budget (7,11,13) = (scalaron, ‖Pl(K)‖₁, Δ_Q) [I]; TWO ANCHOR MICRO-IDENTITIES: e₁² + e₂² = 41 = 10·b₁ (the anchor Pythagoras for the abelian coefficient, companion to Δ_Y = 25 = 9+16) and p₁² + p₂² = 52 = the carrier coset root count (40+12, v128) [I]; reading [P]: the flavor algebra lives on a 2d surface whose walls are the discrete atoms and whose axes are democratic winding and the Q₊ progression — compiler semantics replacing the matrix list; no gate status changes", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv135_det_surface.py", "sourceSha256": "1e513c8f35422948b174a337871c146d734af42d64081e2f0908afe729ced486", "linkedClaimIds": [ "FLAV.SURF.01" ], "sectionIds": [ "section:2678ed3ba0ed508e2d8e", "section:2ff762f6d6932ac2b2c5", "section:51e91159532ef7479ff8", "section:6a93c4dd5fe420e1990e", "section:7a7de20f53ed3e69fb6f", "section:95036dacfe44edfdb2c9", "section:9bab697ba19c86420aea", "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:b37031f13445096fcccf", "section:d90bd5e1e6d8fa41397d" ], "activeSectionIds": [ "section:2ff762f6d6932ac2b2c5", "section:51e91159532ef7479ff8", "section:7a7de20f53ed3e69fb6f", "section:95036dacfe44edfdb2c9", "section:9bab697ba19c86420aea", "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:b37031f13445096fcccf" ], "evidenceId": "python_verification:verification/v135_det_surface.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v135_det_surface.py", "pubMirrorHash": "1e513c8f35422948b174a337871c146d734af42d64081e2f0908afe729ced486", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v135_det_surface.py" }, { "id": "v136_dual_normal_selector", "filename": "v136_dual_normal_selector.py", "path": "verification/v136_dual_normal_selector.py", "cluster": "registry", "synopsis": "THE DUAL-NORMAL SELECTOR ((d,n) pins R COLUMNWISE; the R4′ residue is bounded): COLUMN NORMAL FORM [I]: d·c_j = a_j and n·c_j = 8δ₁ⱼ for the columns of R; the common kernel of (d,n) is the primitive vector (6,8,7) (audit: p₂, rank E₈, scalaron-7), so within the address box {0..5}³ each line contains at most one lattice point — brute-force census (216 per column): c₁ = (1,1,2) = a, c₂ = (3,5,5), c₃ = (0,2,3) are each the UNIQUE solution, so R4′ shrinks from a 6⁹ matrix census (v121) to three 1-of-216 column problems: (d,n) ⇒ R; HONESTY [I]: K is NOT pinned directly (dᵀK = (1,1/2,1), nᵀK = (14,1,−6)); det K = 4 follows via the diamond (μ₄ wall, v135); SPECTRAL NORMAL [I]: the A₀* zero mode v = (−√2,3,−√5)/3 has signed squares = −(2,−9,5) = −(|ℤ₂|, −N_fam², g_car), with NEW atoms ‖v‖² = 16/9 (16 = dim S⁺) and adj(A₀*) = (2/9)·P_v where 2/9 = the SdS entropy curvature; SIGMA RELATIONS [I]: σ·1 = −|ℤ₂|, σ·a = N_fam, n·σ = 121 = ‖Pl(K)‖₁² (the v119 audit constant); ORBIT CONTROL [I]: |W(A₃)| = 24 exactly, the only real orbit images of σ are its signed copies, NO image proportional to n — the naive cofactor/orbit lift FAILS as the review predicted: the step σ → n is a genuine mechanism beyond the monodromy group; R4′ RESTATED [P]: derive the PAIR (d,n); then R is forced columnwise", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv136_dual_normal_selector.py", "sourceSha256": "cbd564df37a3002b8eafda9ce99aa62af054b58817c8f2e8760904890fc66862", "linkedClaimIds": [ "GATE.UWALL.10" ], "sectionIds": [ "section:20ef03b5c6c62b042300", "section:213a1f15f7373957fc2f", "section:568b5e9acdb7b04367d3", "section:6a93c4dd5fe420e1990e", "section:72b43011ac4fb932c47a", "section:81a6dc002dc46cf7b6c5", "section:95036dacfe44edfdb2c9", "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d", "section:f0ac30137703825661c6", "section:fdf63a1d99769ab37ccb" ], "activeSectionIds": [ "section:20ef03b5c6c62b042300", "section:213a1f15f7373957fc2f", "section:72b43011ac4fb932c47a", "section:81a6dc002dc46cf7b6c5", "section:95036dacfe44edfdb2c9", "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:fdf63a1d99769ab37ccb" ], "evidenceId": "python_verification:verification/v136_dual_normal_selector.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v136_dual_normal_selector.py", "pubMirrorHash": "cbd564df37a3002b8eafda9ce99aa62af054b58817c8f2e8760904890fc66862", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v136_dual_normal_selector.py" }, { "id": "v137_qplus_cohomology", "filename": "v137_qplus_cohomology.py", "path": "verification/v137_qplus_cohomology.py", "cluster": "registry", "synopsis": "THE Q₊ GRADING IS COHOMOLOGY (the R5/GATE.QGEO dictionary at the spectrum level): BASIS + CHARACTERS [I]: b₁(ℙ¹∖μ₄) = 3 = N_fam with holomorphic basis ω_k = z^(k−1)dz/(z⁴−1), k = 1,2,3 (regular at infinity; the trivial character is absent); the μ₄ character of ω_k is i^k, so H¹ = χ₁⊕χ₂⊕χ₃ with each nontrivial character exactly once, and the residue vector over the punctures is the character vector ζ^k/4 exactly; THE GRADING IS Spec(Q₊) [I]: the character degrees (1,2,3) are exactly Spec(Q₊) (Q₊ = 3·cusp + 1, v69/v72), and NEW: the cusp weights {0, 1/3, 2/3} are spec(A₀*) (v115) — Mehta–Seshadri weights, cusp classes, cohomology characters and the flavor operator Q₊ are ONE spectrum in four readouts; A₃ EXPONENTS [I]: (1,2,3) are the exponents of A₃ (W(A₃) = S₄, v117) with Coxeter number h(A₃) = 4 = |μ₄| — the Q₊ generation grading IS the A₃ exponent grading, realised on the seam curve's cohomology; RESIDUE [P]: what remains of GATE.QGEO is the NATURALITY of the identification — the canonical map from the H¹ character basis to the V-axis generation basis (rowsum(V) = (1,2,3) verbatim, v135); spectrum equality is [I], the canonical map is the residue", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv137_qplus_cohomology.py", "sourceSha256": "f5c697e9cba9cb14d788a3cbe3844d4539928413be30f9326513c72844f8a80a", "linkedClaimIds": [ "FLAV.QGEO.04" ], "sectionIds": [ "section:22fb298fcb28accfbf39", "section:2678ed3ba0ed508e2d8e", "section:2f06593b8d87effdfab6", "section:307c4c95a7c84b5efc0b", "section:436dbc6f3b40e9aa8035", "section:55b733511958e907bad8", "section:5ae06930f472e00a9545", "section:6a93c4dd5fe420e1990e", "section:701d23928f8e38ea7d4b", "section:72b43011ac4fb932c47a", "section:749d598aa0815d32790b", "section:81a6dc002dc46cf7b6c5", "section:83cee7585db61c131b9a", "section:93b8868beb643874af75", "section:9a6aaf6fc60f9b74b301", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:cc5f650209aae2bdc4e6", "section:d90bd5e1e6d8fa41397d", "section:e1f5b724a85f51ec5624", "section:eb00caf29086b02d5bf5", "section:f1cb1505fb0d067d8745" ], "activeSectionIds": [ "section:22fb298fcb28accfbf39", "section:2f06593b8d87effdfab6", "section:436dbc6f3b40e9aa8035", "section:55b733511958e907bad8", "section:72b43011ac4fb932c47a", "section:749d598aa0815d32790b", "section:81a6dc002dc46cf7b6c5", "section:83cee7585db61c131b9a", "section:9a6aaf6fc60f9b74b301", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:cc5f650209aae2bdc4e6", "section:f1cb1505fb0d067d8745" ], "evidenceId": "python_verification:verification/v137_qplus_cohomology.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v137_qplus_cohomology.py", "pubMirrorHash": "f5c697e9cba9cb14d788a3cbe3844d4539928413be30f9326513c72844f8a80a", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v137_qplus_cohomology.py" }, { "id": "v138_vw_firewall", "filename": "v138_vw_firewall.py", "path": "verification/v138_vw_firewall.py", "cluster": "registry", "synopsis": "THE VOLKOV–WIPF FIREWALL (R1 typed closure; external values verified against arXiv:2506.02142 Table 4.1, which agrees with Volkov–Wipf hep-th/0003081): EXTERNAL DATUM [I, typed external]: α_bulk = 22/45, α_edge = −8/3, α_PI = −98/45 for d = 3 (S²×S², 4d); THE EDGE MATCH [I] — the structural finding: α_edge = −8/3 = 2 × (−4/3), the external edge factor consists of TWO IDENTICAL COPIES (one per horizon) and the per-copy magnitude 4/3 = e₁/p₀ is EXACTLY the v133 reduced seam budget (= the seed gain; −2/3 per sector) — the TFPT reduced route lands on the EDGE sector of the external bulk/edge split, the bulk 22/45 is the ideal graviton gas which the seam clock does not contain, and two copies = the horizon pair = the sheet doubling (v101; v133's 3+3 zero-mode split); FIREWALL ARITHMETIC [I]: −98/45 + 60/45 = −38/45 with 38 = 2·19 — neither −98/45 nor −38/45 nor 22/45 is an anchor atom, consistent with v133's non-atomic naive route (different operator content, recorded); TYPING DECISION [P]: R1 = the reduced zero-mode/RPA seam clock = an EDGE-sector object; the full 4d Volkov–Wipf determinant is the GRAVITY FIREWALL (its −98/45 absorbed in the μ₀/(ΛG)³ normalisation), not a TFPT atom", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv138_vw_firewall.py", "sourceSha256": "fecb8ef949ce6cf6490d9cd863acf801e52a2b818a6c23f119eb8c8ac4562e5d", "linkedClaimIds": [ "HOR.CLOCK.11" ], "sectionIds": [ "section:213a1f15f7373957fc2f", "section:81a6dc002dc46cf7b6c5", "section:8ae7510979d5941b1583", "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:f4ce21377eb152ef27fe" ], "activeSectionIds": [ "section:213a1f15f7373957fc2f", "section:81a6dc002dc46cf7b6c5", "section:8ae7510979d5941b1583", "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:f4ce21377eb152ef27fe" ], "evidenceId": "python_verification:verification/v138_vw_firewall.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v138_vw_firewall.py", "pubMirrorHash": "fecb8ef949ce6cf6490d9cd863acf801e52a2b818a6c23f119eb8c8ac4562e5d", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v138_vw_firewall.py" }, { "id": "v139_selector_triangle", "filename": "v139_selector_triangle.py", "path": "verification/v139_selector_triangle.py", "cluster": "registry", "synopsis": "THE SELECTOR TRIANGLE (anchor + A₀* zero mode + three atoms ⇒ R; the R4′ residue shrinks to three pairings): d IS ANCHOR DATA [I]: d = (3/2)a − 2·1 exactly — the dual anchor (v134) has a closed form that never mentions R, so the first selector of the pair (d,n) is DERIVED, not residual; THE FRAME [I]: (1, a, σ) is a basis of ℤ³ with det(1|a|σ) = 11 = ‖Pl(K)‖₁ — the quark constant as the frame volume (σ = the A₀* zero-mode signature, v136); n FROM THREE ATOMS [I]: n = (5,−9,6) is the UNIQUE solution of n·1 = 2 = |ℤ₂|, n·a = 8 = rank E₈, n·σ = 121 = 11² — the cofactor definition (v95) is replaced by frame data plus three atoms; THE SQUARE SELECTS [I]: on the line n·1 = 2, n·a = 8 the σ-pairing is 11(11+t) — divisible by 11 for every t and a positive perfect square exactly at t = 0, the true n; THE REVIEW LIFT EXACT (audit) [I]: n = reverse(σ) + |μ₄|e₃ (generation flip + μ₄ lift at the third slot, as the external review predicted), and n − σ = N_fam·e₁ + e₃; RESIDUE [P]: R4′ = derive the three pairings (|ℤ₂|, rank E₈, ‖Pl(K)‖₁²) — everything else in the chain anchor → (d,n) → R (v136) is exact (since v142: two — the third pairing is integrality-forced)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv139_selector_triangle.py", "sourceSha256": "858853ca4424f20262c2272d9f71fa1c3fb05837897701500bbdce26e2ba27f9", "linkedClaimIds": [ "GATE.UWALL.11" ], "sectionIds": [ "section:20ef03b5c6c62b042300", "section:213a1f15f7373957fc2f", "section:298ca201062fd482dafa", "section:3934f91cc921c9b43fab", "section:4d3487ca2d27735cbff3", "section:568b5e9acdb7b04367d3", "section:5d8f619883df80c56b36", "section:6a93c4dd5fe420e1990e", "section:6ff4670b89c8b83d4b0f", "section:72b43011ac4fb932c47a", "section:7a667667edab66880567", "section:95036dacfe44edfdb2c9", "section:a660765e3a391c14ceef", "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:c6a172fae7d467d3744c", "section:d90bd5e1e6d8fa41397d", "section:de1edf5378afcd852d3e", "section:ef3ac63aa9e6dcddf33d", "section:f0ac30137703825661c6", "section:fdf63a1d99769ab37ccb" ], "activeSectionIds": [ "section:20ef03b5c6c62b042300", "section:213a1f15f7373957fc2f", "section:298ca201062fd482dafa", "section:3934f91cc921c9b43fab", "section:4d3487ca2d27735cbff3", "section:5d8f619883df80c56b36", "section:72b43011ac4fb932c47a", "section:95036dacfe44edfdb2c9", "section:a660765e3a391c14ceef", "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:fdf63a1d99769ab37ccb" ], "evidenceId": "python_verification:verification/v139_selector_triangle.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v139_selector_triangle.py", "pubMirrorHash": "858853ca4424f20262c2272d9f71fa1c3fb05837897701500bbdce26e2ba27f9", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v139_selector_triangle.py" }, { "id": "v140_canonical_map", "filename": "v140_canonical_map.py", "path": "verification/v140_canonical_map.py", "cluster": "registry", "synopsis": "THE CANONICAL MAP EXISTS AND IS RIGID (the GATE.QGEO naturality residue collapses to ONE ℤ₃ choice): THREE μ₄ ACTIONS, ONE MATCH [I]: the plain deck U = diag(1,i,−i) has characters (0,1,3) — an invariant line, missing 2 — and CANNOT match H¹; the sheet-twisted deck −U (characters (2,3,1)) and the cusp exponential i^{Q₊} (characters (1,2,3)) both carry the character SET {1,2,3} = the H¹ set (v137) — only the SIGN-TWISTED actions match, by the same sheet twist that builds the v118 hexagon; RIGIDITY (Schur) [I]: both sides are multiplicity-free μ₄-modules with equal character sets, so the equivariant isomorphism exists and is unique up to one scalar per character (commutant = diagonal algebra) — the canonical map is WELL-DEFINED, existence and uniqueness are no longer open; GRADING TRANSPORT [I]: under the i^{Q₊}-equivariant map the H¹ Euler degree pulls back to Q₊ itself (assignment (1,2,3)); under the −U-map to Q₊∘ρ with ρ = the (123) family rotation (assignment (2,3,1)) — the two candidate actions differ by EXACTLY one ℤ₃ rotation; RESIDUE [P]: GATE.QGEO collapses from 'prove naturality' to ONE discrete choice — which sign-twisted action is the geometric boundary deck on generation space (−U monodromy sheet twist vs i^{Q₊} cusp exponential) (the choice since derived, v141)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv140_canonical_map.py", "sourceSha256": "514549015070d48fa329a5b3e37958b6ee69e18b874b04e4a880561f4e60f7cd", "linkedClaimIds": [ "FLAV.QGEO.05" ], "sectionIds": [ "section:20ef03b5c6c62b042300", "section:2678ed3ba0ed508e2d8e", "section:2b8d2aba4baeb7a0c36b", "section:303925994b6f141b3a0e", "section:9bab697ba19c86420aea", "section:a7805cce6b04546f1147", "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:bb2a02a767e560376342", "section:e09bf94c77ca8cb235a1", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:20ef03b5c6c62b042300", "section:9bab697ba19c86420aea", "section:a7ddfbed7669a08bf2ee", "section:ab9e7e520130ecc7da7c", "section:bb2a02a767e560376342", "section:e09bf94c77ca8cb235a1", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v140_canonical_map.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v140_canonical_map.py", "pubMirrorHash": "514549015070d48fa329a5b3e37958b6ee69e18b874b04e4a880561f4e60f7cd", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v140_canonical_map.py" }, { "id": "v141_deck_selection", "filename": "v141_deck_selection.py", "path": "verification/v141_deck_selection.py", "cluster": "registry", "synopsis": "deck selection: the v140 ℤ₃ choice DERIVED — the integer deck G=T_A·Σ (v97/v98) pairs the Q₊=1 line with the self-conjugate character 2, excluding i^{Q₊} and selecting the sheet-twisted −U assignment (2,3,1); only the established sheet ℤ₂ remains; Euler grading = Q₊∘ρ", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv141_deck_selection.py", "sourceSha256": "8c29d8bdc2b0e8c6953343ab41b9d3311cb35145318cda013df7b0cacf0721a0", "linkedClaimIds": [ "FLAV.QGEO.06" ], "sectionIds": [ "section:2678ed3ba0ed508e2d8e", "section:298ca201062fd482dafa", "section:3934f91cc921c9b43fab", "section:436dbc6f3b40e9aa8035", "section:5ae06930f472e00a9545", "section:7a667667edab66880567", "section:81a6dc002dc46cf7b6c5", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:c6a172fae7d467d3744c", "section:e09bf94c77ca8cb235a1", "section:e1f5b724a85f51ec5624" ], "activeSectionIds": [ "section:298ca201062fd482dafa", "section:3934f91cc921c9b43fab", "section:436dbc6f3b40e9aa8035", "section:81a6dc002dc46cf7b6c5", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:e09bf94c77ca8cb235a1" ], "evidenceId": "python_verification:verification/v141_deck_selection.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v141_deck_selection.py", "pubMirrorHash": "8c29d8bdc2b0e8c6953343ab41b9d3311cb35145318cda013df7b0cacf0721a0", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v141_deck_selection.py" }, { "id": "v142_frame_integrality", "filename": "v142_frame_integrality.py", "path": "verification/v142_frame_integrality.py", "cluster": "registry", "synopsis": "frame integrality (R4′): integer covectors in the (1,a,σ) dual frame = index-11 sublattice (x−3y+z ≡ 0 mod 11); with (2,8) established the σ-pairing is forced ≡ 0 mod 11; primitivity forces even line parameter — three pairings reduce to two (since v145: the values are atom identities — residue = one lift map)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv142_frame_integrality.py", "sourceSha256": "2e837d439484778fdf4ec32493e2b7b838a3d721861375ed679408f279444ea8", "linkedClaimIds": [ "GATE.UWALL.12" ], "sectionIds": [ "section:213a1f15f7373957fc2f", "section:298ca201062fd482dafa", "section:3934f91cc921c9b43fab", "section:436dbc6f3b40e9aa8035", "section:5ae06930f472e00a9545", "section:6a93c4dd5fe420e1990e", "section:7a667667edab66880567", "section:95036dacfe44edfdb2c9", "section:a660765e3a391c14ceef", "section:ab9e7e520130ecc7da7c", "section:c6a172fae7d467d3744c", "section:d90bd5e1e6d8fa41397d", "section:de1edf5378afcd852d3e", "section:e09bf94c77ca8cb235a1", "section:e1f5b724a85f51ec5624" ], "activeSectionIds": [ "section:213a1f15f7373957fc2f", "section:298ca201062fd482dafa", "section:3934f91cc921c9b43fab", "section:436dbc6f3b40e9aa8035", "section:95036dacfe44edfdb2c9", "section:a660765e3a391c14ceef", "section:ab9e7e520130ecc7da7c", "section:e09bf94c77ca8cb235a1" ], "evidenceId": "python_verification:verification/v142_frame_integrality.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v142_frame_integrality.py", "pubMirrorHash": "2e837d439484778fdf4ec32493e2b7b838a3d721861375ed679408f279444ea8", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v142_frame_integrality.py" }, { "id": "v143_graded_frobenius", "filename": "v143_graded_frobenius.py", "path": "verification/v143_graded_frobenius.py", "cluster": "registry", "synopsis": "graded Frobenius (R2): the ℤ₄-graded hull carries exact coset duality (−C₁=C₃), the glue average is the carrier projector (index 4), each sector is one Weyl orbit (simple current) — the ℂ[ℤ₄] Q-system realised at the finite Lie level; residual = the conformal-net step", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv143_graded_frobenius.py", "sourceSha256": "5fa32b7534810c8008f334309d490d646b17c8683a94b8dc4b9b58c9123ffa05", "linkedClaimIds": [ "GATE.METRIC.09" ], "sectionIds": [ "section:2525c189f32461c9368a", "section:298ca201062fd482dafa", "section:65e6ea58d3d1fb647f95", "section:6cd1a267e72b20619327", "section:7a7de20f53ed3e69fb6f", "section:888628823bf71f709698", "section:93b8868beb643874af75", "section:9a6aaf6fc60f9b74b301", "section:ab9e7e520130ecc7da7c", "section:b7b42d68bfe9bb72f6b0", "section:b93e6ae7b00f32ee1201", "section:c004d2ee68ddeaaf26ff", "section:d0d4a62b7872b9bb3a1c", "section:d21a62fafd64ff24f0b6", "section:e09bf94c77ca8cb235a1", "section:eb00caf29086b02d5bf5" ], "activeSectionIds": [ "section:298ca201062fd482dafa", "section:65e6ea58d3d1fb647f95", "section:7a7de20f53ed3e69fb6f", "section:888628823bf71f709698", "section:9a6aaf6fc60f9b74b301", "section:ab9e7e520130ecc7da7c", "section:b7b42d68bfe9bb72f6b0", "section:c004d2ee68ddeaaf26ff", "section:d0d4a62b7872b9bb3a1c", "section:d21a62fafd64ff24f0b6", "section:e09bf94c77ca8cb235a1" ], "evidenceId": "python_verification:verification/v143_graded_frobenius.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v143_graded_frobenius.py", "pubMirrorHash": "5fa32b7534810c8008f334309d490d646b17c8683a94b8dc4b9b58c9123ffa05", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v143_graded_frobenius.py" }, { "id": "v144_detratio_family", "filename": "v144_detratio_family.py", "path": "verification/v144_detratio_family.py", "cluster": "registry", "synopsis": "det-ratio cancellation (R1): r_b·r_c = 1−Δ²/3 exact (e₂-rigidity) ⇒ det′-ratio = (1−Δ²/3)^{4/3}: no first-order term in the horizon split; deficit coefficient 32/27 = |μ₄|(2/3)³; the finite-weight absorption stays [P] with its obstruction stated sharply (the bend since shown det′-clean, v147)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv144_detratio_family.py", "sourceSha256": "9ef10ed07f1305fe87da50e221954f7ba9645cd0a259b3c2f020cb51feb02052", "linkedClaimIds": [ "HOR.CLOCK.12" ], "sectionIds": [ "section:213a1f15f7373957fc2f", "section:298ca201062fd482dafa", "section:4d3487ca2d27735cbff3", "section:81a6dc002dc46cf7b6c5", "section:ab9e7e520130ecc7da7c", "section:e09bf94c77ca8cb235a1", "section:f4ce21377eb152ef27fe" ], "activeSectionIds": [ "section:213a1f15f7373957fc2f", "section:298ca201062fd482dafa", "section:4d3487ca2d27735cbff3", "section:81a6dc002dc46cf7b6c5", "section:ab9e7e520130ecc7da7c", "section:e09bf94c77ca8cb235a1", "section:f4ce21377eb152ef27fe" ], "evidenceId": "python_verification:verification/v144_detratio_family.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v144_detratio_family.py", "pubMirrorHash": "9ef10ed07f1305fe87da50e221954f7ba9645cd0a259b3c2f020cb51feb02052", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v144_detratio_family.py" }, { "id": "v145_pairing_atoms", "filename": "v145_pairing_atoms.py", "path": "verification/v145_pairing_atoms.py", "cluster": "registry", "synopsis": "R4′ values = ATOM IDENTITIES: given the lift n = w₀(σ)+|μ₄|e₃ (w₀ = A₃ exponent duality), n·1 = |μ₄|−|ℤ₂| = 2, n·a = |μ₄|·a₃ = 8 via the new closure |μ₄|+g_car = N_fam² (4+5=9, σ⊥w₀(a)), n·σ = ‖σ‖²−N²+|μ₄|g = 121 — residue = derive the ONE map", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv145_pairing_atoms.py", "sourceSha256": "9ebf6510ab0289bf2fe78162cbf27ca5789ba3d8f48edb0d8e7158ee50980364", "linkedClaimIds": [ "GATE.UWALL.13" ], "sectionIds": [ "section:213a1f15f7373957fc2f", "section:436dbc6f3b40e9aa8035", "section:4d3487ca2d27735cbff3", "section:5ae06930f472e00a9545", "section:6a93c4dd5fe420e1990e", "section:81a6dc002dc46cf7b6c5", "section:95036dacfe44edfdb2c9", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d", "section:e1f5b724a85f51ec5624" ], "activeSectionIds": [ "section:213a1f15f7373957fc2f", "section:436dbc6f3b40e9aa8035", "section:4d3487ca2d27735cbff3", "section:81a6dc002dc46cf7b6c5", "section:95036dacfe44edfdb2c9", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v145_pairing_atoms.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v145_pairing_atoms.py", "pubMirrorHash": "9ebf6510ab0289bf2fe78162cbf27ca5789ba3d8f48edb0d8e7158ee50980364", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v145_pairing_atoms.py" }, { "id": "v146_moebius_d4", "filename": "v146_moebius_d4.py", "path": "verification/v146_moebius_d4.py", "cluster": "registry", "synopsis": "Möbius-D4 realisation (R5 floor): ⟨z↦iz, z↦1/z⟩ = D4 acts on H¹(P¹∖μ₄) EXACTLY as the integer model ⟨G,T_A,Σ⟩ — ι swaps χ₁↔χ₃ with +1 on χ₂ (det −1) = T_A; δι = Σ; parities and reflection classes match — the premise reduces to the module identification itself", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv146_moebius_d4.py", "sourceSha256": "a8f22458c32d9912d2d89fd823bcdee181607f8f4349e144f24dc095b3622f1a", "linkedClaimIds": [ "FLAV.QGEO.07" ], "sectionIds": [ "section:2678ed3ba0ed508e2d8e", "section:436dbc6f3b40e9aa8035", "section:4d3487ca2d27735cbff3", "section:5ae06930f472e00a9545", "section:81a6dc002dc46cf7b6c5", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:e1f5b724a85f51ec5624" ], "activeSectionIds": [ "section:436dbc6f3b40e9aa8035", "section:4d3487ca2d27735cbff3", "section:81a6dc002dc46cf7b6c5", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v146_moebius_d4.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v146_moebius_d4.py", "pubMirrorHash": "a8f22458c32d9912d2d89fd823bcdee181607f8f4349e144f24dc095b3622f1a", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v146_moebius_d4.py" }, { "id": "v147_clock_gaussian", "filename": "v147_clock_gaussian.py", "path": "verification/v147_clock_gaussian.py", "cluster": "registry", "synopsis": "clock = Gaussian zero-mode integral (R1): variance ratio (1−α) (norm=area, v131) ⇒ Born² Γ-ratio (1−α)^{p₂}, rate = −p₂ln(1−α) = the v127 ring sum term by term; the BEND log_{3/2}3 lives between the two Nariai levels of ONE geometry ⇒ det′-clean; obstruction localised to the α=0 reference", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv147_clock_gaussian.py", "sourceSha256": "b0626988e151de097182f5f1938d13c16d3831d303d2a497246719e297ada4f3", "linkedClaimIds": [ "HOR.CLOCK.13" ], "sectionIds": [ "section:4d3487ca2d27735cbff3", "section:81a6dc002dc46cf7b6c5", "section:ab9e7e520130ecc7da7c", "section:f4ce21377eb152ef27fe" ], "activeSectionIds": [ "section:4d3487ca2d27735cbff3", "section:81a6dc002dc46cf7b6c5", "section:ab9e7e520130ecc7da7c", "section:f4ce21377eb152ef27fe" ], "evidenceId": "python_verification:verification/v147_clock_gaussian.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v147_clock_gaussian.py", "pubMirrorHash": "b0626988e151de097182f5f1938d13c16d3831d303d2a497246719e297ada4f3", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v147_clock_gaussian.py" }, { "id": "v148_fock_census", "filename": "v148_fock_census.py", "path": "verification/v148_fock_census.py", "cluster": "registry", "synopsis": "NS/R census (R2 scoped, corrected): the untwisted (NS) module carries only even classes {0,2}×{0,2} — the odd glue sectors are RAMOND modules; 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THE LOAD [P]: v56's gapped PF uniqueness lives on the 3-dim scalar transfer spectrum {1,(2/3)^6,(1/3)^6}, while the seam correlation cone has C(16,4)=1820, C(16,6)=8008 cumulant directions ⇒ (A) reduces to the single internal statement 'the admissible TFPT transport is primitive + spectrally gapped on the FULL Schwinger cone, not only the readout spectrum'.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv160_seam_gaussianity_from_pf.py", "sourceSha256": "b1df030b7f9645e7915490180c20b70c14fa7dfe1c12006edd1018f0e7a19e00", "linkedClaimIds": [ "GATE.METRIC.16" ], "sectionIds": [ "section:013b22f7d203ce0c7da1", "section:03b9058ca08ba4829ac7", "section:05558e866dc724bc0fcb", "section:2525c189f32461c9368a", "section:2585b5d786c3bdb7ddb7", "section:41a8556f07331f818583", "section:4a157afd200102fcaaee", "section:55b733511958e907bad8", "section:5b9fc9c550f79525abcd", "section:5f8b87dd447560390c4e", "section:6a93c4dd5fe420e1990e", "section:6cd1a267e72b20619327", "section:7144b70a605254dfecbc", "section:7a7de20f53ed3e69fb6f", "section:81a6dc002dc46cf7b6c5", "section:888628823bf71f709698", "section:8e4972dbe899b5debb90", "section:901199b7ffce4a10a268", "section:93b8868beb643874af75", "section:9a6aaf6fc60f9b74b301", "section:a153934887244824336d", "section:a9e4936094020237f825", "section:ab9e7e520130ecc7da7c", "section:b7b42d68bfe9bb72f6b0", "section:b93e6ae7b00f32ee1201", "section:bc61b0e372551b770dfb", "section:c39fabd7834a6c050a87", "section:cc5f650209aae2bdc4e6", "section:ce5afee193d0ce1ea07e", "section:d90bd5e1e6d8fa41397d", "section:e16d657ff22e85d37e54", "section:eb00caf29086b02d5bf5", "section:f97072f658fe6bcec8d8", "section:fd15b9954fc0175fba1b" ], "activeSectionIds": [ "section:013b22f7d203ce0c7da1", "section:05558e866dc724bc0fcb", "section:2585b5d786c3bdb7ddb7", "section:41a8556f07331f818583", "section:4a157afd200102fcaaee", "section:55b733511958e907bad8", "section:5b9fc9c550f79525abcd", "section:5f8b87dd447560390c4e", "section:7144b70a605254dfecbc", "section:7a7de20f53ed3e69fb6f", "section:81a6dc002dc46cf7b6c5", "section:888628823bf71f709698", "section:8e4972dbe899b5debb90", "section:901199b7ffce4a10a268", "section:9a6aaf6fc60f9b74b301", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:b7b42d68bfe9bb72f6b0", "section:bc61b0e372551b770dfb", "section:c39fabd7834a6c050a87", "section:cc5f650209aae2bdc4e6", "section:ce5afee193d0ce1ea07e", "section:e16d657ff22e85d37e54", "section:f97072f658fe6bcec8d8" ], "evidenceId": "python_verification:verification/v160_seam_gaussianity_from_pf.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v160_seam_gaussianity_from_pf.py", "pubMirrorHash": "b1df030b7f9645e7915490180c20b70c14fa7dfe1c12006edd1018f0e7a19e00", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v160_seam_gaussianity_from_pf.py" }, { "id": "v161_one_particle_reduction", "filename": "v161_one_particle_reduction.py", "path": "verification/v161_one_particle_reduction.py", "cluster": "registry", "synopsis": "the cone reduces to one particle (discharges v160's scope premise via Bogoliubov second quantisation): a quasi-free transport is T = Γ(t), the second quantisation of a one-particle contraction t; Γ(t) acts on the degree-m correlator sector as the exterior power Λ^m(t), so (1) spec(Γ(t)|deg m) = products of m one-particle eigenvalues [E]; (2) THE CONE GAP EQUALS THE ONE-PARTICLE GAP — sub-leading eigenvalue over the whole cone = (2/3)^6 exactly [E]; (3) the eigenvalue-1 sector = wedges of the fixed subspace (disconnected Wick powers), no independent fixed higher cumulant; uniqueness closed by v113 (one polarization ⇔ one state) [E]; (4) quasi-freeness FORCED not assumed — the 120 = dim so(16) chiral currents ARE the Bogoliubov generators and v158 makes every non-Gaussian deformation irrelevant [C]. RESIDUAL [O]: v160's three full-cone premises collapse to ONE 16-dim one-particle statement (seam symbol = gapped Calderón Bogoliubov map, fixed = rank-8 K_Σ, gap (2/3)^6); all numbers supplied, only the physical identification (Kawahigashi-Longo class, = the A2 net residual) stays open.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv161_one_particle_reduction.py", "sourceSha256": "5f68aecdddf9be30df446de0a452b6b7c154615b81a9c604f18c43fa00ee1896", "linkedClaimIds": [ "GATE.METRIC.17" ], "sectionIds": [ "section:013b22f7d203ce0c7da1", "section:190cc30037d75411e25f", "section:6a93c4dd5fe420e1990e", "section:7a7de20f53ed3e69fb6f", "section:901199b7ffce4a10a268", "section:93b8868beb643874af75", "section:9a6aaf6fc60f9b74b301", "section:a153934887244824336d", "section:a9e4936094020237f825", "section:ab9e7e520130ecc7da7c", "section:bc61b0e372551b770dfb", "section:cc5f650209aae2bdc4e6", "section:d90bd5e1e6d8fa41397d", "section:e16d657ff22e85d37e54", "section:eb00caf29086b02d5bf5" ], "activeSectionIds": [ "section:013b22f7d203ce0c7da1", "section:190cc30037d75411e25f", "section:7a7de20f53ed3e69fb6f", "section:901199b7ffce4a10a268", "section:9a6aaf6fc60f9b74b301", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:bc61b0e372551b770dfb", "section:cc5f650209aae2bdc4e6", "section:e16d657ff22e85d37e54" ], "evidenceId": "python_verification:verification/v161_one_particle_reduction.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v161_one_particle_reduction.py", "pubMirrorHash": "5f68aecdddf9be30df446de0a452b6b7c154615b81a9c604f18c43fa00ee1896", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v161_one_particle_reduction.py" }, { "id": "v162_seam_transport_identification", "filename": "v162_seam_transport_identification.py", "path": "verification/v162_seam_transport_identification.py", "cluster": "registry", "synopsis": "the final identification, forced as far as it goes — the v161 one-particle statement carries NO new open content: (1) the gap (2/3)^6 is FORCED — cusp weights = spec(A0*) = {0,1/3,2/3} (parabolic residue, v115), transfer eigenvalue (1-α)^{p2}, p2 = 6 = |R+(A3)|, all carrier data [E]; (2) μ4-equivariance forces the generator diagonal in the cusp basis — Σ_k U^k X U^{-k} = |μ4| diag(X), commutant of U = diagonal algebra — so the gapped μ4-equivariant generator has spectrum = cusp weights, gap (2/3)^6 [E]; (3) the cusp grading IS the A3 grading on the 16 Majoranas (v137) [E]; (4) the fixed space = rank-8 Calderón polarization (v113/v156/v157) [E]. CLOSURE [C/O]: with v160+v161, (A) closes given only μ4-equivariance + admissibility, whose two non-derived inputs are the ALREADY-open A2 (net existence) and R1 (seam clock, HOR.CLOCK) — so (A) factors exactly into A2 + R1, adds NO new open item, and is closed CONDITIONALLY on them (a unification, not an unconditional proof).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv162_seam_transport_identification.py", "sourceSha256": "1d3a80006bcff439f88b83d7f3b64d03a7b8d9cea15308ca7c68fde86beb5225", "linkedClaimIds": [ "GATE.METRIC.18" ], "sectionIds": [ "section:22fb298fcb28accfbf39", "section:2f06593b8d87effdfab6", "section:55b733511958e907bad8", "section:5b9fc9c550f79525abcd", "section:6a93c4dd5fe420e1990e", "section:7a7de20f53ed3e69fb6f", "section:83cee7585db61c131b9a", "section:8e4972dbe899b5debb90", "section:93b8868beb643874af75", "section:9a6aaf6fc60f9b74b301", "section:ab9e7e520130ecc7da7c", "section:bc61b0e372551b770dfb", "section:c99473f27f0afd476930", "section:cc5f650209aae2bdc4e6", "section:d90bd5e1e6d8fa41397d", "section:eb00caf29086b02d5bf5", "section:f771351de25bd70c1da6" ], "activeSectionIds": [ "section:22fb298fcb28accfbf39", "section:2f06593b8d87effdfab6", "section:55b733511958e907bad8", "section:5b9fc9c550f79525abcd", "section:7a7de20f53ed3e69fb6f", "section:83cee7585db61c131b9a", "section:8e4972dbe899b5debb90", "section:9a6aaf6fc60f9b74b301", "section:ab9e7e520130ecc7da7c", "section:bc61b0e372551b770dfb", "section:c99473f27f0afd476930", "section:cc5f650209aae2bdc4e6" ], "evidenceId": "python_verification:verification/v162_seam_transport_identification.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v162_seam_transport_identification.py", "pubMirrorHash": "1d3a80006bcff439f88b83d7f3b64d03a7b8d9cea15308ca7c68fde86beb5225", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v162_seam_transport_identification.py" }, { "id": "v163_rg_stability_flavor", "filename": "v163_rg_stability_flavor.py", "path": "verification/v163_rg_stability_flavor.py", "cluster": "registry", "synopsis": "F_transfer scale-tagging: the lepton-mixing seeds (sin²θ₁₂=1/3−φ₀/2=0.3067, sin²θ₁₃=φ₀·e^(−5/6)=0.0231) are RG-STABLE — PMNS running is y_τ²-suppressed (~1.8e-5 ≪ precision), so seam value = measured value; the quark mass-ratio readouts (m_t/m_b~41) run through y_t² ~ O(10–15%) and carry a scale tag. The only mixing-ROTATING Yukawa term (3/2)YY†Y carries y_max² (PyR@TE SM RGEs back the asymmetry).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv163_rg_stability_flavor.py", "sourceSha256": "003d51e2802a67f94111c48eba5b2048a841abc5a0a248b2da67469abba8416c", "linkedClaimIds": [ "FLAV.RGSTAB.01" ], "sectionIds": [ "section:593d2f8d7dd5d5b3f6dd", "section:72a14eb552d3c9fdbe67", "section:8e700f46596426722c86", "section:ab9e7e520130ecc7da7c" ], "activeSectionIds": [ "section:593d2f8d7dd5d5b3f6dd", "section:72a14eb552d3c9fdbe67", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v163_rg_stability_flavor.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v163_rg_stability_flavor.py", "pubMirrorHash": "003d51e2802a67f94111c48eba5b2048a841abc5a0a248b2da67469abba8416c", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v163_rg_stability_flavor.py" }, { "id": "v164_qcd_scale", "filename": "v164_qcd_scale.py", "path": "verification/v164_qcd_scale.py", "cluster": "registry", "synopsis": "the QCD confinement scale is parameter-free from the carrier b3=−7: running α_s(M_Z) down (2-loop, n_f thresholds) gives α_s(m_b)~0.22, α_s(m_c)~0.38 and confinement (α_s~1) at ~0.5 GeV — so the QCD-scale NUMERATOR of m_p/m_e is independently sourced (dimensional transmutation), while the ratio 1836 stays the honest 'Open / not forced' frontier non-claim (m_p = O(1)·Λ is lattice).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv164_qcd_scale.py", "sourceSha256": "faaabb153858738bc5e69b76ac2a3a3c77e70d3d6b781c28e5163f399b5624c4", "linkedClaimIds": [ "QCD.LAMBDA.01" ], "sectionIds": [ "section:1fc598d7241c419069ab", "section:2805350687457d7649bf", "section:4376c1a8c4e207cfb1f6", "section:593d2f8d7dd5d5b3f6dd", "section:6f0af99769531bda7e90", "section:72a14eb552d3c9fdbe67", "section:7e48439cd9f5f65a12df", "section:8e700f46596426722c86", "section:ab9e7e520130ecc7da7c", "section:cc7b2d0df421c394451c" ], "activeSectionIds": [ "section:2805350687457d7649bf", "section:4376c1a8c4e207cfb1f6", "section:593d2f8d7dd5d5b3f6dd", "section:72a14eb552d3c9fdbe67", "section:7e48439cd9f5f65a12df", "section:ab9e7e520130ecc7da7c", "section:cc7b2d0df421c394451c" ], "evidenceId": "python_verification:verification/v164_qcd_scale.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v164_qcd_scale.py", "pubMirrorHash": "faaabb153858738bc5e69b76ac2a3a3c77e70d3d6b781c28e5163f399b5624c4", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v164_qcd_scale.py" }, { "id": "v165_premise_a_closure", "filename": "v165_premise_a_closure.py", "path": "verification/v165_premise_a_closure.py", "cluster": "registry", "synopsis": "premise (A), the honest maximal closure — the two residual gates are pinned to their floor, so (A) carries ZERO independent open content: (1) A2 (net existence) closes by ASSEMBLY of established mathematics [C] — 16 free Majoranas => free-fermion net (BMT/Böckenhauer-Evans), holomorphic c=8 lattice net = (E8)1 (Frenkel-Kac-Segal/Dong-Xu/Kawahigashi-Longo), μ4 extension = Longo Q-system index 4 (v125), μ(B)=16/16=1, 248=120+128, character E4/η⁸=j^{1/3} (v156); the only TFPT input (seam Calderón kernel = free-fermion 2-point fn) is done via DtN=|k| (v156/v157); (2) R1 (seam clock) reduces to GATE.QGEO [C] — μ4-equivariance forces diagonal-in-cusp, the flat μ4-equivariant generator is UNIQUE = A0* (v115/v116) so the gap (2/3)^6 is forced, residual = 'seam boundary = the μ4-punctured sphere P¹∖μ4' = GATE.QGEO (cohomology established, v137); (3) the irreducible core stays {π,v_geo}, a THEOREM by the No-Unit Theorem (v153). FINAL ACCOUNTING: (A) = A2 assembly [C] + R1=GATE.QGEO + the {π,v_geo} core => ZERO independent open gates; a unification + re-typing, NOT an unconditional proof.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv165_premise_a_closure.py", "sourceSha256": "29856e7a16a0eb13abd43d3c94e573a6da161bcdf5820b63205e571a515b91ec", "linkedClaimIds": [ "GATE.METRIC.19" ], "sectionIds": [ "section:2525c189f32461c9368a", "section:2585b5d786c3bdb7ddb7", "section:55b733511958e907bad8", "section:6a93c4dd5fe420e1990e", "section:6cd1a267e72b20619327", "section:7a7de20f53ed3e69fb6f", "section:81a6dc002dc46cf7b6c5", "section:888628823bf71f709698", "section:93b8868beb643874af75", "section:9a6aaf6fc60f9b74b301", "section:ab9e7e520130ecc7da7c", "section:b7b42d68bfe9bb72f6b0", "section:b93e6ae7b00f32ee1201", "section:bc61b0e372551b770dfb", "section:d90bd5e1e6d8fa41397d", "section:eb00caf29086b02d5bf5", "section:f771351de25bd70c1da6" ], "activeSectionIds": [ "section:2585b5d786c3bdb7ddb7", "section:55b733511958e907bad8", "section:7a7de20f53ed3e69fb6f", "section:81a6dc002dc46cf7b6c5", "section:888628823bf71f709698", "section:9a6aaf6fc60f9b74b301", "section:ab9e7e520130ecc7da7c", "section:b7b42d68bfe9bb72f6b0", "section:bc61b0e372551b770dfb" ], "evidenceId": "python_verification:verification/v165_premise_a_closure.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v165_premise_a_closure.py", "pubMirrorHash": "29856e7a16a0eb13abd43d3c94e573a6da161bcdf5820b63205e571a515b91ec", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v165_premise_a_closure.py" }, { "id": "v166_higgs_free_seam", "filename": "v166_higgs_free_seam.py", "path": "verification/v166_higgs_free_seam.py", "cluster": "registry", "synopsis": "the Higgs quartic from the free seam (premise A / v158): a Gaussian seam UV forces lambda(M_seam)=0 AND beta_lambda(M_seam)=0 (Shaposhnikov-Wetterich double criticality, here MOTIVATED not assumed). 2-loop PyR@TE-sourced SM running with the measured (m_H,m_t) gives lambda(Mbar)~0.002, beta_lambda(Mbar)~0 at the reduced Planck mass — the famous SM near-criticality, now EXPLAINED by the free seam (2-loop sharpens lambda(Mbar) from ~0.022 to ~0.002). The double condition predicts m_H~129-134 GeV; the same condition at the scalaron scale gives ~107 GeV (too low) => the BC lives at M̄ (seam=Planck). Fills the Higgs-sector gap.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv166_higgs_free_seam.py", "sourceSha256": "f37c92faff063f7846df6a05c404bb2b8b1454fbaec171a548ea703cbfb18149", "linkedClaimIds": [ "HIGGS.FREESEAM.01" ], "sectionIds": [ "section:1d709d6b4fbbfe522d4a", "section:ab9e7e520130ecc7da7c", "section:b0bd96461774b2724095", "section:cc7b2d0df421c394451c" ], "activeSectionIds": [ "section:1d709d6b4fbbfe522d4a", "section:ab9e7e520130ecc7da7c", "section:b0bd96461774b2724095", "section:cc7b2d0df421c394451c" ], "evidenceId": "python_verification:verification/v166_higgs_free_seam.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v166_higgs_free_seam.py", "pubMirrorHash": "f37c92faff063f7846df6a05c404bb2b8b1454fbaec171a548ea703cbfb18149", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v166_higgs_free_seam.py" }, { "id": "v167_inventory_post_closure", "filename": "v167_inventory_post_closure.py", "path": "verification/v167_inventory_post_closure.py", "cluster": "registry", "synopsis": "the terminal residual inventory (post premise-(A) closure; line v105 → v123 → v167): after the (A)-chain (v160–v165), premise (A) is NO LONGER an independent structural class (GATE.METRIC.16–19). The residual collapses from v123's FIVE classes to: Tier 0 — the irreducible core {π, v_geo}, a THEOREM (No-Unit, v153, ANCHOR.VGEO.01/02), nothing to close; Tier 1 — ONE hinge (seam = flavour = horizon): A2 net existence (assembly of established net constructions, GATE.METRIC.11/13) + GATE.QGEO (seam boundary = ℙ¹∖μ4, cohomology b1=N_fam=3, cusp = A3 exponents) — the old clock/net/Q-realisation all collapse here; Tier 2 — FOLDED (EH step → v_geo via v152; ambient measure → G_net via v76); Tier 3 — F_transfer, one functor with four typed conditional interfaces (Koide FR.KOIDE, η_B FR.ETAB.01, m_p/m_e QCD.LAMBDA.01, axion scenario), eta_B carrying the most open computational room. Completeness: a sixth independent structural class fails the script. A unification + re-typing, NOT an unconditional proof.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv167_inventory_post_closure.py", "sourceSha256": "b53e28c16db22f958cca682a6f7ca2cca3ebaa20053b999ce11bf06dc18e038c", "linkedClaimIds": [ "SYNTH.INVENTORY.03" ], "sectionIds": [ "section:2525c189f32461c9368a", "section:6cd1a267e72b20619327", "section:888628823bf71f709698", "section:a3835ef2388efb1a54cd", "section:ab9e7e520130ecc7da7c", "section:b3882fb1623949f1d1b5", "section:b93e6ae7b00f32ee1201" ], "activeSectionIds": [ "section:888628823bf71f709698", "section:a3835ef2388efb1a54cd", "section:ab9e7e520130ecc7da7c", "section:b3882fb1623949f1d1b5" ], "evidenceId": "python_verification:verification/v167_inventory_post_closure.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v167_inventory_post_closure.py", "pubMirrorHash": "b53e28c16db22f958cca682a6f7ca2cca3ebaa20053b999ce11bf06dc18e038c", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v167_inventory_post_closure.py" }, { "id": "v168_qgeo_rigidity", "filename": "v168_qgeo_rigidity.py", "path": "verification/v168_qgeo_rigidity.py", "cluster": "registry", "synopsis": "the QGEO Rigidity Theorem — the FINITE half of the Tier-1 hinge GATE.QGEO, hardened. EXACT: μ4={1,i,−1,−i} has cross-ratio 2 and Möbius stabiliser ⟨z→iz, z→1/z⟩ of order 8=|D4| (faithful: 4-cycle + reflection) ⇒ four marks with faithful D4 are the μ4 square up to Möbius; H¹(ℙ¹∖μ4) rank 4−1=3=N_fam; the forms ω_k=z^{k−1}dz/(z⁴−1) (k=1,2,3) are μ4-eigenforms with z→iz eigenvalue i^k = the three nontrivial characters χ1,χ2,χ3, weights (1,2,3) = A3 exponents = Spec(Q+). QGEO.RIGID.01 [E] (the math half closed); QGEO.REALIZE.01 [C] (seam-collar = ℙ¹∖μ4 stays the realisation premise). Not a new structural class — it hardens the existing hinge.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv168_qgeo_rigidity.py", "sourceSha256": "e521cf3ea8006ff2a7da0b0abcc1dc393ee637183ae013fec2c8195c3c1cf5c0", "linkedClaimIds": [ "QGEO.RIGID.01", "QGEO.REALIZE.01" ], "sectionIds": [ "section:0bcac4df826bc0d57d23", "section:12f49e008971e532539c", "section:22fb298fcb28accfbf39", "section:2f06593b8d87effdfab6", "section:307c4c95a7c84b5efc0b", "section:6a93c4dd5fe420e1990e", "section:701d23928f8e38ea7d4b", "section:7750a727b522e861fdbc", "section:7d0e50b6a6c30535730d", "section:83cee7585db61c131b9a", "section:8e4972dbe899b5debb90", "section:93b8868beb643874af75", "section:9a6aaf6fc60f9b74b301", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b3882fb1623949f1d1b5", "section:b63f8484d81bde8026ec", "section:cca5b83aae425d5f0e88", "section:d90bd5e1e6d8fa41397d", "section:e16d657ff22e85d37e54", "section:e415b5fb585454314b5d", "section:eb00caf29086b02d5bf5", "section:f68163cf343646a0f102" ], "activeSectionIds": [ "section:0bcac4df826bc0d57d23", "section:12f49e008971e532539c", "section:22fb298fcb28accfbf39", "section:2f06593b8d87effdfab6", "section:7750a727b522e861fdbc", "section:83cee7585db61c131b9a", "section:8e4972dbe899b5debb90", "section:9a6aaf6fc60f9b74b301", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b3882fb1623949f1d1b5", "section:b63f8484d81bde8026ec", "section:e16d657ff22e85d37e54", "section:e415b5fb585454314b5d", "section:f68163cf343646a0f102" ], "evidenceId": "python_verification:verification/v168_qgeo_rigidity.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v168_qgeo_rigidity.py", "pubMirrorHash": "e521cf3ea8006ff2a7da0b0abcc1dc393ee637183ae013fec2c8195c3c1cf5c0", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v168_qgeo_rigidity.py" }, { "id": "v169_etaB_boltzmann_interface", "filename": "v169_etaB_boltzmann_interface.py", "path": "verification/v169_etaB_boltzmann_interface.py", "cluster": "registry", "synopsis": "the η_B leptogenesis transfer operationalised (Tier-3 F_transfer, NOT a new class): type-I thermal leptogenesis η_B ~ 0.96e-2·ε₁·κ_f (sphaleron 28/79) fed by TFPT's NO neutrino spectrum + the predicted δ_CP=240°. Davidson-Ibarra ε₁=(3/16π)M1·m3/v² ~ 8.5e-7 for M1=1e10 GeV; efficiency κ_f(m̃₁) ~ 0.03–0.19. KILL TEST: over natural M1∈[3e9,3e10] GeV and washout, η_B spans [8.4e-11, 4.7e-9] which BRACKETS the observed 6.1e-10 (canonical M1=1e10, m̃₁=5e-3 gives 6.0e-10, NOT tuned) ⇒ the route is VIABLE; but M1/washout are scenario inputs so η_B stays [C]. If excluded, the route falls, not the theory.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv169_etaB_boltzmann_interface.py", "sourceSha256": "f65ced038e6818cef17e22471760ff31e7ffa4c99a0c72822ede6bd10c8e189d", "linkedClaimIds": [ "FR.ETAB.02" ], "sectionIds": [ "section:1fc598d7241c419069ab", "section:6f0af99769531bda7e90", "section:7e48439cd9f5f65a12df", "section:ab9e7e520130ecc7da7c", "section:b3882fb1623949f1d1b5", "section:d0c4725137a9427c8a0b" ], "activeSectionIds": [ "section:7e48439cd9f5f65a12df", "section:ab9e7e520130ecc7da7c", "section:b3882fb1623949f1d1b5", "section:d0c4725137a9427c8a0b" ], "evidenceId": "python_verification:verification/v169_etaB_boltzmann_interface.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v169_etaB_boltzmann_interface.py", "pubMirrorHash": "f65ced038e6818cef17e22471760ff31e7ffa4c99a0c72822ede6bd10c8e189d", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v169_etaB_boltzmann_interface.py" }, { "id": "v170_diamond_slice_compression", "filename": "v170_diamond_slice_compression.py", "path": "verification/v170_diamond_slice_compression.py", "cluster": "registry", "synopsis": "E8 Slice Compression Lemma: the seven E8 audit slices are ONE projection of two alphabets — anchor power sums P=(3,4,6,10) (p_n=2+2^n) and Sheet-Diamond determinants D=(3,4,8,14,20,32). The K4 edge products (12,18,30,24,40,60) are all carrier blocks; ΣdetM=81=N_fam⁴; all seven 248-slices (D8,D5×A3,E6×A2,E7×A1,F4×G2,A4×A4,A8) follow from P,D,Δ=13,(e1,e2,dimS+); one affine map row(C+sU+tV)=(7,11,13)+s(3,3,3)+t(1,2,3) gives every flavour row budget; 78=dimE6=p2·Δ. The atlas is a closed grammar over two typed alphabets, not seven trophy lists. Exact; reading is audit (anti-numerology).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv170_diamond_slice_compression.py", "sourceSha256": "8d4a49363e582ee1b58f234df2ba416232af75287ac38000902780ed4e42aea4", "linkedClaimIds": [ "E8.SLICE.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:63da5b8be1d09edb111a", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:8a517836f882378cde88", "section:8a623c8ec8a4cfe2a678", "section:93b8868beb643874af75", "section:a719d5d4b287729fc27d", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:e36b11d50051a79291df", "section:eb00caf29086b02d5bf5" ], "activeSectionIds": [ "section:63da5b8be1d09edb111a", "section:8a517836f882378cde88", "section:ab9e7e520130ecc7da7c", "section:e36b11d50051a79291df" ], "evidenceId": "python_verification:verification/v170_diamond_slice_compression.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v170_diamond_slice_compression.py", "pubMirrorHash": "8d4a49363e582ee1b58f234df2ba416232af75287ac38000902780ed4e42aea4", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v170_diamond_slice_compression.py" }, { "id": "v171_os_moment_cluster", "filename": "v171_os_moment_cluster.py", "path": "verification/v171_os_moment_cluster.py", "cluster": "registry", "synopsis": "Atomic OS Moment Lemma + Sugawara Gap Safety: spec(T)={1,64/729,1/729} makes C(n)=A+Br^n+Cs^n a positive moment sequence, so every OS Hankel matrix factorises as a Vandermonde Gram ⇒ reflection positivity (a clean proof, not a numeric Gram test); cluster constant 729/665, correlation length ξ=0.41105, Källén-Lehmann masses 6log(3/2),6log3; gap safety Δ_eff=6log(3/2)−31/(4π²)>0 with 31=1+h^∨(E8) and c((E8)1)=248/31=8 — the A3 transfer gap beats the E8 Sugawara metric budget.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv171_os_moment_cluster.py", "sourceSha256": "f74b0058b3e3f13dc5135796e220e07ad5c6032bcaa2db35f3a4aaa455041097", "linkedClaimIds": [ "QFT.OSMOMENT.01" ], "sectionIds": [ "section:5ff3f529ae7be4541192", "section:93b8868beb643874af75", "section:ab9e7e520130ecc7da7c", "section:e36b11d50051a79291df", "section:eb00caf29086b02d5bf5" ], "activeSectionIds": [ "section:5ff3f529ae7be4541192", "section:ab9e7e520130ecc7da7c", "section:e36b11d50051a79291df" ], "evidenceId": "python_verification:verification/v171_os_moment_cluster.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v171_os_moment_cluster.py", "pubMirrorHash": "f74b0058b3e3f13dc5135796e220e07ad5c6032bcaa2db35f3a4aaa455041097", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v171_os_moment_cluster.py" }, { "id": "v172_trace_anomaly_seed", "filename": "v172_trace_anomaly_seed.py", "path": "verification/v172_trace_anomaly_seed.py", "cluster": "registry", "synopsis": "trace-anomaly origin of the seed prefactor 4/3: over the seam S² (χ=2) the (E8)1 (c=8) Weyl anomaly is c·χ/6=8/3, halved by the one-sided |Z2| to 4/3 = dimS+/dim g_SM = 16/12 = the seed base (4/3)c3=1/(6π). Plus QCD b3=11−⅔N_f=7 = scalaron exponent Ω_adm−10b1=48−41 (confinement↔inflation share one integer), and the Volkov-Wipf factorisation −98/45=−2·7²/dim(D5) (audit). Gives the seed prefactor and the QCD/scalaron integer a first-principles CFT/QFT origin.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv172_trace_anomaly_seed.py", "sourceSha256": "7995cda376f028270d677497044a561255dbc394b574c13385bcb11a39ef0637", "linkedClaimIds": [ "SEED.ANOMALY.01" ], "sectionIds": [ "section:610e7b9e8a68e0834305", "section:70e249c656b3bbd339e9", "section:ab9e7e520130ecc7da7c", "section:e36b11d50051a79291df" ], "activeSectionIds": [ "section:70e249c656b3bbd339e9", "section:ab9e7e520130ecc7da7c", "section:e36b11d50051a79291df" ], "evidenceId": "python_verification:verification/v172_trace_anomaly_seed.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v172_trace_anomaly_seed.py", "pubMirrorHash": "7995cda376f028270d677497044a561255dbc394b574c13385bcb11a39ef0637", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v172_trace_anomaly_seed.py" }, { "id": "v173_pfaffian_cp_car", "filename": "v173_pfaffian_cp_car.py", "path": "verification/v173_pfaffian_cp_car.py", "cluster": "registry", "synopsis": "Strong CP as Pfaffian reality: a self-dual CAR (16-Majorana) model demonstration of θ_eff=0 — the sheet-odd Calderón involution {D,Σ}=0 pairs the spectrum (±λ), γ5-Hermiticity (D†=γ5Dγ5) makes the fermion-measure Pfaffian real (arg∈{0,π}), and reflection positivity (Z>0) selects the positive branch ⇒ θ_eff=0. The CAR/Pfaffian form of the tfpt_2 polar+γ5+sheet+RP derivation.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv173_pfaffian_cp_car.py", "sourceSha256": "4564783e2df7707fbe132bf0c5559fb6678b38a32b5828638e6ae6f7117a136d", "linkedClaimIds": [ "FLAV.STRONGCP.02" ], "sectionIds": [ "section:2d043e484362d7a8bd90", "section:ab9e7e520130ecc7da7c", "section:e36b11d50051a79291df", "section:e563b224f9d38e2a2c72" ], "activeSectionIds": [ "section:ab9e7e520130ecc7da7c", "section:e36b11d50051a79291df", "section:e563b224f9d38e2a2c72" ], "evidenceId": "python_verification:verification/v173_pfaffian_cp_car.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v173_pfaffian_cp_car.py", "pubMirrorHash": "4564783e2df7707fbe132bf0c5559fb6678b38a32b5828638e6ae6f7117a136d", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v173_pfaffian_cp_car.py" }, { "id": "v174_seam_fock_readings", "filename": "v174_seam_fock_readings.py", "path": "verification/v174_seam_fock_readings.py", "cluster": "registry", "synopsis": "seam Fock-space readings: (1) CAR cone compression — dim Λ^even(ℝ¹⁶)=2¹⁵=32768 reduces to a 16-dim one-particle problem under quasi-free Bogoliubov (2¹⁵/16=2¹¹), the explicit count behind v161 (''the QFT cone is large but not independent''); (2) Witten index = the Plücker norm 11 = Σ_{k≤2}C(4,k), with 11=dim S⁺ − g_car (full 4-corner Fock 2⁴=16) and c_u/c_d=55/117 reading the QBL-protected boundary state space; (3) Affleck-Ludwig g-theorem: c_UV=5+3=8=c_IR((E8)₁) so Δc=0 forces an exact isometry (boundary-entropy form of v157/v158). Exact; readings audit.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv174_seam_fock_readings.py", "sourceSha256": "0890cda9da4a02287de37fbd809dce0f388877ae79854d5a0f12fc48b511b063", "linkedClaimIds": [ "QFT.FOCK.01" ], "sectionIds": [ "section:05aaf35318c9e1bb8204", "section:115c4091b215e2a670ca", "section:190cc30037d75411e25f", "section:282f1dffd6a2c2edfae1", "section:63da5b8be1d09edb111a", "section:7a7de20f53ed3e69fb6f", "section:ab9e7e520130ecc7da7c" ], "activeSectionIds": [ "section:05aaf35318c9e1bb8204", "section:115c4091b215e2a670ca", "section:190cc30037d75411e25f", "section:63da5b8be1d09edb111a", "section:7a7de20f53ed3e69fb6f", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v174_seam_fock_readings.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v174_seam_fock_readings.py", "pubMirrorHash": "0890cda9da4a02287de37fbd809dce0f388877ae79854d5a0f12fc48b511b063", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v174_seam_fock_readings.py" }, { "id": "v184_etaB_anchored_boltzmann", "filename": "v184_etaB_anchored_boltzmann.py", "path": "verification/v184_etaB_anchored_boltzmann.py", "cluster": "registry", "synopsis": "", "publicationNotes": [ "Non-scientific synopsis omitted." ], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv184_etaB_anchored_boltzmann.py", "sourceSha256": "bc5ddc18ee89b55ea628b687a7b444c8a35eb64ba3d2a700a6ae97895c1f785f", "linkedClaimIds": [ "FR.ETAB.03" ], "sectionIds": [ "section:1baa0cb6fdd6a6b16124", "section:1fc598d7241c419069ab", "section:20ef03b5c6c62b042300", "section:366ba63a37a50edd34ea", "section:51b5da5a67a36e5155ae", "section:568b5e9acdb7b04367d3", "section:697c671889813baf24f5", "section:6f0af99769531bda7e90", "section:7e48439cd9f5f65a12df", "section:ab9e7e520130ecc7da7c", "section:b559ae6d59524fc410e4", "section:d0c4725137a9427c8a0b", "section:f0ac30137703825661c6", "section:f4b6348640da84580573", "section:fdf63a1d99769ab37ccb" ], "activeSectionIds": [ "section:1baa0cb6fdd6a6b16124", "section:20ef03b5c6c62b042300", "section:366ba63a37a50edd34ea", "section:697c671889813baf24f5", "section:7e48439cd9f5f65a12df", "section:ab9e7e520130ecc7da7c", "section:b559ae6d59524fc410e4", "section:d0c4725137a9427c8a0b", "section:f4b6348640da84580573", "section:fdf63a1d99769ab37ccb" ], "evidenceId": "python_verification:verification/v184_etaB_anchored_boltzmann.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v184_etaB_anchored_boltzmann.py", "pubMirrorHash": "bc5ddc18ee89b55ea628b687a7b444c8a35eb64ba3d2a700a6ae97895c1f785f", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v184_etaB_anchored_boltzmann.py" }, { "id": "v185_axion_relic_solver", "filename": "v185_axion_relic_solver.py", "path": "verification/v185_axion_relic_solver.py", "cluster": "registry", "synopsis": "axion relic, honest misalignment estimate: the determinant-line axion f_a=M_scal/128≈2.39e11 GeV (m_a≈23.8 µeV) CAN provide all dark matter, but ONLY near the θ_i≈170° hilltop where the relic is exponentially sensitive — so the axion DM branch stays a [C] SCENARIO. The harmonic misalignment UNDER-produces at this f_a (prefactor ~0.026/θ², θ~O(1) gives ~21% of Ω_DM, need θ_eff²~4.7), so the 170° hilltop anharmonic enhancement is REQUIRED to reach Ω_DM; near the hilltop the relic is exponentially sensitive (and QCD/string-sensitive), hence a scenario, not a sharp prediction. Contract F_relic(f_a,θ_i,N_DW)=?Ω_DM is a kill test for the BRANCH not the theory (no free singlet WIMP: 128=(16,4)+(16,4) matter spinor).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv185_axion_relic_solver.py", "sourceSha256": "34483faac9fa93b3efb570f3c6546f5f22d5606ceb46dcce38e59123f20279c7", "linkedClaimIds": [ "FR.DM.03" ], "sectionIds": [ "section:1fc598d7241c419069ab", "section:208cd3e2a794336cad9d", "section:3af896f0e07d57463462", "section:51b5da5a67a36e5155ae", "section:568b5e9acdb7b04367d3", "section:64a9e573649942dd32e9", "section:697c671889813baf24f5", "section:6f0af99769531bda7e90", "section:7e48439cd9f5f65a12df", "section:989e899750d5a86edf1e", "section:ab9e7e520130ecc7da7c", "section:b559ae6d59524fc410e4", "section:cb81efd922f7b6f4776f", "section:f0ac30137703825661c6", "section:f4b6348640da84580573", "section:fdf63a1d99769ab37ccb" ], "activeSectionIds": [ "section:208cd3e2a794336cad9d", "section:3af896f0e07d57463462", "section:64a9e573649942dd32e9", "section:697c671889813baf24f5", "section:7e48439cd9f5f65a12df", "section:989e899750d5a86edf1e", "section:ab9e7e520130ecc7da7c", "section:b559ae6d59524fc410e4", "section:cb81efd922f7b6f4776f", "section:f4b6348640da84580573", "section:fdf63a1d99769ab37ccb" ], "evidenceId": "python_verification:verification/v185_axion_relic_solver.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v185_axion_relic_solver.py", "pubMirrorHash": "34483faac9fa93b3efb570f3c6546f5f22d5606ceb46dcce38e59123f20279c7", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v185_axion_relic_solver.py" }, { "id": "v189_riemann_roch_carrier", "filename": "v189_riemann_roch_carrier.py", "path": "verification/v189_riemann_roch_carrier.py", "cluster": "registry", "synopsis": "the Riemann-Roch carrier reading: (g_car, N_fam)=(5,3) are the two canonical invariants of ONE object, the four-point seam divisor D=µ₄ on P¹. [E] math: h⁰(P¹,O(µ₄))=deg+1=5 (function side) and rank H₁(P¹∖µ₄)=deg−1=3 (cycle side, already QGEO.COHOM.01/v177); g_car=5=rank(D₅) (carrier=so(10) half-spinor, rank D₅+rank A₃=5+3=8, v1), N_fam=3=(dim S⁺−1)/g_car. [C]: 'carrier = the meromorphic seam-mode space H⁰(P¹,O(µ₄))' is a geometric reading (less number, more geometry) matched by rank(D₅)=5, but the physical identification is conjectural and does NOT replace the over-determined g_car=5 (Pascal/bootstrap/Lean) — a fourth, geometric reading. h⁰ and rank H₁ are both fixed by deg=4 (one object, two invariants).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv189_riemann_roch_carrier.py", "sourceSha256": "4d84ef7b00722363f833c1e43b289b31e9d62056b78b8a70e8176db08c94602a", "linkedClaimIds": [ "ARCH.RRCAR.01" ], "sectionIds": [ "section:09b49009253acb5a0dfb", "section:3cc790136e8b9bd3c188", "section:46614e805445fc78e7af", "section:584e87a9c163ac38f92f", "section:64a9e573649942dd32e9", "section:ab9e7e520130ecc7da7c", "section:c926c39e5cf2b4b2f828", "section:eb0bd97fda8c0fedefad", "section:fe43532db2385fecd956" ], "activeSectionIds": [ "section:46614e805445fc78e7af", "section:584e87a9c163ac38f92f", "section:64a9e573649942dd32e9", "section:ab9e7e520130ecc7da7c", "section:c926c39e5cf2b4b2f828", "section:fe43532db2385fecd956" ], "evidenceId": "python_verification:verification/v189_riemann_roch_carrier.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v189_riemann_roch_carrier.py", "pubMirrorHash": "4d84ef7b00722363f833c1e43b289b31e9d62056b78b8a70e8176db08c94602a", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v189_riemann_roch_carrier.py" }, { "id": "v190_nariai_entropy_bound", "filename": "v190_nariai_entropy_bound.py", "path": "verification/v190_nariai_entropy_bound.py", "cluster": "registry", "synopsis": "the one-line Nariai entropy bound: the SdS entropy ratio S_tot/S_dS=(x²+1)/Φ₃(x) (x=r_b/r_c; Φ₃=x²+x+1 the N_fam=3 cyclotomic; already in tfpt_horizon_readouts) satisfies S_tot ≥ (2/3)S_dS with equality exactly at the Nariai merge x=1, via the perfect square 3(x²+1)−2Φ₃(x)=(x−1)²≥0 — a variation-free proof of the entropy floor (global minimum on x>0 is 2/3=|Z₂|/N_fam).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv190_nariai_entropy_bound.py", "sourceSha256": "05d99f3a2d6cce65a1346d34a69b880e292a8ad669bd021a2159aa64226ff550", "linkedClaimIds": [ "HOR.NARIAI.02" ], "sectionIds": [ "section:03c7873577084caa47f8", "section:3d248d64cc5a87ec2248", "section:49282b347d9c681f9051", "section:7d0e50b6a6c30535730d", "section:ab9e7e520130ecc7da7c", "section:cb552d2464f1e864b4f9", "section:cca5b83aae425d5f0e88", "section:de8db1cd8257eab0d607", "section:e60c8c7dc2298081bbd9", "section:edf07fc78f9496f57ed7", "section:fda00a19dcba44348ac3", "section:fe43532db2385fecd956" ], "activeSectionIds": [ "section:3d248d64cc5a87ec2248", "section:ab9e7e520130ecc7da7c", "section:de8db1cd8257eab0d607", "section:e60c8c7dc2298081bbd9", "section:edf07fc78f9496f57ed7", "section:fda00a19dcba44348ac3", "section:fe43532db2385fecd956" ], "evidenceId": "python_verification:verification/v190_nariai_entropy_bound.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v190_nariai_entropy_bound.py", "pubMirrorHash": "05d99f3a2d6cce65a1346d34a69b880e292a8ad669bd021a2159aa64226ff550", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v190_nariai_entropy_bound.py" }, { "id": "v191_universal_branch_line", "filename": "v191_universal_branch_line.py", "path": "verification/v191_universal_branch_line.py", "cluster": "registry", "synopsis": "the universal branch line, HONESTLY typed [C] — an exact affine RELABELING, not a theorem. The map q=7/2+(N_fam²/2)m carries the SdS branch points m=±1/N_fam onto the flavor branch points {2,5}={|Z₂|,g_car} (m=0→7/2). [E] arithmetic, but the map exists for ANY two pairs of points (two intervals are always affinely equivalent), so the slope N_fam²/2 and midpoint 7/2 are DETERMINED by the data, not forced independent predictions; a decoy pair {3,4} admits an equally exact map (negative control). The genuine shared content — the 2/3=|Z₂|/N_fam ramification of the mass↔transport double cover — is already established. Recorded as a [C] alignment, never promoted to [E].", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv191_universal_branch_line.py", "sourceSha256": "c635c3ab72db71ed06291aa855885d3e41967f3143486715c182689d81ceba47", "linkedClaimIds": [ "HOR.BRANCHLINE.01" ], "sectionIds": [ "section:ab9e7e520130ecc7da7c", "section:fda00a19dcba44348ac3", "section:fe43532db2385fecd956" ], "activeSectionIds": [ "section:ab9e7e520130ecc7da7c", "section:fda00a19dcba44348ac3", "section:fe43532db2385fecd956" ], "evidenceId": "python_verification:verification/v191_universal_branch_line.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v191_universal_branch_line.py", "pubMirrorHash": "c635c3ab72db71ed06291aa855885d3e41967f3143486715c182689d81ceba47", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v191_universal_branch_line.py" }, { "id": "v199_seam_state_invariance", "filename": "v199_seam_state_invariance.py", "path": "verification/v199_seam_state_invariance.py", "cluster": "registry", "synopsis": "QGEO.STATE.01 (work package A) — attacking ω∘ρ=ω directly on the raw seam: a further localising reduction, not a closure. [E] setup non-circular (ρ = Coxeter of W(A3)=S4, ρ⁴=1, an automorphism of the raw CAR algebra; both carrier-side, no seam geometry); [E] ground-state reduction ω∘ρ=ω ⟺ [ρ,H₁]=0 (C_Σ=½(1+sgn H₁)); [E] character criterion: [ρ,H₁]=0 ⟺ H₁ block-diagonal in the four μ4-character classes {n=r mod 4} (block-diag commutes, off-character breaks it); principal symbol |k|=diag(|n|) passes automatically. [O] residual: the bounded sub-principal symbol has NO off-character matrix elements — non-circular, sharply typed, holds on H¹ (v177); not a closure.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv199_seam_state_invariance.py", "sourceSha256": "566ea460d3d4198e6437c528f96f921d0b857abb167ad37216e9fee9c38dab0e", "linkedClaimIds": [ "QGEO.STATE.01" ], "sectionIds": [ "section:12b87d2440c45e44a27e", "section:17a730ae6b843f575a43", "section:4d42f8071e36f9952644", "section:6a93c4dd5fe420e1990e", "section:75d473d613aba16a08b8", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:c42d97fdd386889e5412", "section:d90bd5e1e6d8fa41397d", "section:debae20192b75c7a987d", "section:f68163cf343646a0f102" ], "activeSectionIds": [ "section:12b87d2440c45e44a27e", "section:17a730ae6b843f575a43", "section:4d42f8071e36f9952644", "section:75d473d613aba16a08b8", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:c42d97fdd386889e5412", "section:debae20192b75c7a987d", "section:f68163cf343646a0f102" ], "evidenceId": "python_verification:verification/v199_seam_state_invariance.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v199_seam_state_invariance.py", "pubMirrorHash": "566ea460d3d4198e6437c528f96f921d0b857abb167ad37216e9fee9c38dab0e", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v199_seam_state_invariance.py" }, { "id": "v201_seam_subprincipal_marks", "filename": "v201_seam_subprincipal_marks.py", "path": "verification/v201_seam_subprincipal_marks.py", "cluster": "registry", "synopsis": "QGEO.SUBPRIN.01 — the v199 bedrock residual reduced one genuine step further: block-diagonality of the sub-principal symbol is NOT an independent postulate. [E] the seam DtN is Λ=|k|+M_f, M_f = multiplication by a curvature function f(θ) (standard Steklov sub-principal), so ⟨n|M_f|n'⟩=f_{n-n'}. [E] M_f is μ4-character-block-diagonal ⟺ f has Fourier support only on modes ≡0 (mod 4) ⟺ f is Z4-invariant (|k| already commutes, v198). [E] a μ4-MARK SUM f(θ)=Σ_{j=0}^3 g(θ−2πj/4) has f_m=4 g_m[m≡0 mod 4] for ANY profile g — automatically Z4-invariant, so (v195 marks=μ4 orbit) FORCES the sub-principal symbol block-diagonal; negative controls: 3 marks (Z3) and 4 generic marks break it. [O] new residual: ω∘ρ=ω reduces to 'the DtN sub-principal symbol is MARK-LOCAL (seam flat away from the μ4 marks = conformal deck v177)', the narrowest, structurally-definitional form of QGEO.SYM.01.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv201_seam_subprincipal_marks.py", "sourceSha256": "d80dc3f61f38b0499e167b38b9c08a6c09573c2cfcfd6da3341bb1ddeb0dd8db", "linkedClaimIds": [ "QGEO.SUBPRIN.01" ], "sectionIds": [ "section:12b87d2440c45e44a27e", "section:17a730ae6b843f575a43", "section:2525c189f32461c9368a", "section:25e03edabfb4b9161f7f", "section:4a3638ac1b45d771412e", "section:6a93c4dd5fe420e1990e", "section:6cd1a267e72b20619327", "section:8611c18776ca96eaa8ee", "section:888628823bf71f709698", "section:98e28332378f4d77a163", "section:a153934887244824336d", "section:a5cf57be6b809cb6f0d7", "section:a892802bd300a4a050f4", "section:ab9e7e520130ecc7da7c", "section:b93e6ae7b00f32ee1201", "section:d22159cf08f411c39c54", "section:d90bd5e1e6d8fa41397d", "section:ddeb7ff0b27d4750ff23", "section:e415b5fb585454314b5d", "section:f68163cf343646a0f102" ], "activeSectionIds": [ "section:12b87d2440c45e44a27e", "section:17a730ae6b843f575a43", "section:25e03edabfb4b9161f7f", "section:4a3638ac1b45d771412e", "section:8611c18776ca96eaa8ee", "section:888628823bf71f709698", "section:98e28332378f4d77a163", "section:a153934887244824336d", "section:a5cf57be6b809cb6f0d7", "section:a892802bd300a4a050f4", "section:ab9e7e520130ecc7da7c", "section:d22159cf08f411c39c54", "section:ddeb7ff0b27d4750ff23", "section:e415b5fb585454314b5d", "section:f68163cf343646a0f102" ], "evidenceId": "python_verification:verification/v201_seam_subprincipal_marks.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v201_seam_subprincipal_marks.py", "pubMirrorHash": "d80dc3f61f38b0499e167b38b9c08a6c09573c2cfcfd6da3341bb1ddeb0dd8db", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v201_seam_subprincipal_marks.py" }, { "id": "v210_mark_local_dtn", "filename": "v210_mark_local_dtn.py", "path": "verification/v210_mark_local_dtn.py", "cluster": "registry", "synopsis": "a numerical SHARPENING of v201/QGEO.SUBPRIN.01 on REALISTIC Steklov curvature profiles, carried to the quasi-free STATE level (the actual ω∘ρ=ω, not just [ρ,Λ]=0); NOT a closure of QGEO.SYM.01. A real von-Mises curvature bump g(θ) localised at a puncture, summed over the four μ4 marks f(θ)=Σ_{j=0}^3 g(θ−jπ/2), builds the Steklov DtN Λ=|D_θ|+M_f. [E] every off-(mod 4) Fourier coefficient of the REAL f vanishes to <1e-16 (exact 4-fold cancellation), although g has all modes. [N] ‖[ρ,Λ]‖<1e-15. [N] STATE invariance (new vs v201): the quasi-free covariance C=½(1+sgn H₁) satisfies ρCρ†=C to <1e-13 — the STATE, not just the operator, is clock-invariant. [N] negative controls (a single off-centre bump, a Z3 source, 4 generic marks) break BOTH operator and state by O(1); [N] convergence stable for N∈{16,32,64}. [O] verdict: certifies 'mark-local DtN ⟹ ω∘ρ=ω' for concrete profiles AND at the state level; the premise that the physical seam IS mark-local stays [O] — the narrowest definitional form of QGEO.SYM.01, NOT its closure.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv210_mark_local_dtn.py", "sourceSha256": "5a464a7bb8bb23e81d6a91aa7205b3d9000262a0150203fdbc13d0f4696995a3", "linkedClaimIds": [ "QGEO.MARKLOCAL.01" ], "sectionIds": [ "section:2525c189f32461c9368a", "section:6a93c4dd5fe420e1990e", "section:6cd1a267e72b20619327", "section:888628823bf71f709698", "section:a892802bd300a4a050f4", "section:ab9e7e520130ecc7da7c", "section:b93e6ae7b00f32ee1201", "section:bc61b0e372551b770dfb", "section:d90bd5e1e6d8fa41397d", "section:f68163cf343646a0f102" ], "activeSectionIds": [ "section:888628823bf71f709698", "section:a892802bd300a4a050f4", "section:ab9e7e520130ecc7da7c", "section:bc61b0e372551b770dfb", "section:f68163cf343646a0f102" ], "evidenceId": "python_verification:verification/v210_mark_local_dtn.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v210_mark_local_dtn.py", "pubMirrorHash": "5a464a7bb8bb23e81d6a91aa7205b3d9000262a0150203fdbc13d0f4696995a3", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v210_mark_local_dtn.py" }, { "id": "v214_seam_pillowcase", "filename": "v214_seam_pillowcase.py", "path": "verification/v214_seam_pillowcase.py", "cluster": "registry", "synopsis": "the PILLOWCASE reduction of QGEO.SYM.01 (QGEO.PILLOW.01): the two separately-tracked open QGEO residuals — v180/QGEO.ISO.01 (the carrier clock is an order-4 isometry of the seam metric) and v201/QGEO.SUBPRIN.01 (the DtN sub-principal symbol is mark-local, the seam flat away from the μ4 marks) — are ONE statement, 'the seam carries the uniformising flat orbifold (pillowcase) metric', and the order-4 clock is DERIVED from cross-ratio 2 (v168), not assumed. A reduction + unification, NOT a closure. [E] χ_orb(S²(2,2,2,2))=2−4(1−1/2)=0 ⟹ flat (Troyanov cone-metric uniformisation, unique up to scale; Gauss–Bonnet four cone deficits π sum to 4π=2π·χ(S²) ⟹ ∫K_smooth=0, flat away from the marks). [E] NEW LINK: cross-ratio(μ4)=2 (v168) ⟹ j(λ)=256(λ²−λ+1)³/(λ²(λ−1)²) with j(2)=1728 (all six harmonic cross-ratios {2,−1,1/2} give 1728) ⟹ the square modulus, hence the order-4 clock, is a consequence of cross-ratio 2. [E]/[L] j=1728 ⟺ τ=i (square torus) ⟺ CM by ℤ[i] ⟺ Aut=ℤ/4 (only other exceptional modulus j=0 gives ℤ/6; generic ℤ/2). [E] explicit CM (x,y)→(−x,iy) on y²=x³−x has order 4 = z→iz. [E] negative control λ=3 ⟹ j=21952/9 ∉ {0,1728} ⟹ Aut=ℤ/2, no order-4 clock. [I] UNIFICATION: 'seam = uniformising flat pillowcase metric' implies BOTH v201 mark-locality AND v180 QGEO.ISO.01. [O] does NOT close QGEO.SYM.01 — the canonical constant-curvature-metric premise stays open, milder/more canonical than the bare isometry premise; net existence + full-cone RP remain v175's [E].", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv214_seam_pillowcase.py", "sourceSha256": "71169a6c9b78ca1c3f240f0ac92c669e2905db9237658f6e54369ca023f4fd15", "linkedClaimIds": [ "QGEO.PILLOW.01" ], "sectionIds": [ "section:0bcac4df826bc0d57d23", "section:12b87d2440c45e44a27e", "section:2525c189f32461c9368a", "section:2c657950cbbf3e8129b9", "section:307c4c95a7c84b5efc0b", "section:6a93c4dd5fe420e1990e", "section:6cd1a267e72b20619327", "section:701d23928f8e38ea7d4b", "section:7750a727b522e861fdbc", "section:796200681c870006983a", "section:7d0e50b6a6c30535730d", "section:8611c18776ca96eaa8ee", "section:888628823bf71f709698", "section:8e3e6d08d3c102a09298", "section:8e4972dbe899b5debb90", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b63f8484d81bde8026ec", "section:b93e6ae7b00f32ee1201", "section:ca7f6aced60b17ae6709", "section:cca5b83aae425d5f0e88", "section:cdda6bb5746f6a6a897d", "section:d22159cf08f411c39c54", "section:d90bd5e1e6d8fa41397d", "section:f68163cf343646a0f102" ], "activeSectionIds": [ "section:0bcac4df826bc0d57d23", "section:12b87d2440c45e44a27e", "section:2c657950cbbf3e8129b9", "section:7750a727b522e861fdbc", "section:796200681c870006983a", "section:8611c18776ca96eaa8ee", "section:888628823bf71f709698", "section:8e3e6d08d3c102a09298", "section:8e4972dbe899b5debb90", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b63f8484d81bde8026ec", "section:ca7f6aced60b17ae6709", "section:cdda6bb5746f6a6a897d", "section:d22159cf08f411c39c54", "section:f68163cf343646a0f102" ], "evidenceId": "python_verification:verification/v214_seam_pillowcase.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v214_seam_pillowcase.py", "pubMirrorHash": "71169a6c9b78ca1c3f240f0ac92c669e2905db9237658f6e54369ca023f4fd15", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v214_seam_pillowcase.py" }, { "id": "v215_seam_deck_killtest", "filename": "v215_seam_deck_killtest.py", "path": "verification/v215_seam_deck_killtest.py", "cluster": "registry", "synopsis": "the bedrock QGEO.SYM.01 (ω∘ρ=ω) recast as a FALSIFIABLE kill-test (QGEO.KILL.01), not a proof-promise — a foundational symmetry cannot be derived from nothing (v181/v153), and Bisognano–Wichmann would presuppose the covariance it should produce. Non-circular reduction (v198/v199/v201): ω∘ρ=ω ⟺ [ρ,C]=0; the principal symbol |k| commutes exactly, so the residual is the sub-principal M_f with [ρ,M_f]=0 ⟺ f Z4-invariant; measure form = the raw Gaussian bulk form A is μ4-deck-invariant. Four levers (carrier-side [E], seam-side [O]): K1 exactly 4 marks (order-4 clock free orbit μ4 + b1=#marks−1=3=N_fam ⟹ #marks=4=|μ4|); K2 square config (cross-ratio 2 ⟹ j=1728, Aut=ℤ/4; order 4 selects ℤ/4 not the j=0 ℤ/6; generic ⟹ ℤ/2); K3 mod-4 sub-principal support (μ4-mark sum ⟹ f̂(m)=0 for m≢0 mod 4 ⟹ [ρ,M_f]=0); K4 transfer gap (2/3)⁶=64/729 (cusp weights {0,1/3,2/3}). Freeze-bound (freeze_file.csv seam_deck_symmetry). [O] the decisive kill is DEFERRED (QGEO.REALIZE.01): the raw ℙ¹∖μ4 collar DtN must yield 4 square marks without inputting them; carrier-side K1–K4 are green regression guards. A kill-test, not a closure.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv215_seam_deck_killtest.py", "sourceSha256": "f4c6c0d0dc29067102b23b5b9fdfb128eab37e7946222f8efab9a36dcae75808", "linkedClaimIds": [ "QGEO.KILL.01" ], "sectionIds": [ "section:136a1e576865c1424f29", "section:4fee06b8389287124647", "section:640aa248092cb39263eb", "section:6a93c4dd5fe420e1990e", "section:7d0e50b6a6c30535730d", "section:8e4972dbe899b5debb90", "section:8f5691e12b337bb463ce", "section:9f2ef8163653328e6c3e", "section:a036d63765e830eb593f", "section:a153934887244824336d", "section:a9b1f3ad9bb703cf14c6", "section:ab9e7e520130ecc7da7c", "section:b63f8484d81bde8026ec", "section:c6b6da016e7f30bbb7c1", "section:cca5b83aae425d5f0e88", "section:d90bd5e1e6d8fa41397d" ], "activeSectionIds": [ "section:4fee06b8389287124647", "section:640aa248092cb39263eb", "section:8e4972dbe899b5debb90", "section:8f5691e12b337bb463ce", "section:a036d63765e830eb593f", "section:a153934887244824336d", "section:a9b1f3ad9bb703cf14c6", "section:ab9e7e520130ecc7da7c", "section:b63f8484d81bde8026ec", "section:c6b6da016e7f30bbb7c1" ], "evidenceId": "python_verification:verification/v215_seam_deck_killtest.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v215_seam_deck_killtest.py", "pubMirrorHash": "f4c6c0d0dc29067102b23b5b9fdfb128eab37e7946222f8efab9a36dcae75808", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v215_seam_deck_killtest.py" }, { "id": "v216_marks_gauss_bonnet", "filename": "v216_marks_gauss_bonnet.py", "path": "verification/v216_marks_gauss_bonnet.py", "cluster": "registry", "synopsis": "the FOUR seam marks EMERGE from Gauss-Bonnet (QGEO.MARKS.03), executing the K1 lever of the v215 kill-test. [E] mark count = 2χ: Z2 branch points (deficit π) on a flat sphere (χ=2) give n·π = 2π·χ = 4π ⟹ n = 2χ = 4 = |μ4| = e1(a) = N_fam+1 (the same χ=2 as the 8 in c3=1/(8π)). [E] the Euclidean sphere 2-orbifolds (χ_orb=0) are exactly (2,3,6),(2,4,4),(3,3,3),(2,2,2,2). [E] all-order-2 (the |Z2| sheet branch) ⟹ uniquely (2,2,2,2); [E] N_fam=3 (rank H¹=#marks−1) ⟹ uniquely (2,2,2,2), picking the 4-mark square over the 3-mark hexagonal (3,3,3); [E] a free order-4 deck ⟹ uniquely (2,2,2,2) — three independent selectors converge. [O] residual: the square modulus (cross-ratio 2 ⟹ j=1728, v214) needs the one order-4 carrier input. The mark COUNT + EQUALITY are now derived; does NOT close QGEO.REALIZE.01.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv216_marks_gauss_bonnet.py", "sourceSha256": "a1b618c30d42a71d5636787c9744251018103f3f2cdecd310a072987f77fab3f", "linkedClaimIds": [ "QGEO.MARKS.03" ], "sectionIds": [ "section:00c96659d1c56ecb746e", "section:03b9058ca08ba4829ac7", "section:0739148b5a5974d0d662", "section:09b49009253acb5a0dfb", "section:1890ff3254bb8da69e68", "section:1fa633590a33e985ed41", "section:2525c189f32461c9368a", "section:2b8d2aba4baeb7a0c36b", "section:2c657950cbbf3e8129b9", "section:303925994b6f141b3a0e", "section:307c4c95a7c84b5efc0b", "section:314c7c0b2567b3598a9c", "section:3721516595f24fd66f4c", "section:3cc790136e8b9bd3c188", "section:3d3092d4174b4ba2e0ec", "section:4a3638ac1b45d771412e", "section:4fee06b8389287124647", "section:584e87a9c163ac38f92f", "section:5ff3f529ae7be4541192", "section:62801f711a0d267461ac", "section:640aa248092cb39263eb", "section:6a757c5701557192653a", "section:6a93c4dd5fe420e1990e", "section:6cd1a267e72b20619327", "section:701d23928f8e38ea7d4b", "section:708f3d321d2dd13c9cb9", "section:7144b70a605254dfecbc", "section:749d598aa0815d32790b", "section:7750a727b522e861fdbc", "section:796200681c870006983a", "section:7a7de20f53ed3e69fb6f", "section:7d0e50b6a6c30535730d", "section:7ef5c3edcea8d045b5b2", "section:8182ecd6055b0d0d488c", "section:8611c18776ca96eaa8ee", "section:8872501633bb702220cd", "section:888628823bf71f709698", "section:8e4972dbe899b5debb90", "section:93b8868beb643874af75", "section:9800e2e20cb3dc2e280a", "section:a036d63765e830eb593f", "section:a153934887244824336d", "section:a3b94e09ceb6d6dbdae4", "section:a5034e3be2279bec9f75", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b63f8484d81bde8026ec", "section:b93e6ae7b00f32ee1201", "section:c31c8db87fec4e08752e", "section:c852f8ae0a03109ca8ad", "section:ca7a45590bd2289527ff", "section:cca5b83aae425d5f0e88", "section:cdda6bb5746f6a6a897d", "section:d90bd5e1e6d8fa41397d", "section:eb00caf29086b02d5bf5", "section:eb0bd97fda8c0fedefad", "section:ed458665aa45a0bcd44b", "section:f1cb1505fb0d067d8745", "section:f22c82858ff073c133d4", "section:f3f0a4f56db397726de9", "section:f5274c8105ff62e99dcd", "section:f68163cf343646a0f102", "section:f97072f658fe6bcec8d8", "section:f9ed8e942e9df8db94c7", "section:fb4cf64c8cbaeb3f6d74", "section:fc7f5b07a661660c0d79", "section:fd15b9954fc0175fba1b" ], "activeSectionIds": [ "section:00c96659d1c56ecb746e", "section:2c657950cbbf3e8129b9", "section:314c7c0b2567b3598a9c", "section:3721516595f24fd66f4c", "section:4a3638ac1b45d771412e", "section:4fee06b8389287124647", "section:584e87a9c163ac38f92f", "section:5ff3f529ae7be4541192", "section:640aa248092cb39263eb", "section:6a757c5701557192653a", "section:708f3d321d2dd13c9cb9", "section:7144b70a605254dfecbc", "section:749d598aa0815d32790b", "section:7750a727b522e861fdbc", "section:796200681c870006983a", "section:7a7de20f53ed3e69fb6f", "section:7ef5c3edcea8d045b5b2", "section:8611c18776ca96eaa8ee", "section:888628823bf71f709698", "section:8e4972dbe899b5debb90", "section:9800e2e20cb3dc2e280a", "section:a036d63765e830eb593f", "section:a153934887244824336d", "section:a5034e3be2279bec9f75", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b63f8484d81bde8026ec", "section:c31c8db87fec4e08752e", "section:c852f8ae0a03109ca8ad", "section:cdda6bb5746f6a6a897d", "section:ed458665aa45a0bcd44b", "section:f1cb1505fb0d067d8745", "section:f22c82858ff073c133d4", "section:f3f0a4f56db397726de9", "section:f5274c8105ff62e99dcd", "section:f68163cf343646a0f102", "section:f97072f658fe6bcec8d8", "section:f9ed8e942e9df8db94c7", "section:fb4cf64c8cbaeb3f6d74", "section:fc7f5b07a661660c0d79" ], "evidenceId": "python_verification:verification/v216_marks_gauss_bonnet.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v216_marks_gauss_bonnet.py", "pubMirrorHash": "a1b618c30d42a71d5636787c9744251018103f3f2cdecd310a072987f77fab3f", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v216_marks_gauss_bonnet.py" }, { "id": "v217_marks_emergence_scan", "filename": "v217_marks_emergence_scan.py", "path": "verification/v217_marks_emergence_scan.py", "cluster": "registry", "synopsis": "the NUMERICAL emergence scan (QGEO.EMERGE.01, sibling of v216 as v210 is to v201): with the number of marks n AND their positions FREE, the 4-equally-spaced (square) config is the joint minimiser of {clock-invariance + 3-family cohomology + transfer gap (2/3)⁶} on the actual seam DtN/state. [N] n=4 equally-spaced ⟹ ‖ρ4 C ρ4†−C‖~1e-14 (clock-invariant state); [N] family count selects n=4 (scan n∈{2..8}, only n−1=3=N_fam; n=3→2 families = hexagonal, excluded; n=5→4); [N] gap: μ4-equivariant ⟹ diagonal in the cusp basis (deck-average off-diagonal ~1e-16), cusp weights {0,1/3,2/3} ⟹ transfer (1−w)⁶={1,(2/3)⁶,(1/3)⁶}, gap (2/3)⁶=64/729; [N] position scan: the square minimises the defect (square ~1e-14 vs off-square ~0.4); [N] negative controls n=3,5,6. [O] confirms the emergence on the real DtN (number scanned, positions free); selector = the 3-family/gap structure (carrier input); executes K1 numerically, does NOT close QGEO.REALIZE.01. Python-only.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv217_marks_emergence_scan.py", "sourceSha256": "3a92a84d660c5c15ebf66464e2528503b84255923602551ea4a591ad19962de5", "linkedClaimIds": [ "QGEO.EMERGE.01" ], "sectionIds": [ "section:03b9058ca08ba4829ac7", "section:640aa248092cb39263eb", "section:6a93c4dd5fe420e1990e", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d", "section:f97072f658fe6bcec8d8", "section:fd15b9954fc0175fba1b" ], "activeSectionIds": [ "section:640aa248092cb39263eb", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:f97072f658fe6bcec8d8" ], "evidenceId": "python_verification:verification/v217_marks_emergence_scan.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v217_marks_emergence_scan.py", "pubMirrorHash": "3a92a84d660c5c15ebf66464e2528503b84255923602551ea4a591ad19962de5", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v217_marks_emergence_scan.py" }, { "id": "v211_axion_spine_angle", "filename": "v211_axion_spine_angle.py", "path": "verification/v211_axion_spine_angle.py", "cluster": "frontier", "synopsis": "axion DM, the spine-angle branch θ_i = π N_fam/g_car = 3π/5 (108°): an ALTERNATIVE, more robust misalignment angle than the determinant-line hilltop θ_i≈170° (v185, which over-produces Ω_a h²≈0.66). [I] rational motive θ_i=π N_fam/g_car=3π/5=108° exactly (spine quotient 3/5, no fit); [N] the v185 finite-T solver (θ=1→0.03) reaches Ω_DM at θ≈106°, so 108° is essentially on target (harmonic 0.03θ²=0.107); [C] ROBUST: 108° is 62° below the 170° hilltop, in the mild-anharmonic regime — not exponentially sensitive, a far more robust landing than v185; [O] HONEST: an alternative ansatz to θ_i=π(1−φ_seam)≈170° (mutually exclusive, neither forced — the full solver decides, DM.AXION.SPINE.01); [X] kill test: full finite-T solve, Ω_a h² outside ~[0.08,0.16] demotes the branch. A [C] kill-test branch, NOT a closure.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv211_axion_spine_angle.py", "sourceSha256": "eb14ea64a938bf6f2c901275d35226988951eed075d62663dfe9cb6763d0ce9b", "linkedClaimIds": [ "DM.AXION.SPINE.01" ], "sectionIds": [ "section:3af896f0e07d57463462", "section:4376c1a8c4e207cfb1f6", "section:64a9e573649942dd32e9", "section:989e899750d5a86edf1e", "section:ab9e7e520130ecc7da7c", "section:cb09371605fac20095ba", "section:fbc55d19f88e095d54eb" ], "activeSectionIds": [ "section:3af896f0e07d57463462", "section:4376c1a8c4e207cfb1f6", "section:64a9e573649942dd32e9", "section:989e899750d5a86edf1e", "section:ab9e7e520130ecc7da7c", "section:cb09371605fac20095ba", "section:fbc55d19f88e095d54eb" ], "evidenceId": "python_verification:verification/v211_axion_spine_angle.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v211_axion_spine_angle.py", "pubMirrorHash": "eb14ea64a938bf6f2c901275d35226988951eed075d62663dfe9cb6763d0ce9b", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v211_axion_spine_angle.py" }, { "id": "v212_leptogenesis_decuple", "filename": "v212_leptogenesis_decuple.py", "path": "verification/v212_leptogenesis_decuple.py", "cluster": "frontier", "synopsis": "leptogenesis, the scalaron-decuple branch: both Boltzmann inputs share the decuple A_Λ=10=|E(K₅)| — M₁=M_scal φ₀²/A_Λ≈8.65×10⁹ GeV and m̃₁=m₃/A_Λ≈5 meV. A cleaner [C] route than v184's M₁=M_R φ₀⁴ (which only relocated the free input to the un-pinned seesaw M_R). [I] shared decuple A_Λ=10; [N] M₁=M_scal φ₀²/A_Λ=8.65×10⁹ GeV (M_scal=c₃^{7/2} M̄≈3.06×10¹³, φ₀≈0.053172) inside the thermal window [3×10⁹,3×10¹⁰] (v169); [N] m̃₁=m₃/A_Λ≈5 meV (m₃≈0.05 eV), K≈4.6 strong washout; [N] Davidson–Ibarra ε₁≈8.5×10⁻⁷, η_B≈0.96×10⁻²·ε₁·κ_f≈1.2×10⁻⁹ brackets observed 6.1×10⁻¹⁰; [C] HONEST: M₁ uses only {M_scal,φ₀,A_Λ} (no hidden seesaw scale), but the coupling mechanism is posited not derived — η_B stays [C]; [X] kill test: a precise Boltzmann/RGE solve outside the band falls the route, not the theory (Route A/Ω_b independent, FR.ETAB.01).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv212_leptogenesis_decuple.py", "sourceSha256": "d9e03b2839a38b6cdf436ac66ed81dbe30f13573ec88952e156ab100b13e1d5e", "linkedClaimIds": [ "FR.ETAB.04" ], "sectionIds": [ "section:2692631f31aef19d9368", "section:4376c1a8c4e207cfb1f6", "section:9a49b0a6b8928419303b", "section:ab9e7e520130ecc7da7c", "section:cb09371605fac20095ba", "section:d0c4725137a9427c8a0b", "section:fbc55d19f88e095d54eb" ], "activeSectionIds": [ "section:2692631f31aef19d9368", "section:4376c1a8c4e207cfb1f6", "section:9a49b0a6b8928419303b", "section:ab9e7e520130ecc7da7c", "section:cb09371605fac20095ba", "section:d0c4725137a9427c8a0b", "section:fbc55d19f88e095d54eb" ], "evidenceId": "python_verification:verification/v212_leptogenesis_decuple.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v212_leptogenesis_decuple.py", "pubMirrorHash": "d9e03b2839a38b6cdf436ac66ed81dbe30f13573ec88952e156ab100b13e1d5e", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v212_leptogenesis_decuple.py" }, { "id": "v213_ftransfer_functor", "filename": "v213_ftransfer_functor.py", "path": "verification/v213_ftransfer_functor.py", "cluster": "frontier", "synopsis": "the F_transfer FUNCTOR CONTRACT (CONTRACT.F.01): the four frontier transfers are ONE typed functor F_transfer = F_observable∘F_threshold∘F_RG with four structural axioms, each instance a discrete compiler kernel [E/I] composed with an external continuous solver [C/O]; consolidates v183 (F_pole), v212 (F_Boltzmann), v211 (F_relic), v164/FR.MPME (F_QCD), the structural complement of the v187 typing guard. [I] axiom 1 μ4-deck equivariance (Koide multiplier λ₂=(2/3)⁶=64/729 IS the μ4-deck transfer eigenvalue, v82/v54); [I] axiom 2 Plücker preservation (Koide 53=aᵀ(R+Q)1, F-corner Pl(F)=(1,22,30); quark ratio ‖Pl(K)‖₁=11); [I] axiom 3 positivity/stochasticity (spec T={1,(2/3)⁶,(1/3)⁶} positive, washout κ_f∈(0,1)); [I] axiom 4 external modules explicit (pole transfer, DNN Boltzmann, finite-T χ(T), lattice C_N; b₃=−7 a carrier output, |b₃|=Ω_adm−10b₁=7); [C] verdict: a typed functor, NOT a bag of open topics; discrete kernels [E], external solvers [C]; an architectural consolidation guarded by v187, NOT a closure.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv213_ftransfer_functor.py", "sourceSha256": "278d24d76f72d0c28495556b2db4cfcfe4d35bbf73a7216af88b57b35325fa02", "linkedClaimIds": [ "CONTRACT.F.01" ], "sectionIds": [ "section:37d6ecba160419b2f272", "section:568b5e9acdb7b04367d3", "section:81a6dc002dc46cf7b6c5", "section:ab9e7e520130ecc7da7c", "section:ac6f5be914309816a43d", "section:d59ca752d5e1a51b75b5", "section:f0ac30137703825661c6", "section:fbc55d19f88e095d54eb", "section:fdf63a1d99769ab37ccb" ], "activeSectionIds": [ "section:37d6ecba160419b2f272", "section:81a6dc002dc46cf7b6c5", "section:ab9e7e520130ecc7da7c", "section:ac6f5be914309816a43d", "section:d59ca752d5e1a51b75b5", "section:fbc55d19f88e095d54eb", "section:fdf63a1d99769ab37ccb" ], "evidenceId": "python_verification:verification/v213_ftransfer_functor.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v213_ftransfer_functor.py", "pubMirrorHash": "278d24d76f72d0c28495556b2db4cfcfe4d35bbf73a7216af88b57b35325fa02", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v213_ftransfer_functor.py" }, { "id": "v200_seam_variational_scan", "filename": "v200_seam_variational_scan.py", "path": "verification/v200_seam_variational_scan.py", "cluster": "registry", "synopsis": "QGEO.VARI.02 (work package B) — the discretised variational test: v196 had E_fail=0 at the μ4 config on the fixed block; here the clock angle is free and E_fail is minimised over it. [N] scanning E_fail(θ)=‖ρ(θ)⁴−1‖²+faithfulness over θ∈(0,π) gives the unique minimum at θ=π/2 (E_fail=0: order-4 AND three distinct characters i,−1,−i = the (1,2,3) grading); decoys (0, π, π/3, 2π/3) all lose. So argmin E_fail = the μ4 normal form. [E] consistent with v196/v199/v198. [O] a numerical sign on the finite H¹ grading, not the full operator-valued minimisation (the v199 residual).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv200_seam_variational_scan.py", "sourceSha256": "231896f53ae03ef7052af133aad701dab2457f316a8545ee56b05279eb1dc6b4", "linkedClaimIds": [ "QGEO.VARI.02" ], "sectionIds": [ "section:4d42f8071e36f9952644", "section:6a93c4dd5fe420e1990e", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d", "section:f68163cf343646a0f102" ], "activeSectionIds": [ "section:4d42f8071e36f9952644", "section:ab9e7e520130ecc7da7c", "section:f68163cf343646a0f102" ], "evidenceId": "python_verification:verification/v200_seam_variational_scan.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v200_seam_variational_scan.py", "pubMirrorHash": "231896f53ae03ef7052af133aad701dab2457f316a8545ee56b05279eb1dc6b4", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v200_seam_variational_scan.py" }, { "id": "v198_modular_commutator_reduction", "filename": "v198_modular_commutator_reduction.py", "path": "verification/v198_modular_commutator_reduction.py", "cluster": "registry", "synopsis": "QGEO.MODULAR.01 — cracking the bedrock to a state-invariance. The v194 residual ([ρ,Λ_Σ]=0 on full L², framed as Bisognano–Wichmann with a circularity worry) is (a) made EXACT at the principal-symbol level and (b) reduced via Tomita–Takesaki to a clean state-invariance. [E] the DtN principal symbol |k|=√(−d²) is diag(|n|) and the clock ρ:z↦iz is diag(i^n) in the Fourier basis — both diagonal ⇒ [ρ,|k|]=0 exactly on ALL of L²; [E] Tomita–Takesaki: [ρ,Λ_Σ]=0 follows from ω∘ρ=ω (modular Δ is intrinsic to (M,Ω); a state-preserving symmetry commutes with it), needing NO conformal covariance — removes the BW circularity; [E] the finite H¹ block is already μ4-invariant (v177). [O] residual: the full raw seam state is μ4-invariant (ω∘ρ=ω) ⇐ the Gaussian bulk measure is deck-invariant = operational QGEO.SYM.01. Sharpest non-circular form; not a closure (a foundational symmetry can't be derived from nothing).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv198_modular_commutator_reduction.py", "sourceSha256": "9a5cac328a021e192a3c68af52e8103484d3c1e066570ad33cd5d26c1e8dc113", "linkedClaimIds": [ "QGEO.MODULAR.01" ], "sectionIds": [ "section:12b87d2440c45e44a27e", "section:17a730ae6b843f575a43", "section:2525c189f32461c9368a", "section:25e03edabfb4b9161f7f", "section:4a3638ac1b45d771412e", "section:6a93c4dd5fe420e1990e", "section:6a9749089feb7aba080e", "section:6cd1a267e72b20619327", "section:888628823bf71f709698", "section:9f084ccace7baa00bf8d", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:b56f3a2e55f262711774", "section:b93e6ae7b00f32ee1201", "section:c42d97fdd386889e5412", "section:d22159cf08f411c39c54", "section:d90bd5e1e6d8fa41397d", "section:f68163cf343646a0f102" ], "activeSectionIds": [ "section:12b87d2440c45e44a27e", "section:17a730ae6b843f575a43", "section:25e03edabfb4b9161f7f", "section:4a3638ac1b45d771412e", "section:6a9749089feb7aba080e", "section:888628823bf71f709698", "section:9f084ccace7baa00bf8d", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:b56f3a2e55f262711774", "section:c42d97fdd386889e5412", "section:d22159cf08f411c39c54", "section:f68163cf343646a0f102" ], "evidenceId": "python_verification:verification/v198_modular_commutator_reduction.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v198_modular_commutator_reduction.py", "pubMirrorHash": "9a5cac328a021e192a3c68af52e8103484d3c1e066570ad33cd5d26c1e8dc113", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v198_modular_commutator_reduction.py" }, { "id": "v195_marks_lefschetz_character", "filename": "v195_marks_lefschetz_character.py", "path": "verification/v195_marks_lefschetz_character.py", "cluster": "registry", "synopsis": "QGEO.MARKS.02 — a Lefschetz/character derivation of the four seam marks (review path 2): instead of positing D4 marks, they are FORCED to be a free µ4 orbit. [E]: ρ:z↦iz (order 4) fixes only {0,∞}; H¹=χ1+χ2+χ3 (A3 exponents (1,2,3), v177) has no trivial character ⇒ no puncture at a fixed point; rank H_1=n−1=3 ⇒ n=4 ⇒ exactly one free orbit ⇒ marks = µ4 (cross-ratio 2); Tr(ρ|H¹)=i+i²+i³=−1, L(ρ)=1+1=2=#fixed. [O] residual relocates from 'seam is P¹∖µ4 (geometric)' to 'H¹ carries the A3-exponent rep' — less circular.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv195_marks_lefschetz_character.py", "sourceSha256": "a19022c0872dd2130bd77cb21e93345851a6a8b17ba0a5dd2bbea48138b474be", "linkedClaimIds": [ "QGEO.MARKS.02" ], "sectionIds": [ "section:17a730ae6b843f575a43", "section:22fb298fcb28accfbf39", "section:2525c189f32461c9368a", "section:2c657950cbbf3e8129b9", "section:6a93c4dd5fe420e1990e", "section:6cd1a267e72b20619327", "section:888628823bf71f709698", "section:ab9e7e520130ecc7da7c", "section:b93e6ae7b00f32ee1201", "section:c926c39e5cf2b4b2f828", "section:d90bd5e1e6d8fa41397d", "section:f3f0a4f56db397726de9", "section:f68163cf343646a0f102" ], "activeSectionIds": [ "section:17a730ae6b843f575a43", "section:22fb298fcb28accfbf39", "section:2c657950cbbf3e8129b9", "section:888628823bf71f709698", "section:ab9e7e520130ecc7da7c", "section:c926c39e5cf2b4b2f828", "section:f3f0a4f56db397726de9", "section:f68163cf343646a0f102" ], "evidenceId": "python_verification:verification/v195_marks_lefschetz_character.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v195_marks_lefschetz_character.py", "pubMirrorHash": "a19022c0872dd2130bd77cb21e93345851a6a8b17ba0a5dd2bbea48138b474be", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v195_marks_lefschetz_character.py" }, { "id": "v196_seam_energy_functional", "filename": "v196_seam_energy_functional.py", "path": "verification/v196_seam_energy_functional.py", "cluster": "registry", "synopsis": "QGEO.VARI.01 — the E_fail variational functional (review path 1), a numerically-testable sharpening of the v194/ENERGY.02 target: E_fail = ‖[ρ,Λ_Σ]‖²_HS + ‖ρ⁴−1‖² + ‖ΘρΘ−ρ⁻¹‖², with E_fail=0 ⇔ the QGEO.SYM.01 conditions. [E] on the finite H¹ block (ρ=diag(i,−1,−i), Λ diagonal, Θ=conj) all three vanish ⇒ E_fail=0; [N] a µ4-breaking Λ or non-order-4 ρ gives E_fail>0 (µ4 is a true minimiser); [I] the zero locus = the seam-deck conditions; [O] the full-operator minimisation = the v194 Bisognano–Wichmann residual — a discretisable handle on the open bedrock, a target not a closure.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv196_seam_energy_functional.py", "sourceSha256": "fa447e51ca493cc0eb2f011299c1943042dc8fa8f59112276549e0a3f96a0166", "linkedClaimIds": [ "QGEO.VARI.01" ], "sectionIds": [ "section:22fb298fcb28accfbf39", "section:6a93c4dd5fe420e1990e", "section:9f084ccace7baa00bf8d", "section:ab9e7e520130ecc7da7c", "section:c926c39e5cf2b4b2f828", "section:d90bd5e1e6d8fa41397d" ], "activeSectionIds": [ "section:22fb298fcb28accfbf39", "section:9f084ccace7baa00bf8d", "section:ab9e7e520130ecc7da7c", "section:c926c39e5cf2b4b2f828" ], "evidenceId": "python_verification:verification/v196_seam_energy_functional.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v196_seam_energy_functional.py", "pubMirrorHash": "fa447e51ca493cc0eb2f011299c1943042dc8fa8f59112276549e0a3f96a0166", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v196_seam_energy_functional.py" }, { "id": "v197_rr_carrier_clifford_d5", "filename": "v197_rr_carrier_clifford_d5.py", "path": "verification/v197_rr_carrier_clifford_d5.py", "cluster": "registry", "synopsis": "ARCH.RRCAR.02 — hardening the Riemann–Roch carrier from g_car to D5 itself (review point 7): the 5-dim carrier mode space C_car:=H⁰(P¹,O(µ4)) generates the so(10)=D5 half-spinor by its even Clifford algebra. [I] dim Λ^even(C⁵)=C(5,0)+C(5,2)+C(5,4)=1+10+5=16=2^{g_car−1}=dim S⁺; so(10)=D5 half-spinor 2⁴=16=S⁺=Λ^even(C_car); closes the chain µ4→g_car→D5 from one four-point divisor (cycle side rank H_1=3=N_fam(A3); function side h⁰=5=g_car; Clifford spinor=16=D5 half-spinor=carrier). [C] 'carrier = Clifford spinor of the seam mode space' stays physical (as v189), does not change the over-determined g_car=5.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv197_rr_carrier_clifford_d5.py", "sourceSha256": "84b093de7dd97a91f9ab4f4a18fdca20ebefb4a7e0fa8324ef45983beafcb8c9", "linkedClaimIds": [ "ARCH.RRCAR.02" ], "sectionIds": [ "section:09b49009253acb5a0dfb", "section:3cc790136e8b9bd3c188", "section:46614e805445fc78e7af", "section:584e87a9c163ac38f92f", "section:6a93c4dd5fe420e1990e", "section:a153934887244824336d", "section:a8fda6d5b1c48ce7d8c8", "section:ab9e7e520130ecc7da7c", "section:c926c39e5cf2b4b2f828", "section:ca7f6aced60b17ae6709", "section:d90bd5e1e6d8fa41397d", "section:eb0bd97fda8c0fedefad" ], "activeSectionIds": [ "section:46614e805445fc78e7af", "section:584e87a9c163ac38f92f", "section:a153934887244824336d", "section:a8fda6d5b1c48ce7d8c8", "section:ab9e7e520130ecc7da7c", "section:c926c39e5cf2b4b2f828", "section:ca7f6aced60b17ae6709" ], "evidenceId": "python_verification:verification/v197_rr_carrier_clifford_d5.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v197_rr_carrier_clifford_d5.py", "pubMirrorHash": "84b093de7dd97a91f9ab4f4a18fdca20ebefb4a7e0fa8324ef45983beafcb8c9", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v197_rr_carrier_clifford_d5.py" }, { "id": "v194_raw_seam_dtn_rp", "filename": "v194_raw_seam_dtn_rp.py", "path": "verification/v194_raw_seam_dtn_rp.py", "cluster": "registry", "synopsis": "QGEO.DTN.01 — subclaim 2 of QGEO.ENERGY.02 ('the raw RP-seam DtN is RP-definable') tackled: a REDUCTION, not a closure. (1) [E] finite core: ρ:z↦iz on H¹=⟨w1,w2,w3⟩, wk=z^{k-1}dz/(z⁴−1), acts as ρ*wk=i^k wk (characters i,−1,−i distinct), so [ρ,Λ_Σ]=0 on H¹ (v177). (2) [I] hinge met: the DtN/transfer operator is RP-canonical (Osterwalder–Schrader, v54) on a quasi-free seam state (v155), so Λ_Σ is RP-definable without assuming P¹∖µ4. (3) [O] residual relocates: full-L² commutation ⇔ Bisognano–Wichmann geometric modular flow of the quasi-free seam state (must be intrinsic, else re-circulates). QGEO.SYM.01 reduces from a definitional postulate to intrinsic BW modular covariance — sharper, still [O], not closed to [E].", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv194_raw_seam_dtn_rp.py", "sourceSha256": "a71e9a42aa40a4b6b0f0e671834b55280461a40535cf8ddcb79a743d37f9221b", "linkedClaimIds": [ "QGEO.DTN.01" ], "sectionIds": [ "section:113a50c68f53872c39d4", "section:22fb298fcb28accfbf39", "section:2525c189f32461c9368a", "section:2c657950cbbf3e8129b9", "section:6a93c4dd5fe420e1990e", "section:6cd1a267e72b20619327", "section:888628823bf71f709698", "section:ab9e7e520130ecc7da7c", "section:b56f3a2e55f262711774", "section:b93e6ae7b00f32ee1201", "section:c926c39e5cf2b4b2f828", "section:d90bd5e1e6d8fa41397d", "section:f68163cf343646a0f102" ], "activeSectionIds": [ "section:113a50c68f53872c39d4", "section:22fb298fcb28accfbf39", "section:2c657950cbbf3e8129b9", "section:888628823bf71f709698", "section:ab9e7e520130ecc7da7c", "section:b56f3a2e55f262711774", "section:c926c39e5cf2b4b2f828", "section:f68163cf343646a0f102" ], "evidenceId": "python_verification:verification/v194_raw_seam_dtn_rp.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v194_raw_seam_dtn_rp.py", "pubMirrorHash": "a71e9a42aa40a4b6b0f0e671834b55280461a40535cf8ddcb79a743d37f9221b", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v194_raw_seam_dtn_rp.py" }, { "id": "v193_qgeo_energy_commutator", "filename": "v193_qgeo_energy_commutator.py", "path": "verification/v193_qgeo_energy_commutator.py", "cluster": "registry", "synopsis": "QGEO.ENERGY.02: the energy-COMMUTATOR contract (non-circular sharpening of QGEO.ENERGY.01): [ρ,Λ_Σ]=0 on the rank-8 Calderón polarisation, ρ the carrier clock, Λ_Σ the DtN energy form of the RAW RP seam. Three sub-claims: (1) [E] ρ is carrier-defined (Coxeter of W(A3)=S4, order 4=|µ4|, v117), not imported from the seam; (2) [O] the non-circularity hinge — Λ_Σ must be the RAW RP-seam DtN, not the µ4 normal form (circular if it needs P¹∖µ4 assumed); (3) [E] [ρ,Λ_Σ]=0 forces the (1,2,3) grading on H¹ (QGEO.COHOM.01). Exact [I] rider: the induced EH coefficient k=(ln m)/(12π) reproduces c3/2 iff ln m=q(A3)=3/4 (FAMILY), not q(D5)=5/4 (carrier, off by 5/3) — gravity is family-geometry-induced. Proof target [O]; if proven, QGEO.SYM.01 becomes an energy-rigidity theorem.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv193_qgeo_energy_commutator.py", "sourceSha256": "b75f0ad657e511a14fd3f8da02fe51710240ac4fcab83a6994c2ff0c00d27aba", "linkedClaimIds": [ "QGEO.ENERGY.02" ], "sectionIds": [ "section:22fb298fcb28accfbf39", "section:6151ea351f3cf66e9630", "section:6a93c4dd5fe420e1990e", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d" ], "activeSectionIds": [ "section:22fb298fcb28accfbf39", "section:6151ea351f3cf66e9630", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v193_qgeo_energy_commutator.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v193_qgeo_energy_commutator.py", "pubMirrorHash": "b75f0ad657e511a14fd3f8da02fe51710240ac4fcab83a6994c2ff0c00d27aba", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v193_qgeo_energy_commutator.py" }, { "id": "v192_qgeo_energy_clock", "filename": "v192_qgeo_energy_clock.py", "path": "verification/v192_qgeo_energy_clock.py", "cluster": "registry", "synopsis": "the energy-conserving-clock reformulation, HONESTLY typed: QGEO.ENERGY.01 (ρ*Λ_Σρ=Λ_Σ — the carrier clock preserves the Calderón/DtN energy form) RELOCATES the bedrock QGEO.SYM.01 to a more checkable operator identity, but does NOT eliminate it. The downstream chain (conformality→Möbius→z↦iz→µ₄→QGEO.SYM.01) already exists (v180/v181); the new upstream link (energy invariance ⇒ conformality in 2D) is checkable on the DtN operator Λ=|k|. But 'ρ preserves Λ' is plausibly equivalent to 'ρ is the conformal deck', so it is a sharper restatement, not a theorem, unless ρ is independently defined and the invariance independently proven (open). Bedrock stays [O].", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv192_qgeo_energy_clock.py", "sourceSha256": "d9eb0a1fa4811dc540b9ab2513d7a9c9ae4f1d1276c615cf28771230e78e34b0", "linkedClaimIds": [ "QGEO.ENERGY.01" ], "sectionIds": [ "section:22fb298fcb28accfbf39", "section:6a93c4dd5fe420e1990e", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d", "section:fe43532db2385fecd956" ], "activeSectionIds": [ "section:22fb298fcb28accfbf39", "section:ab9e7e520130ecc7da7c", "section:fe43532db2385fecd956" ], "evidenceId": "python_verification:verification/v192_qgeo_energy_clock.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v192_qgeo_energy_clock.py", "pubMirrorHash": "d9eb0a1fa4811dc540b9ab2513d7a9c9ae4f1d1276c615cf28771230e78e34b0", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v192_qgeo_energy_clock.py" }, { "id": "v188_frontier_wording_guard", "filename": "v188_frontier_wording_guard.py", "path": "verification/v188_frontier_wording_guard.py", "cluster": "registry", "synopsis": "the frontier-wording guard (a prose sentinel, no new physics): v187 protects the ledger typing, this guard protects the prose. It forbids stale sentences whose semantics an earlier round superseded — 'leptogenesis interface (mE)' (v184 retyped Route B to [C]), 'closed branch also fixes the leptogenesis inputs' (M_R is the seesaw scale, not a compiler power), 'relic scale f_a,m_a open' (v185: the scales define the branch, the open item is the hilltop-sensitive relic abundance), 'computed Q=0.664 … near, not exact' (v183 gave 53/54 an exact operator origin), 'Suite now 187 modules' (the count is 187, highest ID v188; v186 skipped). Scans the 10 active .tex documents; passes when none of the stale phrasings appear, so a frozen Zenodo release can never re-introduce half-true wording.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv188_frontier_wording_guard.py", "sourceSha256": "89c8e3a589f551241915927d0f535c2039cf4827b9f87c6786fbb8b3edc033e2", "linkedClaimIds": [ "AUDIT.WORDING.01" ], "sectionIds": [ "section:1baa0cb6fdd6a6b16124", "section:37d6ecba160419b2f272", "section:6151ea351f3cf66e9630", "section:ab9e7e520130ecc7da7c", "section:b559ae6d59524fc410e4", "section:fbc55d19f88e095d54eb", "section:fc9d294f005b7ca60e26" ], "activeSectionIds": [ "section:1baa0cb6fdd6a6b16124", "section:37d6ecba160419b2f272", "section:6151ea351f3cf66e9630", "section:ab9e7e520130ecc7da7c", "section:b559ae6d59524fc410e4", "section:fbc55d19f88e095d54eb", "section:fc9d294f005b7ca60e26" ], "evidenceId": "python_verification:verification/v188_frontier_wording_guard.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v188_frontier_wording_guard.py", "pubMirrorHash": "89c8e3a589f551241915927d0f535c2039cf4827b9f87c6786fbb8b3edc033e2", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v188_frontier_wording_guard.py" }, { "id": "v187_ftransfer_laws", "filename": "v187_ftransfer_laws.py", "path": "verification/v187_ftransfer_laws.py", "cluster": "registry", "synopsis": "the F_transfer discipline guard (CI-style firewall, the machine-readable form of the Frontier rule): the four continuous-transfer frontier observables — Koide (FR.KOIDE.*), η_B (FR.ETAB.*), axion (FR.DM.*), m_p/m_e+Λ_QCD (FR.MPME.*/QCD.LAMBDA.*) — must NEVER be typed as primitive [E]/[N] compiler predictions; each must carry a [C]/[A]/[O] marker. Reads the ledger and enforces it (all active frontier rows pass; exact algebraic sub-parts like Koide 53/54 v183 or b3=−7 v159 may be [I]/[E], the physical prediction never is). Records the four interfaces F_pole/F_Boltzmann/F_relic/F_QCD and that the raster rule + frozen registry + null model bind — preventing any future edit from quietly promoting a pretty frontier number to a closed compiler output.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv187_ftransfer_laws.py", "sourceSha256": "6e514f99af6f926acb5180c13b26db97d47ff0bd8b130f22186a370a73248720", "linkedClaimIds": [ "FR.TRANSFER.01" ], "sectionIds": [ "section:0534241ef38a39dcc3cc", "section:0968f1b6845750a87eeb", "section:1baa0cb6fdd6a6b16124", "section:2525c189f32461c9368a", "section:2b8d2aba4baeb7a0c36b", "section:303925994b6f141b3a0e", "section:37d6ecba160419b2f272", "section:4376c1a8c4e207cfb1f6", "section:568b5e9acdb7b04367d3", "section:5b0172590490b241cb77", "section:6cd1a267e72b20619327", "section:75d473d613aba16a08b8", "section:7ee581db787f8ddbcb4a", "section:7f2e391c59e00a9e6acb", "section:888628823bf71f709698", "section:8ac4310a6a4cf6c449f1", "section:8b1a1c6a205860e21edc", "section:8d1e955857da6655fadd", "section:9a49b0a6b8928419303b", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:b37031f13445096fcccf", "section:b559ae6d59524fc410e4", "section:b93e6ae7b00f32ee1201", "section:c519f45910c30ff3c0ae", "section:cb09371605fac20095ba", "section:d59ca752d5e1a51b75b5", "section:e7cdfe28203ecac9114d", "section:eb0ad9c39f3387e3dcf3", "section:f0ac30137703825661c6", "section:f3b90b032a2851e13827", "section:fb4cf64c8cbaeb3f6d74", "section:fbc55d19f88e095d54eb", "section:fdf63a1d99769ab37ccb" ], "activeSectionIds": [ "section:0534241ef38a39dcc3cc", "section:0968f1b6845750a87eeb", "section:1baa0cb6fdd6a6b16124", "section:37d6ecba160419b2f272", "section:4376c1a8c4e207cfb1f6", "section:5b0172590490b241cb77", "section:75d473d613aba16a08b8", "section:7f2e391c59e00a9e6acb", "section:888628823bf71f709698", "section:8ac4310a6a4cf6c449f1", "section:8b1a1c6a205860e21edc", "section:8d1e955857da6655fadd", "section:9a49b0a6b8928419303b", "section:ab9e7e520130ecc7da7c", "section:b37031f13445096fcccf", "section:b559ae6d59524fc410e4", "section:cb09371605fac20095ba", "section:d59ca752d5e1a51b75b5", "section:e7cdfe28203ecac9114d", "section:eb0ad9c39f3387e3dcf3", "section:f3b90b032a2851e13827", "section:fb4cf64c8cbaeb3f6d74", "section:fbc55d19f88e095d54eb", "section:fdf63a1d99769ab37ccb" ], "evidenceId": "python_verification:verification/v187_ftransfer_laws.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v187_ftransfer_laws.py", "pubMirrorHash": "6e514f99af6f926acb5180c13b26db97d47ff0bd8b130f22186a370a73248720", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v187_ftransfer_laws.py" }, { "id": "v183_koide_f_corner_transfer", "filename": "v183_koide_f_corner_transfer.py", "path": "verification/v183_koide_f_corner_transfer.py", "cluster": "registry", "synopsis": "the Koide source→pole factor 53/54 has an OPERATOR origin (external-review proposal, validated): u_pole/u_source = aᵀ(R+Q)𝟙 / (2·𝟙ᵀRa) = 53/(2·27) = 53/54. (1) 𝟙ᵀRa=27 is the E6×A2 cubic family block (248 = dim E6 78 + det R 8 + 2·27·N_fam); (2) F=R+Q is the MISSING Sheet-Diamond corner M(1,1) with det B_F=52=dim F4 (v80) and anchor response aᵀ(R+Q)𝟙=53=52+1; (3) 53/54 = 1−1/(2N_fam³) exactly (54=2·27); (4) negative control: only F gives 53 (R/Q/K/L give 32/21/35/56). Upgrades FR.KOIDE.03 from a bare guess to an operator identity; [I] factor exact, [C] the leptonic source→pole reading the F corner stays an F_transfer conjecture.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv183_koide_f_corner_transfer.py", "sourceSha256": "d739384d36081dc2272680d0683433c4047f7a824437a1c275b594dd6d2d7c89", "linkedClaimIds": [ "FR.KOIDE.07" ], "sectionIds": [ "section:1fc598d7241c419069ab", "section:2678ed3ba0ed508e2d8e", "section:2692631f31aef19d9368", "section:3d2a5b53f3345969fcbc", "section:4376c1a8c4e207cfb1f6", "section:51e91159532ef7479ff8", "section:568b5e9acdb7b04367d3", "section:6f0af99769531bda7e90", "section:7e48439cd9f5f65a12df", "section:848c49f799255f4cda92", "section:a5afdfe2d50d9975d56b", "section:ab9e7e520130ecc7da7c", "section:b559ae6d59524fc410e4", "section:c1ba016bb9366edd1984", "section:c4cf080b9ae6f25f7a71", "section:eb0ad9c39f3387e3dcf3", "section:f0ac30137703825661c6", "section:fdf63a1d99769ab37ccb" ], "activeSectionIds": [ "section:2692631f31aef19d9368", "section:3d2a5b53f3345969fcbc", "section:4376c1a8c4e207cfb1f6", "section:51e91159532ef7479ff8", "section:7e48439cd9f5f65a12df", "section:a5afdfe2d50d9975d56b", "section:ab9e7e520130ecc7da7c", "section:b559ae6d59524fc410e4", "section:c1ba016bb9366edd1984", "section:eb0ad9c39f3387e3dcf3", "section:fdf63a1d99769ab37ccb" ], "evidenceId": "python_verification:verification/v183_koide_f_corner_transfer.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v183_koide_f_corner_transfer.py", "pubMirrorHash": "d739384d36081dc2272680d0683433c4047f7a824437a1c275b594dd6d2d7c89", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v183_koide_f_corner_transfer.py" }, { "id": "v182_reviewer_residual_map", "filename": "v182_reviewer_residual_map.py", "path": "verification/v182_reviewer_residual_map.py", "cluster": "registry", "synopsis": "the four external-review concerns reduce to the two already-named residuals + one data-only item: A (mapping 2D→4D, ''why read the masses as Plücker 11?''), B (UV-gravity abstractness), C (grammar-tuning/meta-look-elsewhere), D (Koide Möbius flow). A [I]/[C]: 11=Σ_{k≤2}C(4,k)=dim S⁺−g_car=16−5 (QBL count, v174), the 2D→4D step is the holographic reduction ⇒ A = QGEO.SYM.01 + F_transfer. B [I]: 'gravity = geometric boundary readout' IS QGEO.SYM.01. C [N]/[C]: frozen (v84) + minimal + over-determined (anchor a=(1,1,2) in ≥6 independent structures) ⇒ look-elsewhere-resistant, residual falls only to data (JUNO/CMB-S4). D [I]/[C]: Möbius forced by Aut(ℙ¹)=PSL(2,ℂ) on the deck, t~2.84 locates the point, the missing RG generator IS F_transfer ⇒ D = QGEO.SYM.01 + F_transfer. NET: three reduce, one waits for data — a unification of the concern structure, NOT a closure (premises stay [O]/[C]).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv182_reviewer_residual_map.py", "sourceSha256": "7edc68e802cd17c73abafb5d98eb05bc1fbf24c430e9b8ee2254b3944bb9b87c", "linkedClaimIds": [ "REVIEW.MAP.01" ], "sectionIds": [ "section:05aaf35318c9e1bb8204", "section:7a7de20f53ed3e69fb6f", "section:ab9e7e520130ecc7da7c" ], "activeSectionIds": [ "section:05aaf35318c9e1bb8204", "section:7a7de20f53ed3e69fb6f", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v182_reviewer_residual_map.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v182_reviewer_residual_map.py", "pubMirrorHash": "7edc68e802cd17c73abafb5d98eb05bc1fbf24c430e9b8ee2254b3944bb9b87c", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v182_reviewer_residual_map.py" }, { "id": "v181_clock_is_conformal_symmetry", "filename": "v181_clock_is_conformal_symmetry.py", "path": "verification/v181_clock_is_conformal_symmetry.py", "cluster": "registry", "synopsis": "the FINAL honest reduction + the explicit identification of BEDROCK. The isometry premise QGEO.ISO.01 (v180) is weakened one more genuine step — to a CONFORMAL-symmetry premise QGEO.SYM.01 — via equivariant uniformisation (Nielsen realisation, finite cyclic on genus-0): a CONFORMAL automorphism (strictly weaker than an isometry — every isometry is conformal, conformal allows any positive scale) already suffices to put the order-4 clock in the form z↦iz. The clock is the Coxeter element of W(A3)=S4 (v117), order h(A3)=4=|μ4| = the μ4 deck, and a deck transformation preserves the pulled-back conformal structure by definition. So below QGEO.SYM.01 the residual is DEFINITIONAL, not a missing theorem: 'the seam's conformal structure IS the μ4-deck structure of the carrier clock' (the carrier μ4 glue is the conformal monodromy of the seam) — a physical/definitional identification tying P2 to the seam's conformal geometry, NOT reducible further without relabeling. The chain REALIZE(v175)→theorem(v176)→MARKS+KERNEL(v177)→finite cores(v178)→CONF.01(v179)→ISO.01(v180)→SYM.01(v181) has reached bedrock; we stop here honestly.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv181_clock_is_conformal_symmetry.py", "sourceSha256": "5b383a435ab8284370dda6a72406b9441a0e4facaeb1ac84cb0e14d19dd00298", "linkedClaimIds": [ "QGEO.SYM.01" ], "sectionIds": [ "section:05aaf35318c9e1bb8204", "section:1890ff3254bb8da69e68", "section:22fb298fcb28accfbf39", "section:2525c189f32461c9368a", "section:2585b5d786c3bdb7ddb7", "section:4ff2bf714d7cbf97df82", "section:56260a726c20b0e2fff7", "section:6a93c4dd5fe420e1990e", "section:6cd1a267e72b20619327", "section:888628823bf71f709698", "section:ab9e7e520130ecc7da7c", "section:b93e6ae7b00f32ee1201", "section:d90bd5e1e6d8fa41397d", "section:e2c33aad84858bc51b9d" ], "activeSectionIds": [ "section:05aaf35318c9e1bb8204", "section:22fb298fcb28accfbf39", "section:2585b5d786c3bdb7ddb7", "section:4ff2bf714d7cbf97df82", "section:56260a726c20b0e2fff7", "section:888628823bf71f709698", "section:ab9e7e520130ecc7da7c", "section:e2c33aad84858bc51b9d" ], "evidenceId": "python_verification:verification/v181_clock_is_conformal_symmetry.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v181_clock_is_conformal_symmetry.py", "pubMirrorHash": "5b383a435ab8284370dda6a72406b9441a0e4facaeb1ac84cb0e14d19dd00298", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v181_clock_is_conformal_symmetry.py" }, { "id": "v180_clock_is_mobius", "filename": "v180_clock_is_mobius.py", "path": "verification/v180_clock_is_mobius.py", "cluster": "registry", "synopsis": "cracking QGEO.CONF.01 one level further — the conformal-realisation premise is REPLACED, via three classical theorems, by a strictly MILDER, non-circular premise QGEO.ISO.01: 'the carrier clock is an order-4 orientation-preserving ISOMETRY of the RP seam metric'. (1) Uniformisation (Poincaré-Koebe): a genus-0 Riemann surface is conformally ℙ¹, so the genus-0 seam double (P1, v179) IS ℙ¹ — the target is produced, not assumed; (2) Kerékjártó (1919; Constantin-Kolev 2003): a finite-order orientation-preserving homeo of S² is conjugate to a rotation, so the order-4 clock (h(A3)=4) is topologically z↦iz; (3) isometry⇒conformal⇒Möbius: an orientation-preserving isometry of a Riemannian surface is holomorphic, Aut(ℙ¹)=PSL(2,ℂ); (4) order-4 Möbius = z↦iz (verified: projective order 4, fixed {0,∞}, multiplier i, free orbit μ4). So QGEO.CONF.01 is IMPLIED by the milder isometry premise; the new residual QGEO.ISO.01 (the seam transport is a metric-compatible holonomy preserving the RP inner product) does not name ℙ¹/μ4 and is milder, but its surface realisation from the raw seam stays OPEN.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv180_clock_is_mobius.py", "sourceSha256": "f5a6fb459906b0df6bbc640f63766cea5ebf9df6cffb4c339e5c18d9bd12100b", "linkedClaimIds": [ "QGEO.ISO.01" ], "sectionIds": [ "section:10f005ddcd31b0102625", "section:1a1734f3aaab8aa152c3", "section:22fb298fcb28accfbf39", "section:2525c189f32461c9368a", "section:2b8d2aba4baeb7a0c36b", "section:303925994b6f141b3a0e", "section:307c4c95a7c84b5efc0b", "section:414a84d23afa6566ca5e", "section:4ff2bf714d7cbf97df82", "section:6a93c4dd5fe420e1990e", "section:6cd1a267e72b20619327", "section:6fe70b094ab252ec071e", "section:701d23928f8e38ea7d4b", "section:7d0e50b6a6c30535730d", "section:888628823bf71f709698", "section:8f77a4d0f75af29d8c13", "section:954c40e55830e15dd43b", "section:a0bd29de2657307a1b42", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b63f8484d81bde8026ec", "section:b93e6ae7b00f32ee1201", "section:cca5b83aae425d5f0e88", "section:d90bd5e1e6d8fa41397d", "section:e415b5fb585454314b5d", "section:f68163cf343646a0f102", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:10f005ddcd31b0102625", "section:22fb298fcb28accfbf39", "section:414a84d23afa6566ca5e", "section:4ff2bf714d7cbf97df82", "section:6fe70b094ab252ec071e", "section:888628823bf71f709698", "section:954c40e55830e15dd43b", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b63f8484d81bde8026ec", "section:e415b5fb585454314b5d", "section:f68163cf343646a0f102", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v180_clock_is_mobius.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v180_clock_is_mobius.py", "pubMirrorHash": "f5a6fb459906b0df6bbc640f63766cea5ebf9df6cffb4c339e5c18d9bd12100b", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v180_clock_is_mobius.py" }, { "id": "v179_conformal_realisation", "filename": "v179_conformal_realisation.py", "path": "verification/v179_conformal_realisation.py", "cluster": "registry", "synopsis": "the two residual premises (MARKS-residual + KERNEL-residual) collapse to ONE geometric premise QGEO.CONF.01 (honest unification, the conformal realisation stays OPEN). MARKS's residual is NOT three independent assumptions: (1) genus-0 IS P1 — c3=1/(|Z2|·2π·χ(S²))=1/(8π) with χ(S²)=2 ⇒ g=0, the same χ=2 that gives the '8' (v58/v73); (2) the order-4 clock IS the carrier — Coxeter element of W(A3)=S4, order h(A3)=4=|μ4| (v117); (3) marks=one orbit is FORCED — parabolic marks ≠ the 2 elliptic fixed points {0,∞}, a free order-4 orbit has exactly 4=e1(a) points. So MARKS reduces to 'the carrier clock acts conformally on the genus-0 double'. KERNEL then FOLLOWS from that geometry: DtN symbol |k| (Lee-Uhlmann, v156) ⇒ rank-8 c=8 fixed polarisation; no drift (v158); the cusped-surface residual data is H¹=ℂ³=N_fam = the 3-dim gapped transfer block (Schur, v162/v178). Both ⇒ ONE premise QGEO.CONF.01: 'the raw RP seam normal double is conformally (ℙ¹,μ4) with the carrier clock as the order-4 Möbius map'. The two doors of v177/v178 are one geometric realisation — the single structural residual of the whole theory, left honestly OPEN.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv179_conformal_realisation.py", "sourceSha256": "2e5a1a2c044ffb06a92839d91afc806a9acf385fa78c87f12019a6859b83e8fa", "linkedClaimIds": [ "QGEO.CONF.01" ], "sectionIds": [ "section:10f005ddcd31b0102625", "section:22fb298fcb28accfbf39", "section:2525c189f32461c9368a", "section:2585b5d786c3bdb7ddb7", "section:307c4c95a7c84b5efc0b", "section:359527c60ffa08a51bf0", "section:6a93c4dd5fe420e1990e", "section:6cd1a267e72b20619327", "section:701d23928f8e38ea7d4b", "section:888628823bf71f709698", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b93e6ae7b00f32ee1201", "section:d90bd5e1e6d8fa41397d" ], "activeSectionIds": [ "section:10f005ddcd31b0102625", "section:22fb298fcb28accfbf39", "section:2585b5d786c3bdb7ddb7", "section:359527c60ffa08a51bf0", "section:888628823bf71f709698", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5" ], "evidenceId": "python_verification:verification/v179_conformal_realisation.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v179_conformal_realisation.py", "pubMirrorHash": "2e5a1a2c044ffb06a92839d91afc806a9acf385fa78c87f12019a6859b83e8fa", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v179_conformal_realisation.py" }, { "id": "v178_marks_kernel_attempt", "filename": "v178_marks_kernel_attempt.py", "path": "verification/v178_marks_kernel_attempt.py", "cluster": "registry", "synopsis": "an honest ATTEMPT at the two open obligations QGEO.MARKS.01 + QGEO.KERNEL.01 — NOT a closure (they are genuine constructive-geometry/AQFT statements, not finite computations), but a deeper reduction: each finite/algebraic CORE is closed [E] and each obligation reduced to ONE sharper irreducible [O] premise. MARKS finite core [E]: a genus-0 double with an order-4 clock ρ (~z↦iz, fixed points {0,∞}) and sheet reflection τ forces the marks to be a generic ρ-orbit {1,i,−1,−i}=μ₄ (NOT the fixed points), distinct iff b₁=4−1=3=N_fam (collision drops b₁, excluded), τρτ=ρ⁻¹ ⇒ faithful D4 order 8 — so MARKS reduces to the single topological/clock premise. KERNEL finite core [E]: on the 3-dim multiplicity-free H¹ the μ₄ characters (1,2,3) are distinct, so by Schur a μ₄-equivariant operator is forced DIAGONAL and completely determined by its eigenvalue per character — two such with the same forced transfer spectrum {1,(2/3)⁶,(1/3)⁶} (v162) and the unique residue-normalised basis (v177) are EQUAL as operators (the 'spectrum vs operator' worry vanishes on the finite block); so KERNEL reduces to the single full-operator-reduction premise (principal symbol |k| Lee-Uhlmann v156, no drift v158). NET: neither obligation closed; both sharpened to milder premises.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv178_marks_kernel_attempt.py", "sourceSha256": "3d98e1d8ab0a9cbd5f1d9e914818baffa506ca1269cd09ddff0a4d01822c8036", "linkedClaimIds": [ "QGEO.REDUCE.01" ], "sectionIds": [ "section:22fb298fcb28accfbf39", "section:2525c189f32461c9368a", "section:359527c60ffa08a51bf0", "section:6a93c4dd5fe420e1990e", "section:6cd1a267e72b20619327", "section:888628823bf71f709698", "section:ab9e7e520130ecc7da7c", "section:b93e6ae7b00f32ee1201", "section:c99473f27f0afd476930", "section:d90bd5e1e6d8fa41397d" ], "activeSectionIds": [ "section:22fb298fcb28accfbf39", "section:359527c60ffa08a51bf0", "section:888628823bf71f709698", "section:ab9e7e520130ecc7da7c", "section:c99473f27f0afd476930" ], "evidenceId": "python_verification:verification/v178_marks_kernel_attempt.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v178_marks_kernel_attempt.py", "pubMirrorHash": "3d98e1d8ab0a9cbd5f1d9e914818baffa506ca1269cd09ddff0a4d01822c8036", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v178_marks_kernel_attempt.py" }, { "id": "v177_seam_marking_kernel", "filename": "v177_seam_marking_kernel.py", "path": "verification/v177_seam_marking_kernel.py", "cluster": "registry", "synopsis": "the QGEO proof tree — the v176 'one realisation premise' split into its honest constituents: REALIZE = MARKS · UNIFORM · COHOM · MODULE · KERNEL · NET, with FOUR nodes closed CONSTRUCTIVELY as [E] and the open residual sharpened into exactly TWO named obligations. [E] UNIFORM (Lemma 2, constructive): an order-4 Möbius map conjugates to z↦iz, a non-fixed orbit scales to μ₄, the reflection z↦1/z gives στρτ=ρ⁻¹ (D4 order 8) — a genus-0 4-marked faithful-D4 boundary IS (ℙ¹,μ₄); [E] COHOM: ρ*ωk=i^kωk so the H¹ grading is (1,2,3)=A3 exponents=Spec(Q₊); [E] MODULE: the H¹→generation iso is UNIQUE (multiplicity-free + residue normalisation; reflection ω1↔ω3, ω2 fixed); [E] NET (v154/v175): index-4 μ₄ extension of (D5)₁⊗(A3)₁ = (E8)₁. The TWO genuine open obligations [O]: QGEO.MARKS.01 (raw seam → genus-0 four-marked D4 boundary) and QGEO.KERNEL.01 (raw seam Calderón kernel = the μ₄-equivariant free gapped contraction as an OPERATOR). Removes the near-circular v176 framing (which took the marks as a hypothesis); the whole structural residual is now exactly these two doors.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv177_seam_marking_kernel.py", "sourceSha256": "bf6ad1e0d4dd21ca3b66790b004c2d202a67ea1e94a249c4f09437cc4b6a1c09", "linkedClaimIds": [ "QGEO.TREE.01", "QGEO.MARKS.01", "QGEO.KERNEL.01" ], "sectionIds": [ "section:113a50c68f53872c39d4", "section:17a730ae6b843f575a43", "section:22fb298fcb28accfbf39", "section:2525c189f32461c9368a", "section:2f06593b8d87effdfab6", "section:359527c60ffa08a51bf0", "section:6a93c4dd5fe420e1990e", "section:6cd1a267e72b20619327", "section:75d473d613aba16a08b8", "section:888628823bf71f709698", "section:8f77a4d0f75af29d8c13", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:b56f3a2e55f262711774", "section:b93e6ae7b00f32ee1201", "section:bc61b0e372551b770dfb", "section:c2f9c0d9f1b119435aaf", "section:c99473f27f0afd476930", "section:d90bd5e1e6d8fa41397d", "section:f68163cf343646a0f102", "section:fbaeb4d566affaf1be8a" ], "activeSectionIds": [ "section:113a50c68f53872c39d4", "section:17a730ae6b843f575a43", "section:22fb298fcb28accfbf39", "section:2f06593b8d87effdfab6", "section:359527c60ffa08a51bf0", "section:75d473d613aba16a08b8", "section:888628823bf71f709698", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:b56f3a2e55f262711774", "section:bc61b0e372551b770dfb", "section:c2f9c0d9f1b119435aaf", "section:c99473f27f0afd476930", "section:f68163cf343646a0f102", "section:fbaeb4d566affaf1be8a" ], "evidenceId": "python_verification:verification/v177_seam_marking_kernel.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v177_seam_marking_kernel.py", "pubMirrorHash": "bf6ad1e0d4dd21ca3b66790b004c2d202a67ea1e94a249c4f09437cc4b6a1c09", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v177_seam_marking_kernel.py" }, { "id": "v176_seam_collar_realisation", "filename": "v176_seam_collar_realisation.py", "path": "verification/v176_seam_collar_realisation.py", "cluster": "registry", "synopsis": "the Seam Collar Realisation Theorem assembled as ONE central statement + reduction certificate (the single structural proof obligation of the theory, formulated cleanly — NOT a fabricated proof): the theorem 'the seam collar's conformal boundary is ℙ¹∖μ₄ with H¹ grading (1,2,3), Calderón contraction = rank-8 K_Σ, index-4 extension = (E8)₁' decomposes into six steps, FIVE already [E] — geometry/uniformisation (v168: cross-ratio 2, faithful Möbius D4 order 8, b₁=N_fam=3), Calderón DtN symbol |k| (v156), H¹ character = generation grading (1,2,3)=A3 exponents=Spec(Q₊) (v137/v168), μ₄-equivariant one-particle contraction diagonal in the cusp basis with gap (2/3)⁶ (v162), AQFT closure (D5)₁⊗(A3)₁⋊μ₄=(E8)₁ + full-cone RP all m (v154/v175) — so the WHOLE structural residual reduces to EXACTLY one open premise: that the physical seam collar's conformal boundary IS this ℙ¹∖μ₄ (QGEO.REALIZE.01), a constructive-geometry statement left honestly OPEN.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv176_seam_collar_realisation.py", "sourceSha256": "f7f4c9de2010f9b947db1861608469c1b2a67e401640a82d5c3b1b5c6d336061", "linkedClaimIds": [ "QGEO.REALIZE.02" ], "sectionIds": [ "section:22fb298fcb28accfbf39", "section:2525c189f32461c9368a", "section:2f06593b8d87effdfab6", "section:6a93c4dd5fe420e1990e", "section:6cd1a267e72b20619327", "section:7a7de20f53ed3e69fb6f", "section:83cee7585db61c131b9a", "section:888628823bf71f709698", "section:ab9e7e520130ecc7da7c", "section:b93e6ae7b00f32ee1201", "section:d90bd5e1e6d8fa41397d" ], "activeSectionIds": [ "section:22fb298fcb28accfbf39", "section:2f06593b8d87effdfab6", "section:7a7de20f53ed3e69fb6f", "section:83cee7585db61c131b9a", "section:888628823bf71f709698", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v176_seam_collar_realisation.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v176_seam_collar_realisation.py", "pubMirrorHash": "f7f4c9de2010f9b947db1861608469c1b2a67e401640a82d5c3b1b5c6d336061", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v176_seam_collar_realisation.py" }, { "id": "v175_net_existence_full_cone", "filename": "v175_net_existence_full_cone.py", "path": "verification/v175_net_existence_full_cone.py", "cluster": "registry", "synopsis": "the heavy artillery — net existence (A2) and full-cone reflection positivity discharged to [E], isolating QGEO.REALIZE.01 as the single open premise (nothing fabricated): (1) FULL-CONE RP FOR ALL m — the CAR second-quantisation functor Γ(t)=⊕_m Λ^m(t) of the one-particle seam contraction t acts on the complete Fock space Λ^•(ℝ¹⁶) (dim 2¹⁶=65536); the exterior-power spectrum theorem makes every eigenvalue a subset product of spec(t), verified on all 2¹⁶ products to lie in [0,1] (contraction), with eigenvalue-1 multiplicity 2⁸=256 (wedges of the rank-8 K_Σ polarisation) and sub-leading = the one-particle gap (2/3)⁶, so full-cone RP reduces for ALL m to the one-particle contraction (Shale-Stinespring CAR functor), discharging the v160 scope premise by a theorem; (2) A2 net existence assembled + verified — (E8)₁ character E4/η⁸=1+248q+4124q²+34752q³+213126q⁴+1057504q⁵ (level-1=248), conformal embedding 248=120+128, E8 Cartan even unimodular (det 1, the unique rank-8 even unimodular lattice); the net EXISTS by cited theorems (free-fermion net, lattice VOA, index-4 Q-system); (3) both collapse to the SAME seam-kernel identification = QGEO.REALIZE.01, whose finite half is v168 and whose realisation half is left OPEN.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv175_net_existence_full_cone.py", "sourceSha256": "969ccd9c2a6ba5a4edb46219ff3aeeaa5c3e7c67ff01bed49ccc981dc7960426", "linkedClaimIds": [ "QFT.NETRP.01" ], "sectionIds": [ "section:05aaf35318c9e1bb8204", "section:22fb298fcb28accfbf39", "section:2525c189f32461c9368a", "section:2585b5d786c3bdb7ddb7", "section:2f06593b8d87effdfab6", "section:4ff2bf714d7cbf97df82", "section:56260a726c20b0e2fff7", "section:63da5b8be1d09edb111a", "section:6a93c4dd5fe420e1990e", "section:6cd1a267e72b20619327", "section:7a7de20f53ed3e69fb6f", "section:81a6dc002dc46cf7b6c5", "section:83cee7585db61c131b9a", "section:888628823bf71f709698", "section:93b8868beb643874af75", "section:9a6aaf6fc60f9b74b301", "section:a5cf57be6b809cb6f0d7", "section:ab9e7e520130ecc7da7c", "section:b93e6ae7b00f32ee1201", "section:d90bd5e1e6d8fa41397d", "section:e16d657ff22e85d37e54", "section:e2c33aad84858bc51b9d", "section:eb00caf29086b02d5bf5", "section:f7f27b7893f1db12bbb4" ], "activeSectionIds": [ "section:05aaf35318c9e1bb8204", "section:22fb298fcb28accfbf39", "section:2585b5d786c3bdb7ddb7", "section:2f06593b8d87effdfab6", "section:4ff2bf714d7cbf97df82", "section:56260a726c20b0e2fff7", "section:63da5b8be1d09edb111a", "section:7a7de20f53ed3e69fb6f", "section:81a6dc002dc46cf7b6c5", "section:83cee7585db61c131b9a", "section:888628823bf71f709698", "section:9a6aaf6fc60f9b74b301", "section:a5cf57be6b809cb6f0d7", "section:ab9e7e520130ecc7da7c", "section:e16d657ff22e85d37e54", "section:e2c33aad84858bc51b9d", "section:f7f27b7893f1db12bbb4" ], "evidenceId": "python_verification:verification/v175_net_existence_full_cone.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v175_net_existence_full_cone.py", "pubMirrorHash": "969ccd9c2a6ba5a4edb46219ff3aeeaa5c3e7c67ff01bed49ccc981dc7960426", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v175_net_existence_full_cone.py" }, { "id": "v202_rare_kaon", "filename": "v202_rare_kaon.py", "path": "verification/v202_rare_kaon.py", "cluster": "flavor", "synopsis": "the rare kaon sector K → π ν ν̄ from the TFPT CKM point ([C] downstream flavor readout, NOT a compiler power). The kernel fixes the full CKM matrix (s₁₂=λ_C, s₂₃=φ₀/(1+λ_C)=|V_cb|, s₁₃=λ_C³/3, δ=π/3+3λ_C²=1.19823 rad; v18/v88) with no flavor fit; feeding the exact point into the standard Brod–Gorbahn–Stamou short-distance formulas gives BR(K⁺→π⁺νν̄)=9.45×10⁻¹¹ and BR(K_L→π⁰νν̄)=3.33×10⁻¹¹. [I] CKM point + exact apex (ρ̄,η̄)=(0.1374,0.3509), λ_t=V_ts*V_td; [C] the branching ratios (NOT parameter-free — X_t, P_c, κ_± are external EW/QCD input); [N] BR(K⁺)=9.45×10⁻¹¹ lands ON the NA62 2016-2024 combination (9.6 +1.9/-1.8)×10⁻¹¹ (La Thuile 2026), +0.08σ (the 2016-2022 obs (13.0₋₃.₀⁺³·³)×10⁻¹¹ was ~1.2σ above) — a strong consistency hit, but an F_transfer bridge, not a unique TFPT-vs-SM discriminator (SM (8.6±0.4)×10⁻¹¹ also inside the NA62 error); [I] Grossman–Nir ratio 0.352 ≪ 4.3; [X] dated kill test: a stable NA62 BR(K⁺) outside [7,12]×10⁻¹¹, or a KOTO-II BR(K_L) off the GN point, breaks the flavor bridge (core untouched).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv202_rare_kaon.py", "sourceSha256": "04e9e19416c79411fd4af7a7425994f4efb958faa19567039e90ef2a144d126a", "linkedClaimIds": [ "FR.RAREKAON.01" ], "sectionIds": [ "section:2525c189f32461c9368a", "section:6cd1a267e72b20619327", "section:7f2e391c59e00a9e6acb", "section:888628823bf71f709698", "section:9cb3b04ab25cb016cf69", "section:ab9e7e520130ecc7da7c", "section:b93e6ae7b00f32ee1201", "section:ddeb7ff0b27d4750ff23", "section:de65561a933aa5ea02ba" ], "activeSectionIds": [ "section:7f2e391c59e00a9e6acb", "section:888628823bf71f709698", "section:9cb3b04ab25cb016cf69", "section:ab9e7e520130ecc7da7c", "section:ddeb7ff0b27d4750ff23" ], "evidenceId": "python_verification:verification/v202_rare_kaon.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v202_rare_kaon.py", "pubMirrorHash": "04e9e19416c79411fd4af7a7425994f4efb958faa19567039e90ef2a144d126a", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v202_rare_kaon.py" }, { "id": "v203_eht_achromatic", "filename": "v203_eht_achromatic.py", "path": "verification/v203_eht_achromatic.py", "cluster": "horizon", "synopsis": "the EHT achromatic polarization-rotation intercept β_BH around a horizon-scale black hole — the surviving core of the old UFE/BH notes (NOT the RN-type metric, superseded by Nariai/seam=horizon v101–v104/v190; only the polarization signature). [E] the coupling is a compiler number: β_BH(r)=Q_e^eff Q_m^eff/(256π⁴r²)=16c₃⁴(Q_eQ_m/r²), 16c₃⁴=1/(256π⁴) exactly. [E] α-kernel cross-link: 16c₃⁴=δ_top/3, δ_top=48c₃⁴=3/(256π⁴) — the SAME top-form coefficient that fixes the α-kernel precision-zone correction (one row from β_rad=φ₀/4π). [C] TFPT fixes the 1/r² profile, achromaticity, and sign-flip under E·B reversal; the amplitude Q_eQ_m is an MHD/GR weight, not a compiler output. [X] dated kill test: the residual intercept must pass three nulls (frequency/achromatic, spatial 1/r², sign-flip); a null-consistent residual after honest GRMHD subtraction falsifies the channel (core untouched).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv203_eht_achromatic.py", "sourceSha256": "f9881fb5a14cf89a9416a3c90937b4175a95bdb55d58642190026d16b955f0a4", "linkedClaimIds": [ "HOR.EHT.01" ], "sectionIds": [ "section:3d248d64cc5a87ec2248", "section:ab9e7e520130ecc7da7c", "section:ddeb7ff0b27d4750ff23", "section:e60c8c7dc2298081bbd9" ], "activeSectionIds": [ "section:3d248d64cc5a87ec2248", "section:ab9e7e520130ecc7da7c", "section:ddeb7ff0b27d4750ff23", "section:e60c8c7dc2298081bbd9" ], "evidenceId": "python_verification:verification/v203_eht_achromatic.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v203_eht_achromatic.py", "pubMirrorHash": "f9881fb5a14cf89a9416a3c90937b4175a95bdb55d58642190026d16b955f0a4", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v203_eht_achromatic.py" }, { "id": "v204_muon_seam_g2", "filename": "v204_muon_seam_g2.py", "path": "verification/v204_muon_seam_g2.py", "cluster": "frontier", "synopsis": "the muon anomalous magnetic moment a_μ=(g_μ−2)/2 as a seam vertex readout ([C] downstream, NOT a compiler power; archive integration of the old muon-g2 note). The carrier fixes the second-order topological defect δ₂=B·γ·δ_top²=(5/4)δ_top² (δ_top=Ω_adm c₃⁴=48c₃⁴=3/256π⁴, v2/v23; B·γ=(3/2)(5/6)=5/4 the carrier compression quotient, v51); the seam-loop projection a_μ^seam=δ₂/(2π)=45/(524288π⁹)≈2.879×10⁻⁹. [E] the VALUE is an exact compiler number (trace reading δ₂=4!·Tr_{S⁺}(X²)·c₃⁸, Tr=120=5!); [C] the IDENTIFICATION of δ₂/(2π) as a magnetic vertex (1/2π=4c₃ seam unit) is a physical bridge; [N] 0.81σ vs dispersive Δa_μ=(2.49±0.48)×10⁻⁹; [C] HONEST: lattice/CMD-3 HVP shrinks Δa_μ (~1.5×10⁻⁹), the FIXED value then ~1.5σ high; [X] dated kill test: a converged Δa_μ outside 2.879×10⁻⁹±0.5×10⁻⁹ excludes the mechanism (core untouched).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv204_muon_seam_g2.py", "sourceSha256": "3102fef025e71ba421a22c64d14a13bbc934826cc6b8d4ba386bfcd90777e5b4", "linkedClaimIds": [ "FR.MUONG2.01" ], "sectionIds": [ "section:2327b1b5b72d8d0ad7fe", "section:8e607432a187ac5887cb", "section:ab9e7e520130ecc7da7c" ], "activeSectionIds": [ "section:2327b1b5b72d8d0ad7fe", "section:8e607432a187ac5887cb", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v204_muon_seam_g2.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v204_muon_seam_g2.py", "pubMirrorHash": "3102fef025e71ba421a22c64d14a13bbc934826cc6b8d4ba386bfcd90777e5b4", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v204_muon_seam_g2.py" }, { "id": "v205_xi_threequarter", "filename": "v205_xi_threequarter.py", "path": "verification/v205_xi_threequarter.py", "cluster": "gravity", "synopsis": "ξ=c₃/φ_tree=3/4: an INDEPENDENT route to the gravitational 3/4 (archive integration of the old Eliminating-K note). The torsion-compression ansatz κ²=ξφ₀/c₃² with the Einstein limit κ²=8πG fixes ξ=8πc₃²/φ₀=c₃/φ₀ (since 8πc₃²=c₃), and at tree level φ_tree=1/(6π) this is EXACTLY 3/4. [E] tree identity ξ=c₃/φ_tree=(1/8π)/(1/6π)=3/4; [E] Einstein-limit reduction 8πc₃²=c₃ ⇒ G is an output, not an input; [E] OVER-DETERMINATION 3/4=q(A₃)=N_fam/|μ₄|=ln(m/μ) (v152 k=c₃/2) — the torsion-compression ξ and the gapped EH replica are two independent appearances of the same gravitational 3/4; [N] with the retained seed ξ=c₃/φ₀=0.748303 (−0.226% from 3/4); [C] the κ²=ξφ₀/c₃² ansatz is the [C] bridge, the modern derivation is v152/v68, 1/G stays the one anchor (v60/v153).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv205_xi_threequarter.py", "sourceSha256": "2a6898b2cfe36d8030a7eb4add0e7ff5be902d536c8850b1adbf8f18b7896d80", "linkedClaimIds": [ "GRAV.XI.01" ], "sectionIds": [ "section:ab9e7e520130ecc7da7c", "section:f5274c8105ff62e99dcd" ], "activeSectionIds": [ "section:ab9e7e520130ecc7da7c", "section:f5274c8105ff62e99dcd" ], "evidenceId": "python_verification:verification/v205_xi_threequarter.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v205_xi_threequarter.py", "pubMirrorHash": "2a6898b2cfe36d8030a7eb4add0e7ff5be902d536c8850b1adbf8f18b7896d80", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v205_xi_threequarter.py" }, { "id": "v206_h0_lambda_branch", "filename": "v206_h0_lambda_branch.py", "path": "verification/v206_h0_lambda_branch.py", "cluster": "gravity", "synopsis": "the cosmological-constant Letter branch: the seam number δ_Σ=m₁e^{−2πα⁻¹/3} with the lowest-block m₁=Ω_adm=48, the Planck-convention split, and the quantitative H₀=66.5..67.1 (archive integration of the tfpt-31 CC note; sharpens the qualitative H₀-vs-Λ row). [N] δ_Σ^lead=48 e^{−2π·137.036/3}≈1.085×10⁻¹²³; [E] convention split M_Pl⁴/M̄_Pl⁴=(8π)²=631.65 (unreduced vs reduced Planck density — must be displayed); [N] ρ_Λ=M_Pl⁴δ_Σ≈2.4×10⁻⁴⁷ GeV⁴ (observed vacuum order); [N] 123-orders cross-link |log₁₀δ_Σ|≈122.96, consistent with the v60 split 122.948; [C] under flatness closure H₀^lead=66.51, H₀^disc=67.10 km/s/Mpc — 1.6..0.5σ BELOW Planck, ~6σ below SH0ES: the Hubble tension is NOT relieved by raising the vacuum scale; H₀ uses imported Ω_b, ω_DM, so it is a [C] readout.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv206_h0_lambda_branch.py", "sourceSha256": "1efc9a0cab5f4c658651c8819610f77b2332acbc61320cd2269672b10e613e6d", "linkedClaimIds": [ "GRAV.H0.01" ], "sectionIds": [ "section:ab9e7e520130ecc7da7c", "section:f5274c8105ff62e99dcd" ], "activeSectionIds": [ "section:ab9e7e520130ecc7da7c", "section:f5274c8105ff62e99dcd" ], "evidenceId": "python_verification:verification/v206_h0_lambda_branch.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v206_h0_lambda_branch.py", "pubMirrorHash": "1efc9a0cab5f4c658651c8819610f77b2332acbc61320cd2269672b10e613e6d", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v206_h0_lambda_branch.py" }, { "id": "v207_asymptotic_safety", "filename": "v207_asymptotic_safety.py", "path": "verification/v207_asymptotic_safety.py", "cluster": "frontier", "synopsis": "Asymptotic Safety as a SECOND, independent, [P] route to the metric sector (archive integration of the old Five-Problems note). The current theory closes QG via the discrete seam-net/AQFT programme (v175; open premise QGEO.REALIZE.01); this records a COMPLEMENTARY continuum-FRG argument that a non-Gaussian UV fixed point exists from the same axioms — a plausibility cross-check, NOT load-bearing, does NOT close G_metric. [E] the axion coupling is fixed and small y²=16c₃²=1/(4π²)=0.025330 exactly (g_aγγ=−4c₃ from the cubic); [N] existence by IVT: d_t g/g=2+η_R is +2>0 as g→0 and <0 at large g (torsion K² damping) ⇒ a root g_*>0; [N] g_*=2/a₁>0 finite, Reuter-type O(1), no new free input; [P] HONEST: a continuum-FRG ansatz the discrete-compiler theory did NOT adopt, primary stays the seam-net (v175), G_metric open either way.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv207_asymptotic_safety.py", "sourceSha256": "1319afaf79f62e395d26b8c55721a077e6fc3af2a34cd0d902d945614d2a8046", "linkedClaimIds": [ "GRAV.ASYMP.01" ], "sectionIds": [ "section:1d709d6b4fbbfe522d4a", "section:6a93c4dd5fe420e1990e", "section:ab9e7e520130ecc7da7c", "section:bc61b0e372551b770dfb", "section:d90bd5e1e6d8fa41397d", "section:f68163cf343646a0f102" ], "activeSectionIds": [ "section:1d709d6b4fbbfe522d4a", "section:ab9e7e520130ecc7da7c", "section:bc61b0e372551b770dfb", "section:f68163cf343646a0f102" ], "evidenceId": "python_verification:verification/v207_asymptotic_safety.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v207_asymptotic_safety.py", "pubMirrorHash": "1319afaf79f62e395d26b8c55721a077e6fc3af2a34cd0d902d945614d2a8046", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v207_asymptotic_safety.py" }, { "id": "v208_bh_thermodynamics", "filename": "v208_bh_thermodynamics.py", "path": "verification/v208_bh_thermodynamics.py", "cluster": "horizon", "synopsis": "black-hole thermodynamics from the seam: the modular Hawking temperature and the scalaron-corrected Wald entropy (archive integration of the dropped tfpt-42 stationary-horizons/compact-objects section, re-typed through the current Tomita–Takesaki seam work v198/v199). [E] MODULAR T_H: Δ^{it}=e^{−2πtK_H} (Bisognano–Wichmann) ⇒ KMS at β=2π and T_H=κ/(2π); the 2π IS the seam unit 1/(4c₃) (1/2π=4c₃, v58), reproducing T_H=c₃/M (v57); seam↔horizon identification is [P]; [E] WALD ENTROPY: with the induced f(R)=R+R²/(6M_s²) (M_s=c₃^{7/2}M̄, v28), S_W=(f_R A)/(4G)=(A/4G)(1+R_h/3M_s²) — leading A/4G is the c₃ area law (1/4=1/|μ₄|), the correction an EXACT scalaron consequence; [E] SdS T_H=(1/4πr_h)(1−Λr_h²), 1/4π=2c₃; [E] area law S_BH=M²/(2c₃)=4πM²=A/4G.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv208_bh_thermodynamics.py", "sourceSha256": "ed633bb912f464b0a82cd60e348019fb4539a69aa6d8f348857c771da19b7afc", "linkedClaimIds": [ "HOR.BHTHERMO.01" ], "sectionIds": [ "section:03c7873577084caa47f8", "section:49282b347d9c681f9051", "section:6a9749089feb7aba080e", "section:7d0e50b6a6c30535730d", "section:8b84d2fb55ac4a48656b", "section:ab9e7e520130ecc7da7c", "section:cb552d2464f1e864b4f9", "section:cca5b83aae425d5f0e88", "section:d9dfc4ce2d7febed0290", "section:de8db1cd8257eab0d607", "section:edf07fc78f9496f57ed7" ], "activeSectionIds": [ "section:6a9749089feb7aba080e", "section:8b84d2fb55ac4a48656b", "section:ab9e7e520130ecc7da7c", "section:d9dfc4ce2d7febed0290", "section:de8db1cd8257eab0d607", "section:edf07fc78f9496f57ed7" ], "evidenceId": "python_verification:verification/v208_bh_thermodynamics.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v208_bh_thermodynamics.py", "pubMirrorHash": "ed633bb912f464b0a82cd60e348019fb4539a69aa6d8f348857c771da19b7afc", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v208_bh_thermodynamics.py" }, { "id": "v209_bh_regular_core", "filename": "v209_bh_regular_core.py", "path": "verification/v209_bh_regular_core.py", "cluster": "horizon", "synopsis": "the black hole as a seam fixed point (topological defect), NOT a singularity: the honest [P] synthesis of the old Five-Problems BH picture, with the SUPERSEDED torsion/RN-vortex metric DROPPED (RN-type metric superseded by Nariai/seam=horizon v101–v104/v190; cf. v203). Built entirely from established suite atoms. [E] NO SINGULARITY = SEAM FIXED POINT: the gapped attractor multiplier λ₂=(2/3)⁶=64/729 with gap Δ=6log(3/2)>0 (v56) — the core is a fixed point (dφ/dt=0), ρ→∞ replaced by φ→φ_* [P]; [E] MAXIMAL BH = ANCHOR: Nariai cubic t³−3t+2=(t−1)²(t+2), roots (1,1,−2) = the traceless projection of a=(1,1,2) (a−(p₁/3)1=−(1/3)(1,1,−2), p₁=4; v101/v190); [E] INFORMATION stays in the boundary field: Page recovery decays at λ₂=(2/3)⁶ per step (v54), no interior loss [P]; [E] holographic remnant S_BH=A/4G, 1/4=1/|μ₄|, a Planck-scale floor [P]; [P] HONEST: a qualitative structural synthesis (reuses v54/v56/v57/v101/v190), NOT load-bearing, NOT a metric.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv209_bh_regular_core.py", "sourceSha256": "da96da5f8e627e60fdc1563c9c4ef096232ad82f76491d9255b5ed80b8162104", "linkedClaimIds": [ "HOR.BHCORE.01" ], "sectionIds": [ "section:ab9e7e520130ecc7da7c", "section:fda00a19dcba44348ac3" ], "activeSectionIds": [ "section:ab9e7e520130ecc7da7c", "section:fda00a19dcba44348ac3" ], "evidenceId": "python_verification:verification/v209_bh_regular_core.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v209_bh_regular_core.py", "pubMirrorHash": "da96da5f8e627e60fdc1563c9c4ef096232ad82f76491d9255b5ed80b8162104", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v209_bh_regular_core.py" }, { "id": "v218_diamond_axis_geometry", "filename": "v218_diamond_axis_geometry.py", "path": "verification/v218_diamond_axis_geometry.py", "cluster": "registry", "synopsis": "Diamond axis geometry: the Sheet Diamond (v94) is a discrete geometry with two axes around the centered cross (v95: C center, U winding, V sheet), and the missing corner F is the transfer completion. Three exact [E] lemmas + honest audit/heuristic typing, no new numbers. [E] AXIS CURVATURE: det(C+xU)=14+6x linear (winding flat, slope 6=|R⁺(A₃)|), det(C+yV)=14+14y+4y² quadratic with 2nd difference 8=rank E₈; det B(C+xU)=2 det(C+xU), anchor-block sheet 2nd difference 6=|R⁺(A₃)| — curvatures (8,6)=(rank E₈, |R⁺(A₃)|). [E] PLÜCKER TRANSFER LADDER: Pl(K)=(−1,6,4)→Pl(C)=(0,14,14)→Pl(F)=(1,22,30); C−K=(1,8,10)=(N_Φ,rank E₈,A_Λ), F−C=(1,8,16)=(N_Φ,rank E₈,dim S⁺) — decuple 10 then full generation 16 (identity [E], transfer reading [C]). [E] SPECTRAL RAMIFICATION: for Q,K,C,F the cubic discriminant=q(r)²·Disc(q); squares (1,3,4,6)=(N_Φ,N_fam,|μ₄|,|R⁺(A₃)|), kernels (13,48,65,105)=(Δ_Q,Ω_adm,g_car·Δ_Q,N_fam·g_car·7), F carries 105=3·5·7. [I] audit anchor-defect spectrum Δ_a(Q,K,R,C,L,F)=(8,16,18,21,24,26); [I] audit pair-sum atlas {12,24,28,36,40,52} total 64, staircase sum 81=N_fam⁴ — 28=2 dim G₂, 52=dim F₄ audit-only, not spine. [C] heuristic: F the transfer-completion corner, a search principle not a hard filter.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv218_diamond_axis_geometry.py", "sourceSha256": "573a712170900ef327b7ff5188a229201678d76d90e884b02f9792017fd9b0cd", "linkedClaimIds": [ "DIAMOND.AXIS.01", "DIAMOND.PLUCKER.01", "DIAMOND.SPECTRAL.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:1234c1fa7fdc0d6d5b35", "section:2678ed3ba0ed508e2d8e", "section:2ff762f6d6932ac2b2c5", "section:51e91159532ef7479ff8", "section:8872501633bb702220cd", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c" ], "activeSectionIds": [ "section:1234c1fa7fdc0d6d5b35", "section:2ff762f6d6932ac2b2c5", "section:51e91159532ef7479ff8", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v218_diamond_axis_geometry.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v218_diamond_axis_geometry.py", "pubMirrorHash": "573a712170900ef327b7ff5188a229201678d76d90e884b02f9792017fd9b0cd", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v218_diamond_axis_geometry.py" }, { "id": "v219_icosahedral_mckay", "filename": "v219_icosahedral_mckay.py", "path": "verification/v219_icosahedral_mckay.py", "cluster": "core", "synopsis": "McKay bedrock: WHY the atoms are 2,3,5. E₈ is the exceptional TOP of the McKay tower of finite SU(2) subgroups (2T→Ê₆, 2O→Ê₇, 2I→Ê₈). The McKay graph is BUILT from the group: the 120 icosians close to 2I (orders {1,2,3,4,5,6,10}, containing the 2,3,5 axes), 9 conjugacy classes, Dixon irrep degrees {1,2,2,3,3,4,4,5,6} (sum 30=h(E₈), sum² 120=|R⁺(E₈)|); the natural-rep McKay adjacency IS the affine E₈ graph with marks = degrees. Backward certificate of E₈, not a P2 proof.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv219_icosahedral_mckay.py", "sourceSha256": "1281629938617cf116c578e085686bb9f35591f77f5eb240573922914023f0a1", "linkedClaimIds": [ "MCKAY.E8.01" ], "sectionIds": [ "section:00c96659d1c56ecb746e", "section:05558e866dc724bc0fcb", "section:09b49009253acb5a0dfb", "section:0abd9d66066143e08405", "section:2585b5d786c3bdb7ddb7", "section:26a174b789c650ed0ebe", "section:2b8d2aba4baeb7a0c36b", "section:303925994b6f141b3a0e", "section:3cc790136e8b9bd3c188", "section:497660cf26cb0410a678", "section:584e87a9c163ac38f92f", "section:678b949672ccc6aa27ab", "section:6a93c4dd5fe420e1990e", "section:6c5940fdfa107000ca6f", "section:7a7de20f53ed3e69fb6f", "section:81a6dc002dc46cf7b6c5", "section:99fa7c49f30373d04fa1", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:d748a08ff21c7b67a82f", "section:d90bd5e1e6d8fa41397d", "section:eb0bd97fda8c0fedefad", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:00c96659d1c56ecb746e", "section:05558e866dc724bc0fcb", "section:0abd9d66066143e08405", "section:2585b5d786c3bdb7ddb7", "section:497660cf26cb0410a678", "section:584e87a9c163ac38f92f", "section:678b949672ccc6aa27ab", "section:6c5940fdfa107000ca6f", "section:7a7de20f53ed3e69fb6f", "section:81a6dc002dc46cf7b6c5", "section:99fa7c49f30373d04fa1", "section:ab9e7e520130ecc7da7c", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v219_icosahedral_mckay.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v219_icosahedral_mckay.py", "pubMirrorHash": "1281629938617cf116c578e085686bb9f35591f77f5eb240573922914023f0a1", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v219_icosahedral_mckay.py" }, { "id": "v222_cm_norm_duality", "filename": "v222_cm_norm_duality.py", "path": "verification/v222_cm_norm_duality.py", "cluster": "core", "synopsis": "CM-norm duality: the two exceptional moduli give 41 and 7. SQUARE (Gaussian ℤ[i], j=1728): N(g_car+i|μ₄|)=5²+4²=41=10b₁ (the EM index IS the Gaussian norm of the carrier-glue vector); N(3+2i)=13=Δ_Q. HEX (Eisenstein ℤ[ω], j=0): N(3+2ω)=3²−3·2+2²=7=scalaron. The (3,2)=(colour,weak) split generates (5,6,7,13) by sum/product/Eisenstein/Gauss norm; rings rigid (Eisenstein of (5,4)=21≠41).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv222_cm_norm_duality.py", "sourceSha256": "2b4bb2c93f06a91203863bca753f6f5f7b128917c933f0050a7470e0f3c5f105", "linkedClaimIds": [ "CMNORM.DUAL.01" ], "sectionIds": [ "section:09b49009253acb5a0dfb", "section:2678ed3ba0ed508e2d8e", "section:3cc790136e8b9bd3c188", "section:4061f274c55499fb2ed1", "section:436dbc6f3b40e9aa8035", "section:51e91159532ef7479ff8", "section:584e87a9c163ac38f92f", "section:5ae06930f472e00a9545", "section:649c3b4e330a4dfc876d", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:b76309fbfced7aff0c43", "section:bb2a02a767e560376342", "section:e1f5b724a85f51ec5624", "section:eb0bd97fda8c0fedefad" ], "activeSectionIds": [ "section:4061f274c55499fb2ed1", "section:436dbc6f3b40e9aa8035", "section:51e91159532ef7479ff8", "section:584e87a9c163ac38f92f", "section:649c3b4e330a4dfc876d", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:bb2a02a767e560376342" ], "evidenceId": "python_verification:verification/v222_cm_norm_duality.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v222_cm_norm_duality.py", "pubMirrorHash": "2b4bb2c93f06a91203863bca753f6f5f7b128917c933f0050a7470e0f3c5f105", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v222_cm_norm_duality.py" }, { "id": "v223_coxeter_totative_clock", "filename": "v223_coxeter_totative_clock.py", "path": "verification/v223_coxeter_totative_clock.py", "cluster": "horizon", "synopsis": "The μ₄ clock is the order-4 character of the E₈ Coxeter cycle. (ℤ/30)ˣ={1,7,11,13,17,19,23,29}=the E₈ exponents=live Coxeter phases; φ(30)=8=rank E₈, 30=2·3·5. (ℤ/30)ˣ≅ℤ/4×ℤ/2 with order-4 generator 7 (7²=19,7⁴=1 mod 30): a literal μ₄ clock ⟨7⟩={1,7,13,19} on the exponents; conjugate pairs m+(30−m)=30 give |μ₄|=4 invariant planes the clock permutes. Only E₈ has φ(h)=rank AND h=2·3·5.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv223_coxeter_totative_clock.py", "sourceSha256": "16d842f84eb65ef8b98cc4ab256436eca92eb1a8985a891bc869bf3e6c7c6571", "linkedClaimIds": [ "COX.CLOCK.01" ], "sectionIds": [ "section:03d2cc780ce0cfabf94c", "section:05558e866dc724bc0fcb", "section:09b49009253acb5a0dfb", "section:0abd9d66066143e08405", "section:2678ed3ba0ed508e2d8e", "section:26a174b789c650ed0ebe", "section:3cc790136e8b9bd3c188", "section:497660cf26cb0410a678", "section:584e87a9c163ac38f92f", "section:7a7de20f53ed3e69fb6f", "section:99fa7c49f30373d04fa1", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:d748a08ff21c7b67a82f", "section:eb0bd97fda8c0fedefad" ], "activeSectionIds": [ "section:03d2cc780ce0cfabf94c", "section:05558e866dc724bc0fcb", "section:0abd9d66066143e08405", "section:497660cf26cb0410a678", "section:584e87a9c163ac38f92f", "section:7a7de20f53ed3e69fb6f", "section:99fa7c49f30373d04fa1", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v223_coxeter_totative_clock.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v223_coxeter_totative_clock.py", "pubMirrorHash": "16d842f84eb65ef8b98cc4ab256436eca92eb1a8985a891bc869bf3e6c7c6571", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v223_coxeter_totative_clock.py" }, { "id": "v227_degree_exponent_channel_split", "filename": "v227_degree_exponent_channel_split.py", "path": "verification/v227_degree_exponent_channel_split.py", "cluster": "core", "synopsis": "248=120+128 as a magnitude/phase channel typing (replaces the over-strong S⁻-dark-matter reading). E₈ exponents {1,7,11,13,17,19,23,29} sum 120=|R⁺(E₈)| (MAGNITUDE channel); E₈ degrees {2,8,12,14,18,20,24,30} sum 128=2^(rank−1)=rank·dim S⁺ (PHASE/GLUE channel); 248=120+128=adj(D₈)+spinor(D₈); deg−exp sum=rank=8. Ratios+products (Target D) live in 120, the un-covered CP phases in 128; the dark-sector reading of 128 stays Frontier.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv227_degree_exponent_channel_split.py", "sourceSha256": "c750c5787b27b5627cc35dde3c333fd56be5f2c0bfd39b760a0dcbdc1acff600", "linkedClaimIds": [ "E8.CHAN.01" ], "sectionIds": [ "section:7a7de20f53ed3e69fb6f", "section:8a517836f882378cde88", "section:8a623c8ec8a4cfe2a678", "section:a719d5d4b287729fc27d", "section:ab9e7e520130ecc7da7c", "section:f9ed8e942e9df8db94c7" ], "activeSectionIds": [ "section:7a7de20f53ed3e69fb6f", "section:8a517836f882378cde88", "section:ab9e7e520130ecc7da7c", "section:f9ed8e942e9df8db94c7" ], "evidenceId": "python_verification:verification/v227_degree_exponent_channel_split.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v227_degree_exponent_channel_split.py", "pubMirrorHash": "c750c5787b27b5627cc35dde3c333fd56be5f2c0bfd39b760a0dcbdc1acff600", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v227_degree_exponent_channel_split.py" }, { "id": "v228_rr_index_gate", "filename": "v228_rr_index_gate.py", "path": "verification/v228_rr_index_gate.py", "cluster": "core", "synopsis": "P2 as the mode space of a degree-4 seam divisor (a Riemann-Roch INDEX GATE; bedrock language for P2, not a proof from nothing). deg D=4=|μ₄| on P¹ ⇒ h⁰(O(D))=5=g_car (Riemann-Roch, genus 0); rank H₁(P¹ minus 4 marks)=3=N_fam; h⁰+rankH₁=8=rank E₈, h⁰−rankH₁=2=|Z₂|; Λᵉᵛᵉⁿ(C⁵)=1+10+5=16=dim S⁺. Conditional on the raw seam producing the degree-4 divisor (=QGEO.SYM.01).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv228_rr_index_gate.py", "sourceSha256": "eabd3597d3bd5418a88b860523eb1bda7bf6b0432e1e874772a8d1aeb864934c", "linkedClaimIds": [ "QGEO.RR.01" ], "sectionIds": [ "section:09b49009253acb5a0dfb", "section:2585b5d786c3bdb7ddb7", "section:3cc790136e8b9bd3c188", "section:584e87a9c163ac38f92f", "section:6a93c4dd5fe420e1990e", "section:749d598aa0815d32790b", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d", "section:eb0bd97fda8c0fedefad", "section:f1cb1505fb0d067d8745" ], "activeSectionIds": [ "section:2585b5d786c3bdb7ddb7", "section:584e87a9c163ac38f92f", "section:749d598aa0815d32790b", "section:ab9e7e520130ecc7da7c", "section:f1cb1505fb0d067d8745" ], "evidenceId": "python_verification:verification/v228_rr_index_gate.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v228_rr_index_gate.py", "pubMirrorHash": "eabd3597d3bd5418a88b860523eb1bda7bf6b0432e1e874772a8d1aeb864934c", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v228_rr_index_gate.py" }, { "id": "v220_cp_hexagonal_modulus", "filename": "v220_cp_hexagonal_modulus.py", "path": "verification/v220_cp_hexagonal_modulus.py", "cluster": "flavor", "synopsis": "CP lives in the HEXAGONAL phase fiber, not the square seam deck (a geometric sharpening of red-team Target D). The seam deck is the SQUARE modulus j(i)=1728, Aut Z/4 (the μ₄ clock); its exceptional partner is the HEX modulus j(ρ)=0, ρ=e^{iπ/3}, Aut Z/6, CM by ℤ[ω], arg(ρ)=π/3. The frozen leading CKM reading δ=π/3+3λ_C²=68.654° (v88) has leading term π/3=arg(ρ); the |Z₂| alternative π/3+2λ_C² is the frozen look-elsewhere trap. The deck stays Z/4 (v215); CP is the Z/6 fiber over it.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv220_cp_hexagonal_modulus.py", "sourceSha256": "b3b07f2cdfcb6632febbab9a88e4b6b1fc9200984f9da88afcdcde81f4fbeb74", "linkedClaimIds": [ "CP.MOD.01" ], "sectionIds": [ "section:05558e866dc724bc0fcb", "section:0d282444ef07ab3b182d", "section:2b8d2aba4baeb7a0c36b", "section:303925994b6f141b3a0e", "section:7a7de20f53ed3e69fb6f", "section:8e3e6d08d3c102a09298", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:d9254a3f746aa54dd7bd", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:05558e866dc724bc0fcb", "section:7a7de20f53ed3e69fb6f", "section:8e3e6d08d3c102a09298", "section:ab9e7e520130ecc7da7c", "section:d9254a3f746aa54dd7bd", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v220_cp_hexagonal_modulus.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v220_cp_hexagonal_modulus.py", "pubMirrorHash": "b3b07f2cdfcb6632febbab9a88e4b6b1fc9200984f9da88afcdcde81f4fbeb74", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v220_cp_hexagonal_modulus.py" }, { "id": "v225_dual_normal_frame", "filename": "v225_dual_normal_frame.py", "path": "verification/v225_dual_normal_frame.py", "cluster": "flavor", "synopsis": "The dual normal frame (d,n): one boundary compass for flavor+horizon, with CP as orientation. d=aᵀR⁻¹=aᵀL⁻¹=(−1/2,−1/2,1)=−½(1,1,−2) (the Nariai/horizon normal; d·1=0, d·a=1); n=(5,−9,6) with nᵀR=(det R,0,0)=(8,0,0), nᵀL=(20,0,0) (first-generation/torsion selector). Oriented volume det(1,d,n)=21=N_fam·scalaron. CP as orientation: Im det(1,d,ρn)=21 sin(π/3) for ρ=e^{iπ/3} — CP sits where the magnitude bijection (Target D) fails.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv225_dual_normal_frame.py", "sourceSha256": "bd525c278639fe0b204d04137e0e7aa0f720c302760c5526b4b50bfb17672f3a", "linkedClaimIds": [ "DUAL.FRAME.01" ], "sectionIds": [ "section:05558e866dc724bc0fcb", "section:7a7de20f53ed3e69fb6f", "section:ab9e7e520130ecc7da7c" ], "activeSectionIds": [ "section:05558e866dc724bc0fcb", "section:7a7de20f53ed3e69fb6f", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v225_dual_normal_frame.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v225_dual_normal_frame.py", "pubMirrorHash": "bd525c278639fe0b204d04137e0e7aa0f720c302760c5526b4b50bfb17672f3a", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v225_dual_normal_frame.py" }, { "id": "v224_diamond_ftransfer_path", "filename": "v224_diamond_ftransfer_path.py", "path": "verification/v224_diamond_ftransfer_path.py", "cluster": "masses", "synopsis": "F_transfer as ONE path on the Sheet Diamond, not four external interfaces. Family M(s,t)=R+Q diag(s,t,t): the transfer corners K=M(1,−1),C=M(1,0),F=M(1,1) lie on the SHEET axis (s=1). The sheet axis is curved det M(1,t)=4t²+14t+14 (2nd diff 8=rank E₈), the winding axis det M(s,0)=6s+8 flat (slope 6=|R⁺(A₃)|); Plücker ladder Pl(C)−Pl(K)=(1,8,10), Pl(F)−Pl(C)=(1,8,16). F_transfer = the K→C→F sheet geodesic, Koide source→pole its 1-D Möbius projection.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv224_diamond_ftransfer_path.py", "sourceSha256": "1c3ac6a33dab79b97867224405001cb4167dfa2210ceb372d8117222b918a1ae", "linkedClaimIds": [ "FTR.PATH.01" ], "sectionIds": [ "section:2678ed3ba0ed508e2d8e", "section:2ff762f6d6932ac2b2c5", "section:51e91159532ef7479ff8", "section:568b5e9acdb7b04367d3", "section:7ee581db787f8ddbcb4a", "section:8d1e955857da6655fadd", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:c519f45910c30ff3c0ae", "section:f0ac30137703825661c6", "section:fdf63a1d99769ab37ccb" ], "activeSectionIds": [ "section:2ff762f6d6932ac2b2c5", "section:51e91159532ef7479ff8", "section:8d1e955857da6655fadd", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:fdf63a1d99769ab37ccb" ], "evidenceId": "python_verification:verification/v224_diamond_ftransfer_path.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v224_diamond_ftransfer_path.py", "pubMirrorHash": "1c3ac6a33dab79b97867224405001cb4167dfa2210ceb372d8117222b918a1ae", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v224_diamond_ftransfer_path.py" }, { "id": "v229_lepton_frobenius_algebra", "filename": "v229_lepton_frobenius_algebra.py", "path": "verification/v229_lepton_frobenius_algebra.py", "cluster": "masses", "synopsis": "The charged leptons as an étale Frobenius algebra over the μ₆ resolvent. Exact coefficients (c_e,c_μ,c_τ)=(16/7,4/3,7/6), ring closure c_e c_τ=8/3=|Z₂|c_μ, product 32/9=2^g_car/N_fam². A=ℚ[t]/(m), m=∏(t−c): the trace-form Gram is nondegenerate (det=disc(m)≠0, A étale) — a commutative Frobenius algebra. The C₆ shift has charpoly t⁶−1 (spectrum μ₆=μ₃ family ×μ₂ sheet). PMNS extension via Aut(A)+the hex CM point is [C].", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv229_lepton_frobenius_algebra.py", "sourceSha256": "f6fd90fe244764528a3a4144769a6d780bd3fdd6c88dfd284712e37e92d41b7e", "linkedClaimIds": [ "LEP.FROB.01" ], "sectionIds": [ "section:0d282444ef07ab3b182d", "section:ab9e7e520130ecc7da7c", "section:d9254a3f746aa54dd7bd" ], "activeSectionIds": [ "section:ab9e7e520130ecc7da7c", "section:d9254a3f746aa54dd7bd" ], "evidenceId": "python_verification:verification/v229_lepton_frobenius_algebra.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v229_lepton_frobenius_algebra.py", "pubMirrorHash": "f6fd90fe244764528a3a4144769a6d780bd3fdd6c88dfd284712e37e92d41b7e", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v229_lepton_frobenius_algebra.py" }, { "id": "v221_seam_qecc", "filename": "v221_seam_qecc.py", "path": "verification/v221_seam_qecc.py", "cluster": "horizon", "synopsis": "The seam as a FINITE recoverability code (recovery rate (2/3)⁶=64/729). Code dimension dim S⁺=16=2^(g_car−1); the gapped transport T on the cusp-weight 3-space (deviations (1,−1,0) and the Nariai anchor (1,1,−2)) is symmetric, doubly stochastic (CPTP), spectrum {1,(2/3)⁶,(1/3)⁶}; on the trace-zero subspace ||T δ||≤(2/3)⁶||δ|| so ||Tⁿ δ||≤(2/3)^{6n}||δ|| (Knill-Laflamme-type bound); a free ratio breaks it. Holographic/Petz reading [C], gated on the Seam-Horizon theorem. Python-only (numerical contraction bound).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv221_seam_qecc.py", "sourceSha256": "4bb7156fd414a388f64979d0df66ab139aca04291a33bf9de0cc6ed663d30fac", "linkedClaimIds": [ "QEC.SEAM.01" ], "sectionIds": [ "section:01c88746fb95cc0958d7", "section:0739148b5a5974d0d662", "section:09b49009253acb5a0dfb", "section:10e10da547a5ac9014b8", "section:2a4b108348409f980f6d", "section:2b8d2aba4baeb7a0c36b", "section:303925994b6f141b3a0e", "section:3cc790136e8b9bd3c188", "section:4048b27ddae15185c715", "section:4d7b24e6cd695cd3409f", "section:584e87a9c163ac38f92f", "section:5b0172590490b241cb77", "section:5c7b501c80f2e5816761", "section:5ff3f529ae7be4541192", "section:6a93c4dd5fe420e1990e", "section:6c4044608163b007c4c2", "section:830ce3efdf003a4e5049", "section:848c49f799255f4cda92", "section:84ec2c9d7a3c77ec2664", "section:8577ecfeffdca80286f7", "section:8872501633bb702220cd", "section:8b1a1c6a205860e21edc", "section:93b8868beb643874af75", "section:98cf6dab6e992992d2c9", "section:9f084ccace7baa00bf8d", "section:a3401d23c565056512c5", "section:a7805cce6b04546f1147", "section:a9e4936094020237f825", "section:ab9e7e520130ecc7da7c", "section:acb731fecb30c7953915", "section:bc80e633fbb98ca8173d", "section:c4cf080b9ae6f25f7a71", "section:d84c8a8b6b42a871e6ef", "section:d90bd5e1e6d8fa41397d", "section:eb00caf29086b02d5bf5", "section:eb0bd97fda8c0fedefad", "section:edc607bc9be0dce5ac62", "section:f68163cf343646a0f102", "section:f8ad9138e39428999ab9", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:01c88746fb95cc0958d7", "section:10e10da547a5ac9014b8", "section:4d7b24e6cd695cd3409f", "section:584e87a9c163ac38f92f", "section:5b0172590490b241cb77", "section:5ff3f529ae7be4541192", "section:6c4044608163b007c4c2", "section:830ce3efdf003a4e5049", "section:84ec2c9d7a3c77ec2664", "section:8577ecfeffdca80286f7", "section:8b1a1c6a205860e21edc", "section:9f084ccace7baa00bf8d", "section:a3401d23c565056512c5", "section:ab9e7e520130ecc7da7c", "section:acb731fecb30c7953915", "section:bc80e633fbb98ca8173d", "section:d84c8a8b6b42a871e6ef", "section:edc607bc9be0dce5ac62", "section:f68163cf343646a0f102", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v221_seam_qecc.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v221_seam_qecc.py", "pubMirrorHash": "4bb7156fd414a388f64979d0df66ab139aca04291a33bf9de0cc6ed663d30fac", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v221_seam_qecc.py" }, { "id": "v230_center_budget_norms", "filename": "v230_center_budget_norms.py", "path": "verification/v230_center_budget_norms.py", "cluster": "flavor", "synopsis": "The Sheet-Diamond center budget (7,11,13) is the three LOCAL NORMS of the theory. C=R+Q diag(1,0,0), row sums (7,11,13): 7=N_ℤ[ω](3+2ω) (Eisenstein/hex = scalaron), 13=N_ℤ[i](3+2i) (Gauss/square = Δ_Q), 11=C(4,0)+C(4,1)+C(4,2)=1+4+6 (QBL boundary Fock count on 4 μ₄ corners=dim S⁺−g_car=16−5). The two CM rings (v222) and the seam boundary count meet in one operator center; the ring assignment is rigid.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv230_center_budget_norms.py", "sourceSha256": "bb8f9799f91891c2604351fee44f0fd8da1fb22c793b5f280ee076c8e826e61a", "linkedClaimIds": [ "CENTER.NORM.01" ], "sectionIds": [ "section:2678ed3ba0ed508e2d8e", "section:51e91159532ef7479ff8", "section:649c3b4e330a4dfc876d", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:b76309fbfced7aff0c43", "section:bb2a02a767e560376342" ], "activeSectionIds": [ "section:51e91159532ef7479ff8", "section:649c3b4e330a4dfc876d", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:bb2a02a767e560376342" ], "evidenceId": "python_verification:verification/v230_center_budget_norms.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v230_center_budget_norms.py", "pubMirrorHash": "bb8f9799f91891c2604351fee44f0fd8da1fb22c793b5f280ee076c8e826e61a", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v230_center_budget_norms.py" }, { "id": "v231_cp_mu6_phases", "filename": "v231_cp_mu6_phases.py", "path": "verification/v231_cp_mu6_phases.py", "cluster": "flavor", "synopsis": "Both CP phases are mu6 powers of ONE hexagonal CM unit, split by the sheet -- a structural reduction of red-team Target D. With rho=e^{i pi/3} (the j=0 Eisenstein CM unit): delta_CKM leading = arg(rho^1)=pi/3 (quark), delta_PMNS = arg(rho^4)=4pi/3 (lepton, the phase lattice); rho^4=-rho so delta_PMNS = delta_CKM,lead + pi = (CM unit)x(Z2 sheet, rho^3=-1) -- the two CP phases are ONE hexagonal unit on the two sheets, not two independent inputs. The C6/mu6 monodromy carries rho (charpoly t^6-1); the dual-frame orientations are sheet-flipped Im det(1,d,rho^1 n)=+21 sin(pi/3), Im det(1,d,rho^4 n)=-21 sin(pi/3). NEG: mu3 has no -1 (no sheet). Removes one of Target D's two phase inputs; the quark seam correction 3 lambda_C^2 stays the v88 misalignment, the deck stays Z/4.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv231_cp_mu6_phases.py", "sourceSha256": "9e3567f184de3b5ec14f21df3c969d89bf3953d69edc288c29a3b564ccad3b26", "linkedClaimIds": [ "CP.MU6.01" ], "sectionIds": [ "section:05558e866dc724bc0fcb", "section:49c4830cbc40c1211137", "section:4a3638ac1b45d771412e", "section:51b5da5a67a36e5155ae", "section:697c671889813baf24f5", "section:7a7de20f53ed3e69fb6f", "section:ab9e7e520130ecc7da7c" ], "activeSectionIds": [ "section:05558e866dc724bc0fcb", "section:49c4830cbc40c1211137", "section:4a3638ac1b45d771412e", "section:697c671889813baf24f5", "section:7a7de20f53ed3e69fb6f", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v231_cp_mu6_phases.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v231_cp_mu6_phases.py", "pubMirrorHash": "9e3567f184de3b5ec14f21df3c969d89bf3953d69edc288c29a3b564ccad3b26", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v231_cp_mu6_phases.py" }, { "id": "v232_e8_kleinian_seam", "filename": "v232_e8_kleinian_seam.py", "path": "verification/v232_e8_kleinian_seam.py", "cluster": "horizon", "synopsis": "The seam as the E8 Kleinian singularity -- a canonical algebraic-geometric MODEL for the open seam-realisation premise QGEO.REALIZE.01 (the du Val side of the McKay correspondence, v219). The McKay graph of 2I is affine E8; dropping the unique trivial-rep node (single Kac mark=1) leaves the finite E8 Dynkin on 8 nodes = the dual intersection graph of the 8 exceptional P^1's of the minimal resolution of C^2/2I (trivalent node, arms 1,2,4). EIGHT exceptional P^1's = rank E8 = g_car+N_fam = #nontrivial 2I irreps -- a fourth reading of the '8'. The negated intersection form is the E8 Cartan (even, det 1, positive definite; each P^1 a (-2)-curve). One degree-1 irrep => 2I perfect => H1(S^3/2I)=0: the link is the Poincare homology 3-sphere, pi1=2I order 120=|R+(E8)|. Seam reading: the raw RP seam (P^1 with marks) is canonically a du Val exceptional curve -- a model for QGEO.REALIZE.01, not a P2 proof (presupposes E8).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv232_e8_kleinian_seam.py", "sourceSha256": "c561d42e5b6d446d84726549ecf57dd6a878151b771b40fd70c24761c47a0c06", "linkedClaimIds": [ "TOPO.E8.01" ], "sectionIds": [ "section:00c96659d1c56ecb746e", "section:05558e866dc724bc0fcb", "section:09b49009253acb5a0dfb", "section:2585b5d786c3bdb7ddb7", "section:2b8d2aba4baeb7a0c36b", "section:303925994b6f141b3a0e", "section:3cc790136e8b9bd3c188", "section:584e87a9c163ac38f92f", "section:6a93c4dd5fe420e1990e", "section:7a7de20f53ed3e69fb6f", "section:81a6dc002dc46cf7b6c5", "section:a153934887244824336d", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:ca7f6aced60b17ae6709", "section:d90bd5e1e6d8fa41397d", "section:eb0bd97fda8c0fedefad", "section:ee9a2e2d9ccdc3799662", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:00c96659d1c56ecb746e", "section:05558e866dc724bc0fcb", "section:2585b5d786c3bdb7ddb7", "section:584e87a9c163ac38f92f", "section:7a7de20f53ed3e69fb6f", "section:81a6dc002dc46cf7b6c5", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:ca7f6aced60b17ae6709", "section:ee9a2e2d9ccdc3799662", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v232_e8_kleinian_seam.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v232_e8_kleinian_seam.py", "pubMirrorHash": "c561d42e5b6d446d84726549ecf57dd6a878151b771b40fd70c24761c47a0c06", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v232_e8_kleinian_seam.py" }, { "id": "v233_cp_triality_phase", "filename": "v233_cp_triality_phase.py", "path": "verification/v233_cp_triality_phase.py", "cluster": "flavor", "synopsis": "The CP phase is the UNIVERSAL family/triality phase, only sheet-split -- one step past v231 in mu6 = mu3 (family/triality) x mu2 (sheet). mu6=mu3 x mu2 (gcd(3,2)=1): the Z3 triality centre {1,omega,omega^2} = cusp weights {0,1/3,2/3}x2pi, sheet mu2={1,-1}; rho = omega^2*(-1). SAME FAMILY CLASS: rho^4 = rho^1*rho^3 with rho^3 in mu2, so quark (rho^1) and lepton (rho^4) CP phases have the SAME image in mu6/mu2~mu3 and OPPOSITE sheet -- so the CP phase IS the universal triality phase omega^2 (the 2/3 cusp-weight Z3 centre), NOT a free power choice. omega is the mu3 factor of the order-30 (2,3,5) monodromy that builds E8 (v232). Reduces Target D from 'one hexagonal unit + sheet' (v231) to 'the universal triality phase + sheet'; physical CP derivation stays [C].", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv233_cp_triality_phase.py", "sourceSha256": "43b34998aa882f2207fc1ebaa74b67cf157a5c8de977a62afa363d8f0284b94c", "linkedClaimIds": [ "CP.TRIALITY.01" ], "sectionIds": [ "section:05558e866dc724bc0fcb", "section:09b49009253acb5a0dfb", "section:3cc790136e8b9bd3c188", "section:49c4830cbc40c1211137", "section:4a3638ac1b45d771412e", "section:51b5da5a67a36e5155ae", "section:584e87a9c163ac38f92f", "section:697c671889813baf24f5", "section:7a7de20f53ed3e69fb6f", "section:ab9e7e520130ecc7da7c", "section:b3159de77fcabb12cc0c", "section:eb0bd97fda8c0fedefad" ], "activeSectionIds": [ "section:05558e866dc724bc0fcb", "section:49c4830cbc40c1211137", "section:4a3638ac1b45d771412e", "section:584e87a9c163ac38f92f", "section:697c671889813baf24f5", "section:7a7de20f53ed3e69fb6f", "section:ab9e7e520130ecc7da7c", "section:b3159de77fcabb12cc0c" ], "evidenceId": "python_verification:verification/v233_cp_triality_phase.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v233_cp_triality_phase.py", "pubMirrorHash": "43b34998aa882f2207fc1ebaa74b67cf157a5c8de977a62afa363d8f0284b94c", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v233_cp_triality_phase.py" }, { "id": "v234_seam_holomorphy_selection", "filename": "v234_seam_holomorphy_selection.py", "path": "verification/v234_seam_holomorphy_selection.py", "cluster": "frontier", "synopsis": "The Seam-Holomorphy selection certificate: the entire structural residual is ONE condition with THREE equivalent faces, all forcing E8. THE CONDITION: 'the seam carries no nontrivial abelian sector.' (i) AQFT: the boundary net is holomorphic (mu-index 1); (ii) geometry: the seam link is a homology 3-sphere <=> the binary group is perfect <=> 2I; (iii) rep theory: exactly one 1-dim irrep. #(mark-1 affine-Dynkin nodes) = |Gamma^ab| = |H1(S^3/Gamma)| = #(1-dim irreps): A_n->n+1, D_n->4, E6->3, E7->2, E8->1 -- ONLY E8 gives 1 (2I the unique perfect SU(2) subgroup, Poincare the unique homology-sphere space form). Holomorphic c=8=g_car+N_fam => unique even unimodular rank-8 lattice = E8. The three faces (v83/v154, v232, v219) are the SAME E8-selector, so Target A, G_net, P2 and the Kleinian seam are ONE gate. The closing theorem (stated, [O]): RP+gap+chirality => quasi-free bulk (v160) => invertible bulk => holomorphic boundary => E8; the single residual is 'free bulk => holomorphic boundary'.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv234_seam_holomorphy_selection.py", "sourceSha256": "58b8eb3621fcb2705f5a2d8345c31340fd1d279fd5a8d0848e354624f3713396", "linkedClaimIds": [ "GATE.HOLO.01" ], "sectionIds": [ "section:2585b5d786c3bdb7ddb7", "section:355a87dfaea9de9cb7cc", "section:6a93c4dd5fe420e1990e", "section:81a6dc002dc46cf7b6c5", "section:ab9e7e520130ecc7da7c", "section:cb1bdab881371b610e8f", "section:d3f2b7d7ec6acb95794a", "section:d90bd5e1e6d8fa41397d", "section:eea2436d67f35ca41c00", "section:f68163cf343646a0f102" ], "activeSectionIds": [ "section:2585b5d786c3bdb7ddb7", "section:355a87dfaea9de9cb7cc", "section:81a6dc002dc46cf7b6c5", "section:ab9e7e520130ecc7da7c", "section:eea2436d67f35ca41c00", "section:f68163cf343646a0f102" ], "evidenceId": "python_verification:verification/v234_seam_holomorphy_selection.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v234_seam_holomorphy_selection.py", "pubMirrorHash": "58b8eb3621fcb2705f5a2d8345c31340fd1d279fd5a8d0848e354624f3713396", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v234_seam_holomorphy_selection.py" }, { "id": "v235_seam_chern_simons", "filename": "v235_seam_chern_simons.py", "path": "verification/v235_seam_chern_simons.py", "cluster": "frontier", "synopsis": "The closing step in abelian Chern-Simons language: holomorphic <=> det K = 1 -- a genuine reduction (not a closure) of GATE.HOLO.01 into standard anyon-condensation physics. A free gapped bosonic 2+1d bulk = an even integer K-matrix with #anyons = |det K|, edge c = signature(K), holomorphic <=> |det K| = 1. The TFPT extension tower (v92) IS the condensation tower read by det: carrier D5(+)A3 (det 16, 16 anyons) -> SO(16)_1=D8 (det 4) -> (E8)_1 (det 1, holomorphic), all rank 8, c=signature=8=g_car+N_fam. Holomorphic <=> det 1 <=> E8 = the Kitaev E8 quantum-Hall state. Condensation: a Lagrangian glue of order sqrt(16)=|mu4|=4 takes det 16->1 (a partial order-2 isotropic only ->4=D8). NEG: D8 is free+bosonic but has 4 anyons; an odd K is fermionic -- det=1 is the extra condition. Residual: 'the free RP seam condenses the order-|mu4| Lagrangian glue' = the sheet/QGEO selection, now with holomorphy<=>det1 a theorem.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv235_seam_chern_simons.py", "sourceSha256": "47c41d25a809275988e6118db9d2870ed535084da6d05cbca1abd52d03f2d8e3", "linkedClaimIds": [ "GATE.HOLO.02" ], "sectionIds": [ "section:143e259e1ecb29356ac2", "section:2585b5d786c3bdb7ddb7", "section:6a93c4dd5fe420e1990e", "section:81a6dc002dc46cf7b6c5", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d", "section:f68163cf343646a0f102" ], "activeSectionIds": [ "section:143e259e1ecb29356ac2", "section:2585b5d786c3bdb7ddb7", "section:81a6dc002dc46cf7b6c5", "section:ab9e7e520130ecc7da7c", "section:f68163cf343646a0f102" ], "evidenceId": "python_verification:verification/v235_seam_chern_simons.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v235_seam_chern_simons.py", "pubMirrorHash": "47c41d25a809275988e6118db9d2870ed535084da6d05cbca1abd52d03f2d8e3", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v235_seam_chern_simons.py" }, { "id": "v236_brieskorn_capstone", "filename": "v236_brieskorn_capstone.py", "path": "verification/v236_brieskorn_capstone.py", "cluster": "horizon", "synopsis": "The (2,3,5) Brieskorn singularity x^2+y^3+z^5 is the ONE generator of the discrete skeleton -- the capstone of the icosahedral round (v55/v219/v223/v232/v233). Its exponents ARE the atoms (|Z2|,N_fam,g_car)=(2,3,5). Milnor number mu=(2-1)(3-1)(5-1)=1*2*4=8=rank E8 = the '8' in c3=1/(8 pi) (a fifth independent origin). The Milnor monodromy eigenvalues are the eight primitive 30th roots e^{2pi i m/30}, m the E8 exponents (charpoly Phi_30, deg phi(30)=8=mu) -- so it IS the order-30 E8 Coxeter element (v55). Both clocks: the monodromy group =Z/30=Z/2(sheet)xZ/3(family)xZ/5(carrier) carries the mu3 triality (CP, v233) as h^10; the Galois group (Z/30)^x=Z/2xZ/4 carries the mu4 clock (x7, v223). Milnor lattice=E8, link=Poincare sphere. One singularity generates atoms+8+E8+order30+both clocks+seam; a unification, not a closure.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv236_brieskorn_capstone.py", "sourceSha256": "7ddf6def219c8ff696c59a76c9ac94ee4338bbc32ad992fc2a0cb0cfb2bed1b3", "linkedClaimIds": [ "TOPO.BRIESKORN.01" ], "sectionIds": [ "section:0534241ef38a39dcc3cc", "section:09b49009253acb5a0dfb", "section:3cc790136e8b9bd3c188", "section:3ff315fdd4e19bf322ac", "section:584e87a9c163ac38f92f", "section:6a93c4dd5fe420e1990e", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:ca7f6aced60b17ae6709", "section:d90bd5e1e6d8fa41397d", "section:eb0bd97fda8c0fedefad" ], "activeSectionIds": [ "section:0534241ef38a39dcc3cc", "section:3ff315fdd4e19bf322ac", "section:584e87a9c163ac38f92f", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:ca7f6aced60b17ae6709" ], "evidenceId": "python_verification:verification/v236_brieskorn_capstone.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v236_brieskorn_capstone.py", "pubMirrorHash": "7ddf6def219c8ff696c59a76c9ac94ee4338bbc32ad992fc2a0cb0cfb2bed1b3", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v236_brieskorn_capstone.py" }, { "id": "v237_seam_sre_closure", "filename": "v237_seam_sre_closure.py", "path": "verification/v237_seam_sre_closure.py", "cluster": "frontier", "synopsis": "The closing step as a PHYSICAL condition: no topological ground-state degeneracy <=> det K=1 <=> the seam bulk is short-range-entangled (SRE/invertible). Sharpens GATE.HOLO.02's residual from definitional to physical/falsifiable. The K-matrix ground-state degeneracy on a genus-g surface is |det K|^g (carrier D5(+)A3->16, D8->4, E8->1 on the torus), so 'no degeneracy on any closed surface' <=> det K=1. Among rank-8 even positive-definite K (c=8=g_car+N_fam) only E8 has det 1 -- the unique nontrivial bosonic SRE 2+1d phase (Kitaev E8), edge holomorphic; D8/carrier are LRE. A unique vacuum on the plane (RP+gap+cluster) is necessary but not sufficient (the plane cannot see det K, the torus does), so the residual is exactly 'the seam unique-vacuum extends to the torus' = SRE. NEG: an LRE bulk (D8) has 4-fold torus degeneracy + non-holomorphic boundary. Sharpened residual: 'the free RP gapped seam is short-range-entangled (no topological order)' = det K=1 = the Kitaev E8 phase -- a yes/no statement, sharper than v235/QGEO.SYM.01. Not a closure.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv237_seam_sre_closure.py", "sourceSha256": "6c3345697ad31f738a1930f79312aac2d9a586bcbf5a274ea624b801e61f8dd6", "linkedClaimIds": [ "GATE.HOLO.03" ], "sectionIds": [ "section:2585b5d786c3bdb7ddb7", "section:6a93c4dd5fe420e1990e", "section:ab9e7e520130ecc7da7c", "section:d21a62fafd64ff24f0b6", "section:d90bd5e1e6d8fa41397d", "section:f68163cf343646a0f102", "section:fe85126d1b3e41ef8954" ], "activeSectionIds": [ "section:2585b5d786c3bdb7ddb7", "section:ab9e7e520130ecc7da7c", "section:d21a62fafd64ff24f0b6", "section:f68163cf343646a0f102", "section:fe85126d1b3e41ef8954" ], "evidenceId": "python_verification:verification/v237_seam_sre_closure.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v237_seam_sre_closure.py", "pubMirrorHash": "6c3345697ad31f738a1930f79312aac2d9a586bcbf5a274ea624b801e61f8dd6", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v237_seam_sre_closure.py" }, { "id": "v238_modular_lindblad_dynamics", "filename": "v238_modular_lindblad_dynamics.py", "path": "verification/v238_modular_lindblad_dynamics.py", "cluster": "registry", "synopsis": "DYN.SEMIGROUP.01 — the STATIC→DYNAMIC flip: the seam's modular flow (reversible) and its recovery channel read as a Markov/Lindblad generator (irreversible), with the dissipative gap = the OS mass gap. Companion to v196/v198 (modular) and v221/v64 (recovery), which state the structure statically; this reads the SAME objects dynamically. [E] the modular flow σ_t=e^{i t Λ_Σ} is a unitary one-parameter group (Tomita–Takesaki) and the µ4 clock is conserved ⟺ [ρ,Λ_Σ]=0 (the v198 state-invariance), so the static commutator IS the conservation law of modular time. [E] L=log T is a doubly-stochastic/CPTP-classical generator (off-diagonals ≥0, zero row sums), e^{L}=T, and e^{Lτ}→ the democratic projector (the arrow of time, cf. v64's Tⁿ→projector). [E] KEYSTONE: the dissipative gap = −log((2/3)⁶) = 6 log(3/2) = the OS mass gap Δ (v64) — the static recovery bound and the dynamical mass gap are ONE number, one exponentiated. [E] GKSL split (imaginary + real≤0 spectrum); NEG controls on µ4 and the rate. [O] geometric modular flow on the full seam algebra (Connes–Rovelli thermal time = QGEO.SYM.01, v198) — a target, not a closure.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv238_modular_lindblad_dynamics.py", "sourceSha256": "7938425550d9ad7f199e875f22c52609f4eeeb25b9f51df9a49af508a3576645", "linkedClaimIds": [ "DYN.SEMIGROUP.01" ], "sectionIds": [ "section:568b5e9acdb7b04367d3", "section:6a93c4dd5fe420e1990e", "section:817ba5dfc4c0aadf9e21", "section:9f084ccace7baa00bf8d", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:ca7f6aced60b17ae6709", "section:d90bd5e1e6d8fa41397d", "section:f0ac30137703825661c6", "section:f68163cf343646a0f102", "section:f6d50ad015506eb0de3c", "section:fdf63a1d99769ab37ccb" ], "activeSectionIds": [ "section:817ba5dfc4c0aadf9e21", "section:9f084ccace7baa00bf8d", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:ca7f6aced60b17ae6709", "section:f68163cf343646a0f102", "section:f6d50ad015506eb0de3c", "section:fdf63a1d99769ab37ccb" ], "evidenceId": "python_verification:verification/v238_modular_lindblad_dynamics.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v238_modular_lindblad_dynamics.py", "pubMirrorHash": "7938425550d9ad7f199e875f22c52609f4eeeb25b9f51df9a49af508a3576645", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v238_modular_lindblad_dynamics.py" }, { "id": "v239_kms_thermal_time", "filename": "v239_kms_thermal_time.py", "path": "verification/v239_kms_thermal_time.py", "cluster": "registry", "synopsis": "DYN.KMS.01 — KMS / thermal time: the modular flow of v238 makes the seam state a KMS (thermal) state at β=1, and the geometric normalisation fixes the seam temperature via 2π = 1/(4c3). [E] KMS at β=1: ω(A σ_i(B)) = ω(BA) (ω(X)=Tr(ρX), ρ=e^{−Λ_Σ}/Z), so modular time (v238) is a thermal time (Connes–Rovelli); NEG β≠1 fails (Tomita–Takesaki pins β=1). [E] the seam unit β_phys = 2π = 1/(4c3) (v58) makes the KMS temperature the horizon temperature T_H = c3/M (v57/v208) — thermal time = horizon time. [E] one object with v238 (same Λ_Σ generates σ_t and the Gibbs state). 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[E] GNS: ⟨A,B⟩=Tr(ρ A†B) Hermitian positive-definite (ρ>0), dim n², identity cyclic+separating. [E] modular flow σ_t(x)=ρ^{it} x ρ^{−it} is a state-preserving *-automorphism, generator i[log ρ,·]=Λ_Σ (v238). [E] OS Hamiltonian H_OS=−log T (the v221 transfer) is POSITIVE — eigenvalues {0, 6 log(3/2), 6 log 3}≥0, gap = 6 log(3/2) = the v64 mass gap — so OS reconstruction delivers v64's 'H≥0 + mass gap'. [E] H_OS=−L: the OS Hamiltonian is minus the v238 dissipative generator (recovery semigroup = Euclidean time); two Hamiltonians from one seam. 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Carrier form (Lean-verified, FORM.GLUE.01): on Z4×Z4, q(x,y)=(5x²+3y²)/8 mod 1, θ(a)=e^{2πi q(a)}. [E] 16 sectors = Z4×Z4 (= det K_carrier = dim S⁺), fusion = abelian group law. [E] bosonic/condensable ⟺ θ=1 ⟺ isotropic ⟺ 5x²+3y²≡0 mod 8 — the six elements {(0,0),(1,1),(1,3),(2,2),(3,1),(3,3)}. [E] condensation tower = v235/v237: Lagrangian ⟨(1,1)⟩ (order 4, self-dual) → 1 sector = (E8)₁; order-2 ⟨(2,2)⟩ → 4 = D8; carrier 16→D8 4→E8 1. [E] NEG: a non-isotropic anyon (1,0) is confined. [C] sector↔SM-multiplet map is the interpretation; the MTC is exact. 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Same MTC as v241 (Z4×Z4, q=(5x²+3y²)/8, θ=e^{2πi q}). [E] spin-statistics: T=diag(θ_a) → 6 bosons (θ=1), 2 fermions (θ=−1) = {(0,2),(2,0)}, 8 anyons. [E] modular S_ab=(1/√16)e^{−2πi B(a,b)} unitary, symmetric, S²=C (charge conjugation), S⁴=I. [E] Verlinde N_ab^c = Σ_x S_ax S_bx S*_cx / S_0x = δ(c,a+b) — fusion recovered from modular data. [E] Gauss–Milgram (1/√16)Σθ_a = e^{2πi c/8} with c=8=g_car+N_fam = the (E8)₁ central charge (v156/v175) — statistics and c=8 are one fact. [C] the boson/fermion split is the kinematic skeleton; sector↔multiplet map is the interpretation.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv242_spin_statistics_modular.py", "sourceSha256": "8855974b235303c015f8faed6da7058924dcd23d636f1d66480f83f445862278", "linkedClaimIds": [ "DHR.MODULAR.01" ], "sectionIds": [ "section:6a93c4dd5fe420e1990e", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d", "section:f091de1c3533bab48372", "section:f68163cf343646a0f102" ], "activeSectionIds": [ "section:ab9e7e520130ecc7da7c", "section:f091de1c3533bab48372", "section:f68163cf343646a0f102" ], "evidenceId": "python_verification:verification/v242_spin_statistics_modular.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v242_spin_statistics_modular.py", "pubMirrorHash": "8855974b235303c015f8faed6da7058924dcd23d636f1d66480f83f445862278", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v242_spin_statistics_modular.py" }, { "id": "v243_haag_ruelle_braiding", "filename": "v243_haag_ruelle_braiding.py", "path": "verification/v243_haag_ruelle_braiding.py", "cluster": "registry", "synopsis": "DHR.SMATRIX.01 — scattering: the Haag–Ruelle skeleton + the braiding S-matrix. The seam net has a mass gap (v64/v238) so Haag–Ruelle constructs asymptotic states; for the abelian anyon MTC (v241/v242) the 2-particle S-matrix is the monodromy M(a,b)=θ(a+b)/(θ(a)θ(b))=e^{2πi B(a,b)}. [E] mass gap Δ=6 log(3/2)>0 → HR in/out states (gapped-net theorem). [E] 2-particle S = monodromy: |M|=1, diagonal in conserved anyon labels → no particle production, factorised (integrable) scattering. [E] Yang–Baxter: M is a bicharacter → multi-particle factorisation. [E] crossing+symmetry: M(a,b)=M(b,a), M(a,−b)=M(a,b)*. [E] holomorphic point: on the condensed (E8)₁ (single sector) M=1, trivial braiding (det 1/SRE). 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A single Dirac operator whose Tr f(D/Λ) yields gravity AND matter. [E] carrier spinor = one generation: SO(10) half-spinor = dim S⁺ = 2^(g_car−1) = 16 (15 + ν_R), N_fam=3. [E] SM gauge group inside the carrier: SU(3)×SU(2)×U(1) (dim 12) ⊂ SU(5) (24) ⊂ SO(10)=D5 (45); color SU(3) ⊂ A3=SU(4) (Pati-Salam); rank(D5)+rank(A3)=8=rank E8. [E] one Dirac operator → gravity (a2~R, a4~R², v36) + matter (a4 ~ F² Yang–Mills + |Dφ|² Higgs, Gilkey). [X] hooks: g3=g2=√(5/3)g1 + a Higgs-quartic relation (Chamseddine–Connes–Marcolli). [O] CONTRACT.QFT4D.01: obligations (seam→Dirac D; finite geometry = carrier; spectral action reproduces SM couplings) → the 4d SM+gravity Lagrangian is an OUTPUT. 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[E] E8 Cartan even, det 1, positive-definite (the unique even unimodular pos-def rank-8 lattice); [E] K3 lattice L_K3=U^3(+)E8(-1)^2: rank 22=b_2, det -1 (unimodular), even, signature (3,19), E8(-1)^2 an orthogonal summand; [E] seam = T^2/(z->-z): 4=|(Z/2)^2| fixed points, pillowcase S^2(2,2,2,2), orbifold Euler char 0 (the v214/v216 four marks); [E] carrier-16 = Kummer nodes |A[2]|=2^4=16 -> 16 exceptional P^1 = dim S+ = Lambda^even(C^5) = 16 (v197), 16=4x4; [E] honesty: the 16 node classes span the rank-16 Kummer lattice, NOT literally E8(-1)^2 (distinct sublattices of H^2(K3)); [C] two faces of E8 in K3 (local du Val C^2/2I v232/v236; global H^2 summand); [C] unification (lattice [E], carrier<->node identification [C]).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv260_k3_kummer_unification.py", "sourceSha256": "c9c485642e8fec784ba6bb84df03805660cd2bf2f03d7d00f8815e9ead8a40c4", "linkedClaimIds": [ "ARCH.K3.01" ], "sectionIds": [ "section:213a1f15f7373957fc2f", "section:2525c189f32461c9368a", "section:355a87dfaea9de9cb7cc", "section:6a93c4dd5fe420e1990e", "section:6cd1a267e72b20619327", "section:72b43011ac4fb932c47a", "section:7ee581db787f8ddbcb4a", "section:81a6dc002dc46cf7b6c5", "section:888628823bf71f709698", "section:8d1e955857da6655fadd", "section:a153934887244824336d", "section:a29d0e884b184665e5ef", "section:a9e4936094020237f825", "section:ab9e7e520130ecc7da7c", "section:b93e6ae7b00f32ee1201", "section:bc61b0e372551b770dfb", "section:c519f45910c30ff3c0ae", "section:ca7f6aced60b17ae6709", "section:cb1bdab881371b610e8f", "section:cdda6bb5746f6a6a897d", "section:d3f2b7d7ec6acb95794a", "section:d90bd5e1e6d8fa41397d", "section:eea2436d67f35ca41c00", "section:eef94f3ff4627b2515d5", "section:f03ad4dd64724fcfb725", "section:f1a0b6f25c4c201d4774" ], "activeSectionIds": [ "section:213a1f15f7373957fc2f", "section:355a87dfaea9de9cb7cc", "section:72b43011ac4fb932c47a", "section:81a6dc002dc46cf7b6c5", "section:888628823bf71f709698", "section:8d1e955857da6655fadd", "section:a153934887244824336d", "section:a29d0e884b184665e5ef", "section:ab9e7e520130ecc7da7c", "section:bc61b0e372551b770dfb", "section:ca7f6aced60b17ae6709", "section:cdda6bb5746f6a6a897d", "section:eea2436d67f35ca41c00", "section:f1a0b6f25c4c201d4774" ], "evidenceId": "python_verification:verification/v260_k3_kummer_unification.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v260_k3_kummer_unification.py", "pubMirrorHash": "c9c485642e8fec784ba6bb84df03805660cd2bf2f03d7d00f8815e9ead8a40c4", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v260_k3_kummer_unification.py" }, { "id": "v261_modular_spectral_closure", "filename": "v261_modular_spectral_closure.py", "path": "verification/v261_modular_spectral_closure.py", "cluster": "registry", "synopsis": "QFT.MSC.01 — the MODULAR SPECTRAL CLOSURE: the assembly/reduction certificate turning the whole QFT layer (v238-v260) into ONE relative object TFPT_QFT=(A_Sigma,omega_Sigma,Delta_Sigma,rho,A_F,H_F,D_F,J,gamma,S_rel) reduced to ONE open premise (like v176/v234, an assembly cert, not new physics). [E] one index=marks=fixed points=glue order: Jones [B:A]=4 (v89) = |mu4|=4 (v92) = seam marks 2chi=4 (v216) = pillowcase/Kummer fixed points |(Z/2)^2|=4 (v260); [E] one carrier-16: dim S+=Lambda^even(C^5)=Kummer nodes 2^4=16, H_F=2 N_fam 16=96; [E] one gap Delta=-log((2/3)^6)=6log(3/2)>0 = OS mass gap (v240)=recovery rate (v221)=Lindblad gap (v238); [E] the three closures re-derived (Kasparov log((1-C)C^-1)=H v258, KMS cutoff f2/f0=1 v259, K3 lattice signature (3,19)/det-1/even v260); [E] relative-object manifest (10/10 component scripts present); [O] the single residual: the whole QFT layer reduces to QGEO.SYM.01 (seam realisation), ambient QG QG.AMB.01 separate; [C] master statement (Modular Spectral Universality) modulo QGEO.SYM.01 -- the honest sense in which the QFT layer is complete.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv261_modular_spectral_closure.py", "sourceSha256": "48b45cf116968f3f225fc1691d08ac11e466d7faca0948c6a413bc10897b03d0", "linkedClaimIds": [ "QFT.MSC.01" ], "sectionIds": [ "section:213a1f15f7373957fc2f", "section:2525c189f32461c9368a", "section:33f8ca97d5f5599b425b", "section:6a93c4dd5fe420e1990e", "section:6cd1a267e72b20619327", "section:72b43011ac4fb932c47a", "section:7ee581db787f8ddbcb4a", "section:817ba5dfc4c0aadf9e21", "section:81a6dc002dc46cf7b6c5", "section:888628823bf71f709698", "section:8d1e955857da6655fadd", "section:9d6c7d63f5df5a4df579", "section:a153934887244824336d", "section:a29d0e884b184665e5ef", "section:ab9e7e520130ecc7da7c", "section:b93e6ae7b00f32ee1201", "section:c519f45910c30ff3c0ae", "section:ca7f6aced60b17ae6709", "section:d90bd5e1e6d8fa41397d", "section:eef94f3ff4627b2515d5", "section:fe4822aaeee66083bf56" ], "activeSectionIds": [ "section:213a1f15f7373957fc2f", "section:72b43011ac4fb932c47a", "section:817ba5dfc4c0aadf9e21", "section:81a6dc002dc46cf7b6c5", "section:888628823bf71f709698", "section:8d1e955857da6655fadd", "section:9d6c7d63f5df5a4df579", "section:a153934887244824336d", "section:a29d0e884b184665e5ef", "section:ab9e7e520130ecc7da7c", "section:ca7f6aced60b17ae6709", "section:fe4822aaeee66083bf56" ], "evidenceId": "python_verification:verification/v261_modular_spectral_closure.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v261_modular_spectral_closure.py", "pubMirrorHash": "48b45cf116968f3f225fc1691d08ac11e466d7faca0948c6a413bc10897b03d0", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v261_modular_spectral_closure.py" }, { "id": "v262_fqcd_mp_me", "filename": "v262_fqcd_mp_me.py", "path": "verification/v262_fqcd_mp_me.py", "cluster": "registry", "synopsis": "FR.MPME.02 — the F_QCD transfer pipeline for m_p/m_e, implemented as a real solver (the one F_transfer pipeline that was contract-only, experiments/ftransfer/qcd_matching_mp_me). NOT a compiler power -- a [C] standard-physics transfer reproduction. [E] b3=-7=-(11-2 n_f/3) at n_f=6 (the SM/SU(3) one-loop coefficient, the only TFPT number in the run); [N] 2-loop alpha_s(M_Z)=0.1179 run down with thresholds gives alpha_s(2 GeV)~0.30 (real ODE solve); [C] Lambda^(3)_MSbar~0.33 GeV x lattice C_p=m_p/Lambda (external O(1)) over the closed m_e gives m_p/m_e~1824 vs measured 1836.15 within ~7% external budget; [X] firewall: m_p/m_e is not an admissible compiler integer (SU(9) absent from D5(+)A3), stays [C]. 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[E] M_nu=-m_D M_R^{-1} m_D^T symmetric + seesaw-suppressed (light masses an output of D_F, not a fit matrix); [E] mu-tau-symmetric (m_D,M_R) give mu-tau-symmetric M_nu (the v9 texture is in the seesaw image); [C] diagonalising gives theta23=45deg and sin^2 theta12=1/3-phi0/2=0.30675 under the seam misalignment, reproducing v9; [O] theta13=0 in the leading texture (physical sin^2 th13~phi0 e^{-5/6} a separate readout), CP magnitude delta_PMNS=240deg from mu6/triality (v231/v233) not from M_nu, M_R the free seesaw scale. 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Two-step PS solve + d=6 tau_p(p->e+pi0); the carrier-native PS UV branch survives proton decay ONLY with the E8-allowed (15,1,1) [single 45]: minimal 16-Higgs M_GUT~2.4e15 -> tau_p~4.4e33 yr KILLED by Super-K (2.4e34), +(15,1,1) M_GUT~5.9e15 -> tau_p~1.6e35 yr safe now but at the Hyper-K reach (~1.4e35) -> a dated kill test within the decade. Marginal (only ONE 45 in the hull, v247) + O(3) hadronic uncertainty. 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[E] an order-4 Moebius orbit {a,ia,-a,-ia} has cross-ratio 2 (independent of a); [E] cross-ratio 2 <=> j=1728 (only lambda in {-1,1/2,2}) <=> the order-4 CM automorphism (x,y)->(-x,iy) on y^2=x^3-x; [E] downstream forced: square => unique flat pillowcase (Troyanov, v214) => curvature at the 4 marks => Z4-Fourier DtN (v201/v264) => [rho,Lambda]=0 => omega o rho=omega (v198); [E] neg controls (generic j!=1728 only Z2; hexagonal j=0 has Z6, order 6 != 4); [C] arithmetic rigidity ({1,i,-1,-i} over Q, j=1728 CM by Z[i], Belyi/dessins); [O] the bare order-4 symmetry stays the one foundational postulate (like c=const). 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The value sin^2 theta_13 = phi0 e^{-5/6} = 0.0231 was already checked (v16); here the exponent origin is closed exactly: gamma = tr_E Y^2 = 3(1/3)^2+2(1/2)^2 = 5/6 over the 5-slot carrier hypercharge Y=diag(-1/3,-1/3,-1/3,1/2,1/2) (roots of 6Y^2-Y-1=0), complement 1/6 = the neutrino ratio. Own channel: the mu-tau-breaking eps=3phi0/4 (which gives theta_12) induces only ~1.6e-3 << 0.023, so theta_13 is a SEPARATE carrier-trace channel, not the seesaw mu-tau breaking (corrects the tempting 'theta_13 from M_nu' route). 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[E] three distinct layers (the 2d braiding |M|=1 is statistics, not 4d cross-sections); [E] every spectral-action a_4 operator has mass dim <= 4 in 4D (power-counting renormalizable); [E] finite counterterm basis (7 marginal + 3 relevant, no infinite tower); [C] Epstein-Glaser existence -- a renormalizable interaction has an order-by-order S(g)=T exp(i int g L_int) by causal factorisation + finite local extension, no path integral, no UV divergences; [C] adiabatic limit/gap (Delta=6log(3/2)>0) -> S_phys via LSZ; [O] perturbative only, the ambient measure QG.AMB.01 stays open. 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[E] the three angle channels; [E] U=R23·U13(δ)·R12 is exactly unitary; [C] J_PMNS=Im(U_e1 U_mu2 U*_e2 U*_mu1)=-0.02965 (formula and full matrix agree), J_max=0.03424 — a DERIVED CP strength, the leptonic analogue of the CKM J (v88); [C] data: J_max vs NuFIT 0.0332 (~3%), J vs best fit -0.026, negative sign reproduced; [O] δ is the μ6/triality phase (assembled input, NOT from M_ν/D_F) and the absolute ν-mass scale (Σm_ν, M_R) stays open. 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[E] T_1=:L_int: needs no extension, the first extension is T_2; [E] the massless propagator has scaling degree sd=2 in d=4, the one-loop bubble (two propagators) has sd=4=d so the UV singular order omega=sd-d=0; [E] omega=0 => exactly one logarithmic local counterterm (C(omega+d,d)=1, renormalizable, no infinite tower); [E] the loop factor Omega_3/(2(2pi)^4)=1/(16 pi^2) exactly — the same factor that normalises the spectral-action a_4 geometric quartic; [C] the phi^4 one-loop beta = 3 lambda^2/(16 pi^2) (symmetry factor 3 = s,t,u channels), EG initial condition lambda_Phi(UV)=1/(16 pi^2); [O] order-2/one-loop only — the all-order EG construction and the nonperturbative measure QG.AMB.01 stay open. 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[E] the absolute scale reduces to ONE seesaw ratio m₃=(y_ν v_EW)²/M_R — one irreducible UV input like v_geo (v153), while the ratios (m2/m3, ordering, PMNS angles v270) are pinned; [N] the observed m₃=0.050 eV with the TFPT PS→GUT window M_R∈[4.2e13, 2.4e15] GeV (v249) needs a third-gen Dirac Yukawa y_ν∈[0.26, 2.0] — O(1), no tuning; [O] M_R(y=1)=6.1e14 has log_c3(M_R/Mbar)=2.57 (non-integer), not a TFPT power, so the absolute value stays open; [C] the NO floor Σm_ν=0.0586 eV is consistent with cosmology (<0.072–0.12 eV); [X] a cosmological Σ<0.0586 eV excludes the normal-ordered m1~0 spectrum. Closes the PMNS bookkeeping (the last [O] is one seesaw ratio), not the absolute number. Sharpened by v481: under the carrier normalisation y_nu = y_t the (y_nu, M_R) trade-off collapses to one parameter, window-bracketed (candidate class).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv272_nu_mass_scale.py", "sourceSha256": "9de47673cd77626a47c9e15ce3292414cf80514ecd95e4256e38a3a33ffe03e0", "linkedClaimIds": [ "FLAV.NUSCALE.01" ], "sectionIds": [ "section:20ef03b5c6c62b042300", "section:213a1f15f7373957fc2f", "section:3317d161dfba545d677a", "section:366ba63a37a50edd34ea", "section:51b5da5a67a36e5155ae", "section:63427eabab107d1a2a94", "section:697c671889813baf24f5", "section:ab9e7e520130ecc7da7c", "section:bc61b0e372551b770dfb", "section:c00f76407fefd9782fd7", "section:e99d6098550f62e277de" ], "activeSectionIds": [ "section:20ef03b5c6c62b042300", "section:213a1f15f7373957fc2f", "section:3317d161dfba545d677a", "section:366ba63a37a50edd34ea", "section:63427eabab107d1a2a94", "section:697c671889813baf24f5", "section:ab9e7e520130ecc7da7c", "section:bc61b0e372551b770dfb", "section:c00f76407fefd9782fd7", "section:e99d6098550f62e277de" ], "evidenceId": "python_verification:verification/v272_nu_mass_scale.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v272_nu_mass_scale.py", "pubMirrorHash": "9de47673cd77626a47c9e15ce3292414cf80514ecd95e4256e38a3a33ffe03e0", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v272_nu_mass_scale.py" }, { "id": "v273_eg_gauge_running", "filename": "v273_eg_gauge_running.py", "path": "verification/v273_eg_gauge_running.py", "cluster": "registry", "synopsis": "QFT4D.SPERT.03 — the gauge sector of the EG one-loop (v271's quartic mechanism applied to the gauge self-energy). [E] the one-loop gauge 2-point has scaling degree sd=4=d so ω=0 → one counterterm per coupling (same marginal mechanism + loop factor 1/(16π²) as v271); [E] the one-loop b_i from the explicit carrier/SM content: b₃=-(11/3)(3)+(2/3)(6)=-7, b₂=-(11/3)(2)+(2/3)(6)+(1/3)(1/2)=-19/6, b₁=(3/5)[(2/3)(10)+(1/3)(1/2)]=41/10 (the same 41 as the carrier algebra, v159/CAR.SM.01); [C] physical RG directions b₃<0 (asymptotic freedom), b₁>0 (U(1) Landau); [O] the two-loop matrix (v159 PyR@TE) + all-order stay open. Shows the gauge running is an EG order-2 result, the gauge analogue of v271's quartic. 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[E] one anchor (No-Unit, v153): every dimensionful output = pure number × M_bar^d (ρ_Λ/M_bar⁴, M_scal/M_bar=c3^{7/2}, the spectrum); [N] two independent routes to M_bar agree: gravity (8πG)^{-1/2}=2.4353e18 GeV and cosmology (invert ρ_Λ/M_bar⁴=(3/4π²)e^{-2α⁻¹} with ρ_Λ^{1/4}=2.24 meV)=2.438e18 GeV, to 0.11%; [E] the anchor is the gravitational unit (G), the one measured dimensionful input of all physics; [E] theorem not gap: the seam is a conformal c=8 CFT (v157/v158), scale-invariant by construction → no intrinsic scale, the scale is gravitational; [A] scale-complete up to one over-determined anchor = maximal predictivity. 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[E] Tier A gap decoupling: Δ_eff=6log(3/2)-2·248 c3²=1.648>0 (v36/v76), so every low-energy readout is independent of the un-built measure — not a blocker; [E]/[P] Tier B: the bulk measure reduces to identifying the seam-Calderón boundary with the holomorphic (E8)_1 net (c=248/31=8; v77/GATE.METRIC.03), reduced not closed (REDTEAM.A.01); [C] the perturbative layer is in hand (v269/v271/v273); [O] the nonperturbative ambient measure is NOT constructed — the one genuine structural frontier; [X] closes IFF seam net=(E8)_1 AND bulk reconstruction proved. 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[E] c=8 (Sugawara, 248/31=g_car+N_fam), but c=8 alone does not pin the net; [E] the discriminator is holomorphy — det Cartan(E8)=1 (1 primary, holomorphic) vs the c=8 counterexample det Cartan(D8=SO(16))=4 (4 primaries, non-holomorphic), so the single discriminator is |det K|=1; [E] the (E8)₁ character E4/η⁸=j^{1/3}=q^{-1/3}(1+248q+4124q²+…) has a single primary + exactly 248=dim E8 weight-1 currents (240 roots); [E] equivalence chain holomorphic ⟺ det Cartan 1 ⟺ unique even unimodular rank-8 (v83) ⟺ homology-sphere link ⟺ |det K|=1 (v235); [C] seam-side match via v276 (flat τ=i) + v260 (Kummer/K3); [O] residual = the single holomorphy bit, reduced to one bit, NOT closed (rt_A verdict stands).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv277_seam_calderon_e8_match.py", "sourceSha256": "fb151c3f0d8e523d1c96710d79057964c0800aa3cd45913e9c090d33145921da", "linkedClaimIds": [ "QGAMB.TIERB.01" ], "sectionIds": [ "section:213a1f15f7373957fc2f", "section:2ee299d2f97d03685885", "section:355a87dfaea9de9cb7cc", "section:6a93c4dd5fe420e1990e", "section:8e4972dbe899b5debb90", "section:98e28332378f4d77a163", "section:a5034e3be2279bec9f75", "section:ab9e7e520130ecc7da7c", "section:bc61b0e372551b770dfb", "section:c6b6da016e7f30bbb7c1", "section:cb1bdab881371b610e8f", "section:d3f2b7d7ec6acb95794a", "section:d90bd5e1e6d8fa41397d", "section:eea2436d67f35ca41c00", "section:f1a0b6f25c4c201d4774", "section:f5274c8105ff62e99dcd", "section:f68163cf343646a0f102" ], "activeSectionIds": [ "section:213a1f15f7373957fc2f", "section:2ee299d2f97d03685885", "section:355a87dfaea9de9cb7cc", "section:8e4972dbe899b5debb90", "section:98e28332378f4d77a163", "section:a5034e3be2279bec9f75", "section:ab9e7e520130ecc7da7c", "section:bc61b0e372551b770dfb", "section:c6b6da016e7f30bbb7c1", "section:eea2436d67f35ca41c00", "section:f1a0b6f25c4c201d4774", "section:f5274c8105ff62e99dcd", "section:f68163cf343646a0f102" ], "evidenceId": "python_verification:verification/v277_seam_calderon_e8_match.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v277_seam_calderon_e8_match.py", "pubMirrorHash": "fb151c3f0d8e523d1c96710d79057964c0800aa3cd45913e9c090d33145921da", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v277_seam_calderon_e8_match.py" }, { "id": "v278_lsz_bridge_unitarity", "filename": "v278_lsz_bridge_unitarity.py", "path": "verification/v278_lsz_bridge_unitarity.py", "cluster": "registry", "synopsis": "QFT4D.SPERT.04 — the S_pert → S_phys LSZ bridge + one-loop unitarity: connects the EG perturbative S-matrix (v269/v271/v273) to the physical asymptotic S-matrix (S_phys = LSZ on the OS Wightman functions, v240). 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[E] the reduction DAG from 'free RP seam' has 8 closed nodes and EXACTLY ONE open leaf ('the raw seam state IS the flat state'); [E] the geometric side is fixed (flat DtN diagonal, ρ commutes to all orders, Lean FORM.QGEO.04), so the obligation is STATE-IDENTIFICATION not geometric ambiguity; [C] two proof routes (RP-state uniqueness on the flat orbifold, or Troyanov + OS); [F] the all-orders step is a Lean theorem (SeamDeckClosure.flat_all_orders_clock, standard axioms, no sorry); [O] one constructive-QFT statement closes QGEO.SYM.01.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv279_qgeo_obligation_lemma.py", "sourceSha256": "5787b161895ee271bfb1c3497b87bf01bcfbcdd555acc03f78514b80e4adb091", "linkedClaimIds": [ "QGEO.OBLIG.01" ], "sectionIds": [ "section:47adde543bdad0ea081f", "section:6a93c4dd5fe420e1990e", "section:93b8868beb643874af75", "section:ab9e7e520130ecc7da7c", "section:d0d4a62b7872b9bb3a1c", "section:d90bd5e1e6d8fa41397d", "section:eb00caf29086b02d5bf5", "section:f68163cf343646a0f102" ], "activeSectionIds": [ "section:47adde543bdad0ea081f", "section:ab9e7e520130ecc7da7c", "section:d0d4a62b7872b9bb3a1c", "section:f68163cf343646a0f102" ], "evidenceId": "python_verification:verification/v279_qgeo_obligation_lemma.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v279_qgeo_obligation_lemma.py", "pubMirrorHash": "5787b161895ee271bfb1c3497b87bf01bcfbcdd555acc03f78514b80e4adb091", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v279_qgeo_obligation_lemma.py" }, { "id": "v280_pillowcase_steklov", "filename": "v280_pillowcase_steklov.py", "path": "verification/v280_pillowcase_steklov.py", "cluster": "registry", "synopsis": "QGEO.STEKLOV.01 — a direct numerical experiment on the flat τ=i pillowcase orbifold (the seam geometry): the self-investigable test of the QGEO.SYM.01 obligation (does NOT prove the premise). 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[E] #anyons=|det Gram|: E8→1 (holomorphic), D8=SO(16)→4, carrier D5⊕A3→16; [E] the anyon-condensation tower D5⊕A3 (16) → D8 (4) → E8 (1), each step condensing a Lagrangian Z2 boson (|det|/4=2²), the Kitaev E8 endpoint (v92/v235); [E] Gauss-Milgram (D8 spins 0,1/2,1,1) recovers c=8; [E] E8 is the unique holomorphic c=8 (det 1) — SO(16) has the same c=8 but 4 anyons, so holomorphy is THE discriminator (v277); [O] the open bit: does the seam-Calderón net condense to det K=1? 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[E] τ=i is the order-4 CM point (j=1728, the QGEO.SYM.01 flat geometry); [E] χ_E8=j^{1/3} (χ³=q·j as q-series), so χ_E8(i)=1728^{1/3}=12 (the (E8)₁ character at the SAME τ=i, the QG.AMB.01 holomorphy); [E] one object, two faces — τ=i is both the order-4 CM point and the (E8)₁ partition-function modulus; [C] obligation count 2→1: prove 'the raw seam is (E8)₁ at τ=i' and BOTH QGEO.SYM.01 and QG.AMB.01 follow; [O] the unified premise stays open but is now ONE object. A genuine reduction of the open count, not a closure.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv282_e8_tau_i_unification.py", "sourceSha256": "435c7b255f4aaa4c9871979d072a55bdef186bab95e752d9267f487faead5d45", "linkedClaimIds": [ "QGAMB.UNIFY.01" ], "sectionIds": [ "section:213a1f15f7373957fc2f", "section:2b8d2aba4baeb7a0c36b", "section:2c657950cbbf3e8129b9", "section:303925994b6f141b3a0e", "section:5573768c07b5b0367bc7", "section:6a93c4dd5fe420e1990e", "section:8e3e6d08d3c102a09298", "section:98e28332378f4d77a163", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d", "section:f1054498b80cd7df6676", "section:f68163cf343646a0f102", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:213a1f15f7373957fc2f", "section:2c657950cbbf3e8129b9", "section:5573768c07b5b0367bc7", "section:8e3e6d08d3c102a09298", "section:98e28332378f4d77a163", "section:ab9e7e520130ecc7da7c", "section:f1054498b80cd7df6676", "section:f68163cf343646a0f102", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v282_e8_tau_i_unification.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v282_e8_tau_i_unification.py", "pubMirrorHash": "435c7b255f4aaa4c9871979d072a55bdef186bab95e752d9267f487faead5d45", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v282_e8_tau_i_unification.py" }, { "id": "v283_live_killtest_scorecard", "filename": "v283_live_killtest_scorecard.py", "path": "verification/v283_live_killtest_scorecard.py", "cluster": "frontier", "synopsis": "PRED.LIVE.01 — a live kill-test scorecard of the recent round's computable predictions vs current data, each tagged with the decisive experiment. [N] PMNS angles sin²θ₁₂=0.30675 (+0.31σ), sin²θ₁₃=0.02311 (+1.45σ), θ₂₃ maximal; [C] leptonic CP J_PMNS=−0.0297 (J_max ~3% from NuFIT), δ=240° vs ~232(30); [X] Σm_ν NO floor=0.0586 eV (consistent at the edge, DESI/CMB-S4 decisive); [X] proton decay τ_p=1.55e35 yr for +(15,1,1) (safe; minimal excluded; Hyper-K decisive); [N] closed readouts α⁻¹, Ω_b=0.04894, β=0.2424°; [N] all rows consistent < 2σ, 2 sharp near-term kill tests. A consolidation, not new physics.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv283_live_killtest_scorecard.py", "sourceSha256": "bf6361dce5d1e0f00783e55f40fc70e6e2c60558a416b556b95bfe360ba382df", "linkedClaimIds": [ "PRED.LIVE.01" ], "sectionIds": [ "section:5573768c07b5b0367bc7", "section:ab9e7e520130ecc7da7c", "section:bc61b0e372551b770dfb" ], "activeSectionIds": [ "section:5573768c07b5b0367bc7", "section:ab9e7e520130ecc7da7c", "section:bc61b0e372551b770dfb" ], "evidenceId": "python_verification:verification/v283_live_killtest_scorecard.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v283_live_killtest_scorecard.py", "pubMirrorHash": "bf6361dce5d1e0f00783e55f40fc70e6e2c60558a416b556b95bfe360ba382df", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v283_live_killtest_scorecard.py" }, { "id": "v284_route_i_rp_uniqueness", "filename": "v284_route_i_rp_uniqueness.py", "path": "verification/v284_route_i_rp_uniqueness.py", "cluster": "registry", "synopsis": "QGEO.ROUTEI.01 — Route (i) (RP-state uniqueness) decomposed into a 6-lemma chain with every dischargeable lemma discharged and the one irreducible lemma isolated (does NOT prove the open premise). [E] 5/6 lemmas are existing [E]/[F] results — L1 RP→DtN (v194), L2 the four marks force the pillowcase class (v195/v216/v214), L3 the flat orbifold Steklov operator = √(−Δ_flat) (verified: flat-strip DtN(k)/k→1, principal symbol |ξ| with no curvature term), L4 covariance C=(1+e^H)⁻¹ from the DtN (v258), L5 μ4-invariance (v276/Lean/v280); [C] Troyanov reduction: 4 cone points of angle π ⇒ χ_orb=0 ⇒ the unique constant-curvature representative is flat (τ=i), so L_open reduces to 'the raw seam is the constant-curvature geometric state'; [O] the ONE open lemma — the raw RP seam state is the constant-curvature/geometric state (the state-identification theory-selection step).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv284_route_i_rp_uniqueness.py", "sourceSha256": "7932341d652430fffb165ee11990fc6d78e62f749c9bab92e7bba3fd70bba6dd", "linkedClaimIds": [ "QGEO.ROUTEI.01" ], "sectionIds": [ "section:2b8d2aba4baeb7a0c36b", "section:2c657950cbbf3e8129b9", "section:303925994b6f141b3a0e", "section:414a84d23afa6566ca5e", "section:6a93c4dd5fe420e1990e", "section:93b8868beb643874af75", "section:9800e2e20cb3dc2e280a", "section:98e28332378f4d77a163", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:d0d4a62b7872b9bb3a1c", "section:d90bd5e1e6d8fa41397d", "section:eb00caf29086b02d5bf5", "section:f68163cf343646a0f102", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:2c657950cbbf3e8129b9", "section:414a84d23afa6566ca5e", "section:9800e2e20cb3dc2e280a", "section:98e28332378f4d77a163", "section:ab9e7e520130ecc7da7c", "section:d0d4a62b7872b9bb3a1c", "section:f68163cf343646a0f102", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v284_route_i_rp_uniqueness.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v284_route_i_rp_uniqueness.py", "pubMirrorHash": "7932341d652430fffb165ee11990fc6d78e62f749c9bab92e7bba3fd70bba6dd", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v284_route_i_rp_uniqueness.py" }, { "id": "v285_route_ii_seam_condensation", "filename": "v285_route_ii_seam_condensation.py", "path": "verification/v285_route_ii_seam_condensation.py", "cluster": "frontier", "synopsis": "", "publicationNotes": [ "Non-scientific synopsis omitted." ], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv285_route_ii_seam_condensation.py", "sourceSha256": "e93c5a6a989bf457455435854f1b983b820e4703b29ac95af9cf8908b874b516", "linkedClaimIds": [ "QGAMB.ROUTEII.01" ], "sectionIds": [ "section:2c657950cbbf3e8129b9", "section:6a93c4dd5fe420e1990e", "section:98e28332378f4d77a163", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d", "section:f68163cf343646a0f102" ], "activeSectionIds": [ "section:2c657950cbbf3e8129b9", "section:98e28332378f4d77a163", "section:ab9e7e520130ecc7da7c", "section:f68163cf343646a0f102" ], "evidenceId": "python_verification:verification/v285_route_ii_seam_condensation.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v285_route_ii_seam_condensation.py", "pubMirrorHash": "e93c5a6a989bf457455435854f1b983b820e4703b29ac95af9cf8908b874b516", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v285_route_ii_seam_condensation.py" }, { "id": "v286_seam_equivalence_contract", "filename": "v286_seam_equivalence_contract.py", "path": "verification/v286_seam_equivalence_contract.py", "cluster": "frontier", "synopsis": "SEAM.EQUIV.01 — the Seam Equivalence contract: concentrates the whole open structure on ONE named arrow (does NOT prove it). Theorem: the raw RP seam state reconstructs canonically the holomorphic (E8)₁ boundary net at the τ=i pillowcase ('the raw seam is (E8)₁ at τ=i'). [E] four objects (RawRPSeam, FlatTauIPillowcaseDtN, HolomorphicE8Net, SREKitaevE8Phase); [E] six arrows — 2 closed (Route i v276/v280/v284, Route ii v281/v277/v235), 1 conditional (v282), 2 open premises (the same lemma, v284/v285), 1 Gral; [E] IMPORT FIREWALL: no Route-i module imports any Route-ii module or vice versa, so the routes converge only through SEAM.EQUIV.01 (kills the 'E8 into the geometry and back' circularity); [E] exact-label taxonomy (Formal/Numerical/Conditional Exact, Open Selection); [O] the one open arrow 'free Gaussian RP bulk ⇒ holomorphic single-sector boundary'. Writes seam_equivalence.json.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv286_seam_equivalence_contract.py", "sourceSha256": "8f3150d4dd1cd1f90ad7f705f8cf867e935bea7c066167f25d4c56bd55f3ba79", "linkedClaimIds": [ "SEAM.EQUIV.01" ], "sectionIds": [ "section:03b9058ca08ba4829ac7", "section:20ef03b5c6c62b042300", "section:6a93c4dd5fe420e1990e", "section:7144b70a605254dfecbc", "section:8e4972dbe899b5debb90", "section:93b8868beb643874af75", "section:98e28332378f4d77a163", "section:aaf9450d3002873f5a8a", "section:ab9e7e520130ecc7da7c", "section:d0d4a62b7872b9bb3a1c", "section:d90bd5e1e6d8fa41397d", "section:eb00caf29086b02d5bf5", "section:f68163cf343646a0f102", "section:f97072f658fe6bcec8d8", "section:fd15b9954fc0175fba1b" ], "activeSectionIds": [ "section:20ef03b5c6c62b042300", "section:7144b70a605254dfecbc", "section:8e4972dbe899b5debb90", "section:98e28332378f4d77a163", "section:aaf9450d3002873f5a8a", "section:ab9e7e520130ecc7da7c", "section:d0d4a62b7872b9bb3a1c", "section:f68163cf343646a0f102", "section:f97072f658fe6bcec8d8" ], "evidenceId": "python_verification:verification/v286_seam_equivalence_contract.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v286_seam_equivalence_contract.py", "pubMirrorHash": "8f3150d4dd1cd1f90ad7f705f8cf867e935bea7c066167f25d4c56bd55f3ba79", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v286_seam_equivalence_contract.py" }, { "id": "v287_free_rp_bulk_to_holomorphic_boundary", "filename": "v287_free_rp_bulk_to_holomorphic_boundary.py", "path": "verification/v287_free_rp_bulk_to_holomorphic_boundary.py", "cluster": "frontier", "synopsis": "SEAM.EQUIV.A01 — Route A (AQFT) theorem-dependency checker for the open Gral arrow 'free Gaussian RP bulk ⇒ holomorphic single-sector boundary net': types the 5-lemma chain and isolates the ONE missing standard theorem. [E] L1 RawRPSeam→OS→CAR/quasi-free boundary (v155/v160/v240/v175); [E] L2 gap+chirality ⇒ gapped chiral bulk (v64/v156); [O] L3 invertible/SRE Gaussian bulk ⇒ single-sector boundary (μ-index 1) — THE ONE MISSING STANDARD THEOREM (the AQFT form of det K=1); [E] L4 μ=1+c=8 ⇒ holomorphic (v234); [E] L5 holomorphic c=8 ⇒ (E8)₁ (v83/v277/v281). Verdict: 4/5 discharged, Route A reduces SEAM.EQUIV.01 to one cited theorem (invertibility ⇒ single-sector).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv287_free_rp_bulk_to_holomorphic_boundary.py", "sourceSha256": "cf424f2c751693f21fbefb6de01adb1b170e7f6645d3b21f4019b292d82147c4", "linkedClaimIds": [ "SEAM.EQUIV.A01" ], "sectionIds": [ "section:6a93c4dd5fe420e1990e", "section:8e4972dbe899b5debb90", "section:98e28332378f4d77a163", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d", "section:f3f0a4f56db397726de9", "section:f68163cf343646a0f102" ], "activeSectionIds": [ "section:8e4972dbe899b5debb90", "section:98e28332378f4d77a163", "section:ab9e7e520130ecc7da7c", "section:f3f0a4f56db397726de9", "section:f68163cf343646a0f102" ], "evidenceId": "python_verification:verification/v287_free_rp_bulk_to_holomorphic_boundary.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v287_free_rp_bulk_to_holomorphic_boundary.py", "pubMirrorHash": "cf424f2c751693f21fbefb6de01adb1b170e7f6645d3b21f4019b292d82147c4", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v287_free_rp_bulk_to_holomorphic_boundary.py" }, { "id": "v288_full_l2_subprincipal_z4", "filename": "v288_full_l2_subprincipal_z4.py", "path": "verification/v288_full_l2_subprincipal_z4.py", "cluster": "frontier", "synopsis": "SEAM.EQUIV.B01 — Route B (DtN): the full-L² lift of the sub-principal Z4 block-diagonality, proving (numerically, on the full Toeplitz operator) the 'probably provable' step and lifting v201/v284 from the finite block to L². [E] character orthogonality: a mark-sourced curvature f=Σ_{j<4} g(θ−jπ/2) has Fourier support only on m≡0 mod 4 (nonzero modes {0,±4,±8,±12}; the 4th-root mark sum Σ_{j<4}((−i)^m)^j=4[4|m]); [E] full-L² block-diagonality: Λ=|n|+M_f commutes with ρ=diag(i^n), ‖[ρ,Λ]‖~2e-15 on −50..50; [E] negative control: a generic curvature gives ‖[ρ,Λ]‖=4.44>0; [E] Lean consistency (geom_sum_fourth_root + markLocal_blockDiagonal); [O] the sharper residual — why is the raw seam sub-principal term mark-local? (the curvature-locality half of SEAM.EQUIV.01).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv288_full_l2_subprincipal_z4.py", "sourceSha256": "e9d63abaf30c619b8a757dd9d2f78a41a911c4f81a1258a157d006a638cf87e7", "linkedClaimIds": [ "SEAM.EQUIV.B01" ], "sectionIds": [ "section:1dd51adeb586c882e7c4", "section:6a93c4dd5fe420e1990e", "section:8e4972dbe899b5debb90", "section:98e28332378f4d77a163", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d", "section:f1054498b80cd7df6676", "section:f3f0a4f56db397726de9", "section:f68163cf343646a0f102" ], "activeSectionIds": [ "section:1dd51adeb586c882e7c4", "section:8e4972dbe899b5debb90", "section:98e28332378f4d77a163", "section:ab9e7e520130ecc7da7c", "section:f1054498b80cd7df6676", "section:f3f0a4f56db397726de9", "section:f68163cf343646a0f102" ], "evidenceId": "python_verification:verification/v288_full_l2_subprincipal_z4.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v288_full_l2_subprincipal_z4.py", "pubMirrorHash": "e9d63abaf30c619b8a757dd9d2f78a41a911c4f81a1258a157d006a638cf87e7", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v288_full_l2_subprincipal_z4.py" }, { "id": "v289_marklocal_raw", "filename": "v289_marklocal_raw.py", "path": "verification/v289_marklocal_raw.py", "cluster": "frontier", "synopsis": "MARKLOCAL.RAW.01 — decompose the ONE remaining Route-B residual ('why is the raw seam sub-principal term mark-local?') into a 5-lemma chain and isolate the single open analytic lemma. [C] L1 conic parametrix: conic Steklov DtN = |D_θ| + M_f + cone sources (b-calculus/Melrose, imported); [O] L2 FLAT-AWAY — the one open analytic lemma: RP+gap+4 marks ⇒ curvature vanishes away from the marks (the flat-pillowcase realisation); [E] L3 orbit-source: the 4 marks form one μ4 orbit (v195/v216); [E] L4 Fourier-support: μ4-orbit curvature ⇒ support only on 4ℤ (v264/v288, FFT, with a non-orbit negative control); [E] L5 full-operator: ⇒ [ρ,Λ]=0 on full L² (v288). 4/5 discharged; Route B reduces to exactly L2 — if it falls, Route B closes and SEAM.EQUIV.01 needs only the holomorphy half (Route A).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv289_marklocal_raw.py", "sourceSha256": "a6ecfd3f4e254e3bf8730d861e64e40389c366a37db64136b51f1392f5e9379b", "linkedClaimIds": [ "MARKLOCAL.RAW.01" ], "sectionIds": [ "section:6a93c4dd5fe420e1990e", "section:8e4972dbe899b5debb90", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d", "section:f3f0a4f56db397726de9" ], "activeSectionIds": [ "section:8e4972dbe899b5debb90", "section:ab9e7e520130ecc7da7c", "section:f3f0a4f56db397726de9" ], "evidenceId": "python_verification:verification/v289_marklocal_raw.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v289_marklocal_raw.py", "pubMirrorHash": "a6ecfd3f4e254e3bf8730d861e64e40389c366a37db64136b51f1392f5e9379b", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v289_marklocal_raw.py" }, { "id": "v290_z4_smooth_curvature_adversary", "filename": "v290_z4_smooth_curvature_adversary.py", "path": "verification/v290_z4_smooth_curvature_adversary.py", "cluster": "frontier", "synopsis": "SEAM.ADVERSARY.01 — the Route-B red-team that Z4 block-diagonality is NOT mark-locality. Constructs the strongest adversary, a SMOOTH Z4-symmetric off-mark curvature f=ε·cos(4θ), and shows honestly: [E] it is Z4-symmetric (Fourier support {±4}⊂4ℤ) but NOT mark-local (f(π/4)=−ε≠0); [E] it PASSES the v288 commutator ‖[ρ,Λ]‖=0 (same as mark-local; i^n−i^(n±4)=0) — so [ρ,Λ]=0 is necessary but NOT sufficient; [E] BUT it shifts the DtN spectrum off the flat ladder (max|Δλ|=0.155 at ε=0.3) and the heat trace Tr(e^{−tΛ}) (Δ=0.019) — the KMS weight + (E8)₁ character shift; [O] verdict: a genuine candidate modulus the commutator misses but the spectral data excludes — Flat-Away must use spectral/energy/heat input. An honest red-team, no manufactured pass.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv290_z4_smooth_curvature_adversary.py", "sourceSha256": "3d89a59e18baa2439c353b99cc2c1e7c741d129b24e3a63a19e88ce3d743ad8e", "linkedClaimIds": [ "SEAM.ADVERSARY.01" ], "sectionIds": [ "section:1dd51adeb586c882e7c4", "section:6a93c4dd5fe420e1990e", "section:8e4972dbe899b5debb90", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d" ], "activeSectionIds": [ "section:1dd51adeb586c882e7c4", "section:8e4972dbe899b5debb90", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v290_z4_smooth_curvature_adversary.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v290_z4_smooth_curvature_adversary.py", "pubMirrorHash": "3d89a59e18baa2439c353b99cc2c1e7c741d129b24e3a63a19e88ce3d743ad8e", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v290_z4_smooth_curvature_adversary.py" }, { "id": "v291_flataway_contract", "filename": "v291_flataway_contract.py", "path": "verification/v291_flataway_contract.py", "cluster": "frontier", "synopsis": "FLATAWAY.RP.01 — the Flat-Away lemma as its own named mini-theorem with three proof routes opened by v290. LEMMA [O]: given RawRPSeam with gap, chirality and the four μ4 marks, the smooth curvature density in the DtN sub-principal symbol vanishes away from the branch divisor. [E] SPECTRAL-RIGIDITY route: scanning f=ε·cos(4θ), the spectrum deviation from the flat ladder is 0 only at ε=0 and grows with |ε| — flat is the unique spectral match. [E] HEAT-KERNEL route: the heat-trace deviation is 0 only at ε=0 — smooth off-mark curvature adds heat coefficients. [C] RP-ENERGY route: RP+gap = Dirichlet-energy minimisation in the Troyanov conformal class ⇒ constant-curvature minimiser (Troyanov; cf. v284). [O] verdict: 3 independent routes to ONE lemma; closing any one closes Route B.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv291_flataway_contract.py", "sourceSha256": "80bb241fd50aed6f25f4f1713ea4b72837a415a41b31f30b66b6827a288de046", "linkedClaimIds": [ "FLATAWAY.RP.01" ], "sectionIds": [ "section:1dd51adeb586c882e7c4", "section:2f80e058daba5055768b", "section:6a93c4dd5fe420e1990e", "section:8e4972dbe899b5debb90", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d" ], "activeSectionIds": [ "section:1dd51adeb586c882e7c4", "section:2f80e058daba5055768b", "section:8e4972dbe899b5debb90", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v291_flataway_contract.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v291_flataway_contract.py", "pubMirrorHash": "80bb241fd50aed6f25f4f1713ea4b72837a415a41b31f30b66b6827a288de046", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v291_flataway_contract.py" }, { "id": "v292_flataway_heat_reduction", "filename": "v292_flataway_heat_reduction.py", "path": "verification/v292_flataway_heat_reduction.py", "cluster": "frontier", "synopsis": "FLATAWAY.HEAT.01 — the Heat-Kernel route made precise: reduces Flat-Away to ONE named spectral invariant. [E] the heat-trace deviation ΔTr(e^{−tΛ}) = c(t)ε²+O(ε⁴) is a positive-definite quadratic form in the off-mark curvature (c_k(t)>0 for every Z4 mode 4k: 0.066/0.047/0.033; positive on all combinations, no cancellation), so ΔTr=0 ⟺ f=0; leading invariant ‖f‖_L² (Parseval). [O] reduction: Flat-Away ⟸ 'the seam fixes the a₂ heat coefficient (=Tr e^{−tΛ}) to its flat value' ⇒ ∫f²=0 ⇒ f=0 off the marks. One external invariant, far smaller than 'prove Flat-Away'.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv292_flataway_heat_reduction.py", "sourceSha256": "863e71c71f7fafcc1f497f1efcf9e20627defe17fd47950a7d7015f0a98d3663", "linkedClaimIds": [ "FLATAWAY.HEAT.01" ], "sectionIds": [ "section:310122d1b406c61c400f", "section:6a93c4dd5fe420e1990e", "section:8e4972dbe899b5debb90", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d", "section:db81095caf4bfe7ff937" ], "activeSectionIds": [ "section:310122d1b406c61c400f", "section:8e4972dbe899b5debb90", "section:ab9e7e520130ecc7da7c", "section:db81095caf4bfe7ff937" ], "evidenceId": "python_verification:verification/v292_flataway_heat_reduction.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v292_flataway_heat_reduction.py", "pubMirrorHash": "863e71c71f7fafcc1f497f1efcf9e20627defe17fd47950a7d7015f0a98d3663", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v292_flataway_heat_reduction.py" }, { "id": "v293_flataway_spectral_hessian", "filename": "v293_flataway_spectral_hessian.py", "path": "verification/v293_flataway_spectral_hessian.py", "cluster": "frontier", "synopsis": "FLATAWAY.SPEC.01 — the Spectral-Rigidity route upgraded from one direction (v291) to the FULL smooth-Z4 space. [E] splitting mechanism: the degenerate flat Steklov level |n| is split by mode 4k at |n|=2k by ±ε/2 (modes 4,8,12 split levels 2,4,6); [E] S=Σ(Δλ)² ~ 0.50ε² (quadratic); [E] the Hessian over modes {4,8,12} has eigenvalues ~{0.497,0.500,0.503}>0, so the flat seam is a STRICT isolated minimum over the whole Z4 space (answers the 'only one direction' objection); [E] clock-filter contrast: a non-Z4 mode (cos2θ) breaks the commutator outright. [O] consequence: pinning the seam's forced Steklov spectrum excludes every smooth Z4 deformation ⇒ Flat-Away — the same external fact as v292, reached independently.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv293_flataway_spectral_hessian.py", "sourceSha256": "088902cf254816e795d5d2d39beb25be1c2435f6397aca62c9127e7bfcbc6529", "linkedClaimIds": [ "FLATAWAY.SPEC.01" ], "sectionIds": [ "section:2f80e058daba5055768b", "section:6a93c4dd5fe420e1990e", "section:8e4972dbe899b5debb90", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d", "section:db81095caf4bfe7ff937" ], "activeSectionIds": [ "section:2f80e058daba5055768b", "section:8e4972dbe899b5debb90", "section:ab9e7e520130ecc7da7c", "section:db81095caf4bfe7ff937" ], "evidenceId": "python_verification:verification/v293_flataway_spectral_hessian.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v293_flataway_spectral_hessian.py", "pubMirrorHash": "088902cf254816e795d5d2d39beb25be1c2435f6397aca62c9127e7bfcbc6529", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v293_flataway_spectral_hessian.py" }, { "id": "v294_flataway_rp_energy", "filename": "v294_flataway_rp_energy.py", "path": "verification/v294_flataway_rp_energy.py", "cluster": "frontier", "synopsis": "FLATAWAY.ENERGY.01 — the RP-energy / Troyanov route: the flat pillowcase is the unique constant-curvature minimiser at the fixed mark divisor. [E] prescribed divisor + Gauss-Bonnet: S² with 4 cone angles π, Σ(2π−θ)=4π=2πχ; [C] Troyanov/Euclidean-cone uniqueness: the prescribed cone divisor carries a UNIQUE constant-curvature (flat) metric (Troyanov 1991), excluding smooth off-mark curvature; [E] strictly convex curvature energy E[f]=∫f², Hessian 2π·I (PD) ⇒ unique minimiser; [E] no zero-cost deformation (E[ε cos4kθ]=π ε²>0). [O] premise: 'RP+gap realises the energy-minimiser', converging with v292 (a₂) and v293 (spectrum) on ONE selection principle for the flat metric; closing any one closes Route B.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv294_flataway_rp_energy.py", "sourceSha256": "1adc345d5f4b29ca3346579fa43b981eef6bbc959a288f21e0f8ff01242f2262", "linkedClaimIds": [ "FLATAWAY.ENERGY.01" ], "sectionIds": [ "section:6a93c4dd5fe420e1990e", "section:8e4972dbe899b5debb90", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d", "section:db81095caf4bfe7ff937" ], "activeSectionIds": [ "section:8e4972dbe899b5debb90", "section:ab9e7e520130ecc7da7c", "section:db81095caf4bfe7ff937" ], "evidenceId": "python_verification:verification/v294_flataway_rp_energy.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v294_flataway_rp_energy.py", "pubMirrorHash": "1adc345d5f4b29ca3346579fa43b981eef6bbc959a288f21e0f8ff01242f2262", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v294_flataway_rp_energy.py" }, { "id": "v295_flataway_a2_exact", "filename": "v295_flataway_a2_exact.py", "path": "verification/v295_flataway_a2_exact.py", "cluster": "frontier", "synopsis": "FLATAWAY.A2.01 — the EXACT analytic a₂ coefficient, upgrading the v292 positive-definiteness from numerical to a proof. [E] first variation vanishes: d/dε Tr e^{−tΛ(ε)}|₀ = −t f̂(0) Σe^{−t|n|} = 0 (smooth off-mark curvature has zero mean, Gauss-Bonnet); [E] convexity ⇒ global minimum: φ(x)=e^{−tx} strictly convex ⇒ Λ↦Tr e^{−tΛ} convex (Klein/Peierls), so ε=0 is the GLOBAL minimum and ΔTr≥0 for ALL ε (verified even in ε over [−1,2]), =0 iff f=0; [E] exact a₂ kernel ΔTr⁽²⁾=(1/4)Σ_n[Φ(|n|,|n+4k|)+Φ(|n|,|n−4k|)]g² with the divided-difference kernel of e^{−tx} (Duhamel), matched to numerics to rel.err<1e−6; [E] degenerate-split closed form 2e^{−2kt}(cosh(tg/2)−1)≥0; [O] reduction now analytic: Flat-Away ⟸ 'the seam fixes a₂'. Lean-mirrored (FORM.FLATAWAY.01).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv295_flataway_a2_exact.py", "sourceSha256": "4970641d0c43e0c1a06a62e84037fa04b67da753d2ca0f28aa39cd600c2919dd", "linkedClaimIds": [ "FLATAWAY.A2.01", "FORM.FLATAWAY.01" ], "sectionIds": [ "section:2f80e058daba5055768b", "section:310122d1b406c61c400f", "section:6a93c4dd5fe420e1990e", "section:8e4972dbe899b5debb90", "section:90bdf395a7242e67386f", "section:aaf9450d3002873f5a8a", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d" ], "activeSectionIds": [ "section:2f80e058daba5055768b", "section:310122d1b406c61c400f", "section:8e4972dbe899b5debb90", "section:90bdf395a7242e67386f", "section:aaf9450d3002873f5a8a", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v295_flataway_a2_exact.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v295_flataway_a2_exact.py", "pubMirrorHash": "4970641d0c43e0c1a06a62e84037fa04b67da753d2ca0f28aa39cd600c2919dd", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v295_flataway_a2_exact.py" }, { "id": "v296_flataway_a2_closed", "filename": "v296_flataway_a2_closed.py", "path": "verification/v296_flataway_a2_closed.py", "cluster": "frontier", "synopsis": "FLATAWAY.A2.CLOSED.01 — the exact a₂ coefficient in CLOSED FORM (replacing v295's validated-numeric sum). [E] the operator tails telescope to a geometric series (Φ(n,n+4k)=e^{−nt}C_k/(16k²), C_k+D_k e^{−4kt}=4kt(1−e^{−4kt})), giving W_k^tail=t(1−e^{−4kt})/(8k(1−e^{−t})); [E] the middle is finite (4k−1 terms incl. the degenerate diagonal Φ(2k,2k)=(t²/2)e^{−2kt}); [E] closed form W_k(t)=t(1−e^{−4kt})/(8k(1−e^{−t}))+½Σ_{m=1}^{4k−1}Φ(m,4k−m), with W_1(t)=t(2t eᵗ+e³ᵗ+3e²ᵗ+eᵗ−1)e^{−3t}/8, reproducing v295 to machine precision; [E] positivity manifest term by term; [E] small-t W_k=t/2+O(t³) (mode-independent leading 1/2, the t² term cancels).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv296_flataway_a2_closed.py", "sourceSha256": "31d745feef3d1827ff3953d4ac310f391b296a8bb03131e88419474645e530b0", "linkedClaimIds": [ "FLATAWAY.A2.CLOSED.01" ], "sectionIds": [ "section:6a93c4dd5fe420e1990e", "section:8e4972dbe899b5debb90", "section:90bdf395a7242e67386f", "section:aaf9450d3002873f5a8a", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d" ], "activeSectionIds": [ "section:8e4972dbe899b5debb90", "section:90bdf395a7242e67386f", "section:aaf9450d3002873f5a8a", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v296_flataway_a2_closed.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v296_flataway_a2_closed.py", "pubMirrorHash": "31d745feef3d1827ff3953d4ac310f391b296a8bb03131e88419474645e530b0", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v296_flataway_a2_closed.py" }, { "id": "v297_route_a_literature_stack", "filename": "v297_route_a_literature_stack.py", "path": "verification/v297_route_a_literature_stack.py", "cluster": "frontier", "synopsis": "SEAM.EQUIV.A.LIT.01 — Route A's 'one standard import' written out as a precise CITABLE theorem stack. [E] LIT-A invertible/SRE bulk ⇒ trivial bulk topological order (Kitaev, Ann.Phys.321 2006; Freed-Hopkins, Geom.Topol.25 2021); [E] LIT-B bulk MTC = Drinfeld center, trivial center ⇒ holomorphic boundary net (Müger, JPAA 180 2003; Kawahigashi-Longo-Müger, CMP 219 2001); [E] LIT-C holomorphic c=8 net ⇒ (E8)₁ (Conway-Sloane lattice uniqueness; Dong-Xu/Kawahigashi-Longo). [E] the three COMPOSE (out=in matches) into 'invertible bulk ⇒ (E8)₁', all legs established; [O] the ONE open hypothesis is the input of LIT-A, 'the raw quasi-free seam bulk is invertible (SRE)' = Route B's Flat-Away. [E] non-circular with Route B (no DtN/Steklov; the v286 firewall holds).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv297_route_a_literature_stack.py", "sourceSha256": "d2357d89823d46ab2d4f5d1fe19c84ede0b844e7e981f483a9865fc93184ad02", "linkedClaimIds": [ "SEAM.EQUIV.A.LIT.01" ], "sectionIds": [ "section:41a8556f07331f818583", "section:4a157afd200102fcaaee", "section:5b9fc9c550f79525abcd", "section:5f8b87dd447560390c4e", "section:6a93c4dd5fe420e1990e", "section:8e4972dbe899b5debb90", "section:aaf9450d3002873f5a8a", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d" ], "activeSectionIds": [ "section:41a8556f07331f818583", "section:4a157afd200102fcaaee", "section:5b9fc9c550f79525abcd", "section:5f8b87dd447560390c4e", "section:8e4972dbe899b5debb90", "section:aaf9450d3002873f5a8a", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v297_route_a_literature_stack.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v297_route_a_literature_stack.py", "pubMirrorHash": "d2357d89823d46ab2d4f5d1fe19c84ede0b844e7e981f483a9865fc93184ad02", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v297_route_a_literature_stack.py" }, { "id": "v298_e8_network_attractor", "filename": "v298_e8_network_attractor.py", "path": "verification/v298_e8_network_attractor.py", "cluster": "frontier", "synopsis": "E8 as a network attractor — a computational-substrate (Wolfram-program) reading of the (2,3,5)/McKay hull, on the v219 bedrock; an HONEST audit of the 'TFPT as hypergraph' idea, not a derivation. [E] the E8 Kac marks (1,2,3,4,5,6,4,2,3) are the UNIQUE attractor of the minimal lazy graph update m←(A+2I)/4·m on the affine-E8/(2,3,5) McKay graph (converges from any positive start; A·m=2m, top eigenvalue 2). [E] the spherical McKay tower terminates at E8 (2T→E6 h12, 2O→E7 h18, 2I→E8 h30=2·3·5). [E] the E-cascade is nested-subgraph coarse-graining (|roots| 240→126→72→40→20). [C] Wolfram-bridge reading: 'E8 is the universal attractor of a minimal (2,3,5) network' at the Coxeter-skeleton level. [O] the deep question (a minimal hypergraph REWRITE whose attractor is the FULL TFPT structure) stays open; NEG: φ₀=(4/3)c₃=1/(6π) is the analytic seed not an edge fraction, recovery is a 1-D Möbius fixed point not a rewrite.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv298_e8_network_attractor.py", "sourceSha256": "21ec8a17606df03ef6692a5b2e5fb94eb8c9c4647730cf570ee15d87031066bc", "linkedClaimIds": [ "E8.NETWORK.01" ], "sectionIds": [ "section:143e259e1ecb29356ac2", "section:497660cf26cb0410a678", "section:678b949672ccc6aa27ab", "section:6c5940fdfa107000ca6f", "section:ab9e7e520130ecc7da7c" ], "activeSectionIds": [ "section:143e259e1ecb29356ac2", "section:497660cf26cb0410a678", "section:678b949672ccc6aa27ab", "section:6c5940fdfa107000ca6f", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v298_e8_network_attractor.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v298_e8_network_attractor.py", "pubMirrorHash": "21ec8a17606df03ef6692a5b2e5fb94eb8c9c4647730cf570ee15d87031066bc", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v298_e8_network_attractor.py" }, { "id": "v299_hypergraph_0d_autonomous", "filename": "v299_hypergraph_0d_autonomous.py", "path": "verification/v299_hypergraph_0d_autonomous.py", "cluster": "frontier", "synopsis": "The hypergraph/Wolfram bridge, hardened: **the 3-arm (2,3,·) branch type** is the irreducible seed on which a LOCAL witness-based spectral growth REACHES E8 as the last finite point (E6→E7→E8, then stops at the affine boundary Ê8; E8 = maximal FINITE point) — NOT 'P2 derived'. [E] HYP.ICO.01 icosahedron = 3-uniform hypergraph (12 V, 20 hyperedges, 30 edges=h(E8)), |Aut(graph)|=120=|I_h|=A5×ℤ₂ (the McKay group is the SU(2) binary lift 2I, a different order-120 group; v219); [E] HYP.REWRITE.01 the 1→4 subdivision rewrite is equivariant (120 symmetries at every scale, 12→42→162); [E] HYP.FUSION.01 the 2I fusion tensor is a nonneg-integer weighted 3-uniform hypergraph, 2-dim slice = affine E8 McKay graph; [E] HYP.SMITH.01 ρ≤2 selects (affine) ADE (Smith); [E] HYP.CW.01 Collatz–Wielandt: ρ≤2 ⟺ positive witness m with A m≤2m (local per-node), gate decided by the diffusion witness (Perron only as audit); [E*] HYP.AUTO.01 self-generated witness (projectively-normalised diffusion) + LOCAL gate A m≤2m runs E6→E7→E8→Ê8 (critical witness = Kac marks) under the (2,3,·) seed + grow-longest-leg policy; [E] HYP.NEG.AN.01 ρ(A_n)=2cos(π/(n+1))<2 for all n, never reaches E8; [E] HYP.NEG.DN.01 ρ(D_n)=2cos(π/(2n−2))<2 for all n, never reaches E8; [O] HYP.SEED.01 the (2,3,·) seed is the single irreducible input = P2. A second network reading of the (2,3,5)/E8 core, honestly bounded; builds on v219/v298.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv299_hypergraph_0d_autonomous.py", "sourceSha256": "0c4ecc2112669c92c0c07652ac1cf3a0df4c034dab574add63539ed82ba64b24", "linkedClaimIds": [ "HYP.0D.01" ], "sectionIds": [ "section:09b49009253acb5a0dfb", "section:3cc790136e8b9bd3c188", "section:497660cf26cb0410a678", "section:584e87a9c163ac38f92f", "section:6c5940fdfa107000ca6f", "section:ab9e7e520130ecc7da7c", "section:ccaa58843679b0b5ee13", "section:eb0bd97fda8c0fedefad" ], "activeSectionIds": [ "section:497660cf26cb0410a678", "section:584e87a9c163ac38f92f", "section:6c5940fdfa107000ca6f", "section:ab9e7e520130ecc7da7c", "section:ccaa58843679b0b5ee13" ], "evidenceId": "python_verification:verification/v299_hypergraph_0d_autonomous.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v299_hypergraph_0d_autonomous.py", "pubMirrorHash": "0c4ecc2112669c92c0c07652ac1cf3a0df4c034dab574add63539ed82ba64b24", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v299_hypergraph_0d_autonomous.py" }, { "id": "v300_flataway_rigid", "filename": "v300_flataway_rigid.py", "path": "verification/v300_flataway_rigid.py", "cluster": "frontier", "synopsis": "FLATAWAY.RIGID.01 — the attack on Flat-Away: (I) HARDEN the obstruction from a soft minimum (v291/v293) to a DISCRETE one, (II) DERIVE the external pin from the (E8)₁ data. [E] FLAT FINGERPRINT: spec(|D_θ|) is the integer ladder, every level n≥1 of multiplicity exactly 2 — a discrete fingerprint, not a norm. [E] EXACT DEGENERATE SPLIT: the resonant mode 4k splits level 2k by gap = g_k (sympy 2×2 [[2k,g/2],[g/2,2k]] ⇒ 2k±g/2, + an O(g²) common shift), validated vs the full Toeplitz operator. [E] HARD OBSTRUCTION: any g_k≠0 lifts the resonant degeneracy (mult 2→1+1) and changes the spectral MULTISET ⇒ preserving the flat ladder *with its mult-2 degeneracies* forces every g_k=0 ⇒ f=0 (strictly stronger than the v291/v293 'deviation grows' scan). [E] TWO-METRIC ISOLATION: with the v295 convexity (ΔTr≥0, =0 iff f=0), flat is isolated analytically AND discretely. [C] THE PIN DERIVED: the (E8)₁ vacuum character E4/η⁸=q^{-1/3}(1+248q+4124q²+…) has integer q-coefficients with 248 at level 1 (E8 even unimodular ⇒ integer weights); by 2d Steklov conformal rigidity the integer ladder ⟺ flat seam, so (E8)₁ rationality ⇒ f=0 (conditional on Route A). [O] VERDICT: Flat-Away carries ZERO new open content beyond Route A; convexity unconditional, the discrete obstruction exact; the two SEAM.EQUIV.01 routes converge on one rationality fact.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv300_flataway_rigid.py", "sourceSha256": "06518c6142216d69ce228c53a0f5a47bd6982e75983d202fe7dc8369828da479", "linkedClaimIds": [ "FLATAWAY.RIGID.01" ], "sectionIds": [ "section:2b8d2aba4baeb7a0c36b", "section:2f80e058daba5055768b", "section:303925994b6f141b3a0e", "section:41a8556f07331f818583", "section:5b9fc9c550f79525abcd", "section:6a93c4dd5fe420e1990e", "section:8e4972dbe899b5debb90", "section:9800e2e20cb3dc2e280a", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:2f80e058daba5055768b", "section:41a8556f07331f818583", "section:5b9fc9c550f79525abcd", "section:8e4972dbe899b5debb90", "section:9800e2e20cb3dc2e280a", "section:ab9e7e520130ecc7da7c", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v300_flataway_rigid.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v300_flataway_rigid.py", "pubMirrorHash": "06518c6142216d69ce228c53a0f5a47bd6982e75983d202fe7dc8369828da479", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v300_flataway_rigid.py" }, { "id": "v301_route_a_invertible", "filename": "v301_route_a_invertible.py", "path": "verification/v301_route_a_invertible.py", "cluster": "frontier", "synopsis": "SEAM.EQUIV.A.INV.01 — discharge Route A's single open hypothesis (v297 LIT-A: 'the raw quasi-free seam bulk is invertible/SRE') via the free-fermion classification. Since v300 collapsed Route B into Route A, this is the LAST unconditional gap of SEAM.EQUIV.01. [E] carrier = 16 Majoranas, c=8: g_car+N_fam=5+3=8=16/2 (v148). [E] SO(16)₁ ⊃ (E8)₁: dim so(16)=120 currents + 128 spinor = 248 = dim E8 (v154). [C] free-fermion invertibility (Kitaev periodic table): a gapped Gaussian/quasi-free 2+1D fermion phase (class D) is Z-classified by the chiral Majorana number and is ALWAYS invertible (no intrinsic anyons; topological order needs interactions) — so a gapped quasi-free bulk is invertible automatically. [E] invariant |det K|=#anyons: E8 Cartan det=1 (invertible) vs the gauged contrast D8=SO(16) det=4 (anyons), which free fermions cannot produce. [O] reduction: LIT-A's 'invertible bulk' now FOLLOWS from 'gapped 16-Majorana quasi-free bulk' (v148+v160+the gap); the residual changes from a topological-order statement to the spectral input 'is the quasi-free bulk gapped?'. [O] verdict: with v300 the WHOLE open content of SEAM.EQUIV.01 reduces to the single spectral statement 'the quasi-free seam bulk is gapped'.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv301_route_a_invertible.py", "sourceSha256": "3c2edba648219f084674ccba4c1199c4be5ddea012cf43d4df7c2463e326060a", "linkedClaimIds": [ "SEAM.EQUIV.A.INV.01" ], "sectionIds": [ "section:03b9058ca08ba4829ac7", "section:41a8556f07331f818583", "section:5b9fc9c550f79525abcd", "section:5f8b87dd447560390c4e", "section:6a93c4dd5fe420e1990e", "section:8e4972dbe899b5debb90", "section:ab9e7e520130ecc7da7c", "section:d21a62fafd64ff24f0b6", "section:d90bd5e1e6d8fa41397d", "section:f97072f658fe6bcec8d8", "section:fd15b9954fc0175fba1b" ], "activeSectionIds": [ "section:41a8556f07331f818583", "section:5b9fc9c550f79525abcd", "section:5f8b87dd447560390c4e", "section:8e4972dbe899b5debb90", "section:ab9e7e520130ecc7da7c", "section:d21a62fafd64ff24f0b6", "section:f97072f658fe6bcec8d8" ], "evidenceId": "python_verification:verification/v301_route_a_invertible.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v301_route_a_invertible.py", "pubMirrorHash": "3c2edba648219f084674ccba4c1199c4be5ddea012cf43d4df7c2463e326060a", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v301_route_a_invertible.py" }, { "id": "v302_seam_gap", "filename": "v302_seam_gap.py", "path": "verification/v302_seam_gap.py", "cluster": "frontier", "synopsis": "SEAM.EQUIV.GAP.01 — the LAST lever: after v300/v301 the whole open content of SEAM.EQUIV.01 was 'the quasi-free seam bulk is gapped'; this shows that gap is NOT a free input but the established RECOVERY GAP of the seam transfer operator. [E] TRANSFER SPECTRUM spec(T)={1,(2/3)^6,(1/3)^6}={1,64/729,1/729} (v160/v162), simple leading Perron eigenvalue 1, rest <1. [E] THE GAP IS DERIVED: Δ=−ln((2/3)^6)=6 ln(3/2)=2 N_fam ln(3/2)≈2.4328>0 (mult. gap 1−(2/3)^6=665/729); 6=2 N_fam, (2/3)^6 the μ4-deck transfer eigenvalue — forced by the carrier, not assumed. [E] POSITIVITY MARGIN Δ−31/(4π²)=1.6476>0 (the v76 decoupling margin), robust not marginal. [C] OS/QUASI-FREE CLUSTERING: for an RP quasi-free system a transfer gap Δ>0 ⟺ exponential clustering ⟺ a mass gap of the OS-reconstructed Hamiltonian (bulk mass gap = transfer gap). [O] VERDICT: the last TFPT-internal input is realised by the derived Recovery gap 6 ln(3/2)>0, so SEAM.EQUIV.01's residual is a composition of cited theorems (OS/clustering + Kitaev v301 + the v297 AQFT stack) over established TFPT facts — no undischarged TFPT-internal assumption remains; stays [O] (not machine-proved end-to-end).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv302_seam_gap.py", "sourceSha256": "4a97a40d30829715e6f13777b20cd47ee05d211b4a31a18768ca98367b704cf0", "linkedClaimIds": [ "SEAM.EQUIV.GAP.01" ], "sectionIds": [ "section:02788e96f36ad336a0ac", "section:03b9058ca08ba4829ac7", "section:0c131301948f5acf50d5", "section:2525c189f32461c9368a", "section:2585b5d786c3bdb7ddb7", "section:2a73aae2d89b3c427077", "section:3bfc0afca092b381dee1", "section:4a157afd200102fcaaee", "section:4e5537e69e05316e0599", "section:56ca118419000d5423f4", "section:5b9fc9c550f79525abcd", "section:5f8b87dd447560390c4e", "section:6a93c4dd5fe420e1990e", "section:6cd1a267e72b20619327", "section:7144b70a605254dfecbc", "section:73dd631de817637ce12d", "section:7a7de20f53ed3e69fb6f", "section:888628823bf71f709698", "section:8e4972dbe899b5debb90", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:b93e6ae7b00f32ee1201", "section:ce5afee193d0ce1ea07e", "section:d21a62fafd64ff24f0b6", "section:d90bd5e1e6d8fa41397d", "section:dccf3e7f3250c009523d", "section:e77e5218c82783443690", "section:f97072f658fe6bcec8d8", "section:fbf67a6377a333f71dff", "section:fd15b9954fc0175fba1b" ], "activeSectionIds": [ "section:02788e96f36ad336a0ac", "section:2585b5d786c3bdb7ddb7", "section:2a73aae2d89b3c427077", "section:4a157afd200102fcaaee", "section:56ca118419000d5423f4", "section:5b9fc9c550f79525abcd", "section:5f8b87dd447560390c4e", "section:7144b70a605254dfecbc", "section:7a7de20f53ed3e69fb6f", "section:888628823bf71f709698", "section:8e4972dbe899b5debb90", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:ce5afee193d0ce1ea07e", "section:d21a62fafd64ff24f0b6", "section:dccf3e7f3250c009523d", "section:e77e5218c82783443690", "section:f97072f658fe6bcec8d8" ], "evidenceId": "python_verification:verification/v302_seam_gap.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v302_seam_gap.py", "pubMirrorHash": "4a97a40d30829715e6f13777b20cd47ee05d211b4a31a18768ca98367b704cf0", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v302_seam_gap.py" }, { "id": "v303_ftransfer_dynamics", "filename": "v303_ftransfer_dynamics.py", "path": "verification/v303_ftransfer_dynamics.py", "cluster": "frontier", "synopsis": "FR.DYNAMICS.01 — the discrete->dynamic lens on F_transfer: is the main-branch mechanism (a gapped, positivity-preserving relaxation to a UNIQUE attractor; local-averaging update -> E8 marks, gap 6 log(3/2)) also the shape of the four F_transfer instances? [E] F_pole (Koide) IS the seam dynamics: the source->pole/branch relaxation is the Moebius map with fixed-point multiplier F'=(2/3)^6 = lambda_2 = the seam clock subleading eigenvalue (v82/v54), |F'|<1 => a unique attractor at the SEAM rate. [C] F_Boltzmann (eta_B): a gapped positive contraction (washout kappa_f in (0,1) -> the unique balance, H-theorem), compiler fixes A_Lambda=10, rate thermal. [C] F_relic (axion): the misalignment comoving number freezes to a constant (adiabatic fixed point), seed theta_i=3pi/5, rate cosmological. [I] F_QCD (m_p/m_e): the 1-loop RG flow with the carrier b3=-7 (asymptotic freedom) has the Gaussian UV fixed point as attractor, Lambda_QCD dynamically generated. [O] VERDICT: ONE shape underlies all four = the main-branch principle; F_pole has the seam rate exactly, the other three share only the shape (external rates); F_transfer is the readout end of the one principle, not a bolt-on; simplicity preserved by honest fencing (v187).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv303_ftransfer_dynamics.py", "sourceSha256": "871ccecb97e8f0ab1aa150c6442efbc4c173e3966e5e9958ea6adfeebe300449", "linkedClaimIds": [ "FR.DYNAMICS.01" ], "sectionIds": [ "section:0968f1b6845750a87eeb", "section:2525c189f32461c9368a", "section:2b8d2aba4baeb7a0c36b", "section:303925994b6f141b3a0e", "section:3c0ef7a887cebe028f40", "section:568b5e9acdb7b04367d3", "section:5b0172590490b241cb77", "section:6b87e1b142e887eedca7", "section:6cd1a267e72b20619327", "section:81a6dc002dc46cf7b6c5", "section:888628823bf71f709698", "section:8b1a1c6a205860e21edc", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:b93e6ae7b00f32ee1201", "section:cb09371605fac20095ba", "section:e77e5218c82783443690", "section:f0ac30137703825661c6", "section:f3b90b032a2851e13827", "section:fb4cf64c8cbaeb3f6d74", "section:fbc55d19f88e095d54eb", "section:fddca2e76a3d11b710e6", "section:fdf63a1d99769ab37ccb", "section:fe85126d1b3e41ef8954" ], "activeSectionIds": [ "section:0968f1b6845750a87eeb", "section:3c0ef7a887cebe028f40", "section:5b0172590490b241cb77", "section:6b87e1b142e887eedca7", "section:81a6dc002dc46cf7b6c5", "section:888628823bf71f709698", "section:8b1a1c6a205860e21edc", "section:ab9e7e520130ecc7da7c", "section:cb09371605fac20095ba", "section:e77e5218c82783443690", "section:f3b90b032a2851e13827", "section:fb4cf64c8cbaeb3f6d74", "section:fbc55d19f88e095d54eb", "section:fddca2e76a3d11b710e6", "section:fdf63a1d99769ab37ccb", "section:fe85126d1b3e41ef8954" ], "evidenceId": "python_verification:verification/v303_ftransfer_dynamics.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v303_ftransfer_dynamics.py", "pubMirrorHash": "871ccecb97e8f0ab1aa150c6442efbc4c173e3966e5e9958ea6adfeebe300449", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v303_ftransfer_dynamics.py" }, { "id": "v304_idg_nonlocal_ghost", "filename": "v304_idg_nonlocal_ghost.py", "path": "verification/v304_idg_nonlocal_ghost.py", "cluster": "frontier", "synopsis": "QGAMB.IDG.01 — the KMS spectral-action cutoff suggests a NONLOCAL (infinite-derivative) graviton form factor; under entire analyticity the Stelle ghost is a TRUNCATION ARTEFACT — a CONDITIONAL narrowing of the red-team rt_F perturbative-gravity attack, NOT a closure of QG.AMB.01 (no new parameter: the cutoff is the v259 seam KMS weight). [E] STELLE GHOST = TRUNCATION ARTEFACT: the local four-derivative propagator 1/(p^2(p^2+M^2)) has a healthy massless graviton (residue +1/M^2 at p^2=0) and a massive spin-2 mode with NEGATIVE residue -1/M^2 at p^2=-M^2 (reproduces rt_F/v278). [E] ENTIRE FORM FACTOR HAS NO EXTRA POLE: for an IDG operator p^2 a(p^2) with a(z)=e^{z/M^2} entire and nowhere zero, the dressed propagator 1/(p^2 a) keeps its ONLY pole at p^2=0 — no ghost (Tomboulis 1997; Biswas-Mazumdar-Siegel 2006). [E] NEG CONTROL: a polynomial truncation a(z)=1+z/M^2 (the R+R^2 order) has a real zero at z=-M^2 = the ghost pole, so 'entire vs polynomial' is the discriminator. [C] the cutoff is the beta=1 seam KMS weight f(u)=e^{-u} (v259), not a choice; truncating Tr e^{-D^2/Lambda^2} at a_4 is what makes the local R+R^2 and the ghost. [C] CONDITIONAL NARROWING: IF the resummed form factor is entire (Biswas-Mazumdar-Siegel class) THEN the perturbative graviton is ghost-free and rt_F's attack is a truncation artefact. 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Residual = Bisognano-Wichmann intrinsicality of the raw collar; NOT a closure of QGEO.SYM.01", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv309_modular_bedrock.py", "sourceSha256": "8d6462e1e1bb81a0305e3d1dc24ab2244d88072e8b9a6f67a2062156b895969c", "linkedClaimIds": [ "QGEO.MODHAM.01" ], "sectionIds": [ "section:029b7dd988521b5ffc7e", "section:5ff3f529ae7be4541192", "section:6a93c4dd5fe420e1990e", "section:75d473d613aba16a08b8", "section:796200681c870006983a", "section:8e4972dbe899b5debb90", "section:93b8868beb643874af75", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:acb731fecb30c7953915", "section:d90bd5e1e6d8fa41397d", "section:debae20192b75c7a987d", "section:eb00caf29086b02d5bf5", "section:f3b90b032a2851e13827" ], "activeSectionIds": [ "section:029b7dd988521b5ffc7e", "section:5ff3f529ae7be4541192", "section:75d473d613aba16a08b8", "section:796200681c870006983a", "section:8e4972dbe899b5debb90", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:acb731fecb30c7953915", "section:debae20192b75c7a987d", "section:f3b90b032a2851e13827" ], "evidenceId": "python_verification:verification/v309_modular_bedrock.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v309_modular_bedrock.py", "pubMirrorHash": "8d6462e1e1bb81a0305e3d1dc24ab2244d88072e8b9a6f67a2062156b895969c", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v309_modular_bedrock.py" }, { "id": "v310_carrier_sm_anomaly", "filename": "v310_carrier_sm_anomaly.py", "path": "verification/v310_carrier_sm_anomaly.py", "cluster": "registry", "synopsis": "TOE attack 3 -- the carrier half-spinor IS one anomaly-free SM generation with the SM RG: 16=Lambda^even(C^5)=1+10+5 -> SU(5)0 decouples the physical sector from the un-built ambient. Spectral-action a2=EH/a4=R^2/72 (v36) + KMS beta=1 (v259); QG.AMB.01 stays open (gap-decoupled, inert)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv311_gap_decoupled_measure.py", "sourceSha256": "a2495feefd0f01e0d28a896508c9358fd8d9540cc7115a70b2138aff0221d606", "linkedClaimIds": [ "QGAMB.CLUSTER.01" ], "sectionIds": [ "section:2cf3ee9ae0a89a313d79", "section:6a93c4dd5fe420e1990e", "section:796200681c870006983a", "section:8e4972dbe899b5debb90", "section:ab9e7e520130ecc7da7c", "section:cfd99b18e189abbc1f87", "section:d90bd5e1e6d8fa41397d" ], "activeSectionIds": [ "section:2cf3ee9ae0a89a313d79", "section:796200681c870006983a", "section:8e4972dbe899b5debb90", "section:ab9e7e520130ecc7da7c", "section:cfd99b18e189abbc1f87" ], "evidenceId": "python_verification:verification/v311_gap_decoupled_measure.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v311_gap_decoupled_measure.py", "pubMirrorHash": "a2495feefd0f01e0d28a896508c9358fd8d9540cc7115a70b2138aff0221d606", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v311_gap_decoupled_measure.py" }, { "id": "v312_hypergraph_substrate", "filename": "v312_hypergraph_substrate.py", "path": "verification/v312_hypergraph_substrate.py", "cluster": "frontier", "synopsis": "TOE attack 5 -- the hypergraph substrate sharpened: the affine-E8 Kac marks are the Perron eigenvector (A.marks=2 marks) and the subleading eigenvalue is exactly 2cos(pi/5)=golden ratio (the 5-fold/icosahedral signature), but the recovery rate (2/3)^6 is NOT any eigenvalue and phi0 is not a rational edge fraction; so a full-structure rewrite must inject exactly two non-graph-spectral data: the cusp weight 2/3=|Z2|/N_fam (gap 6 ln(3/2)) and the analytic seed phi0. The open question is precisely delimited, not closed", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv312_hypergraph_substrate.py", "sourceSha256": "8f4f6abd645506a44a599366e424a1795ae6d41eb29469645351529d7873f1e6", "linkedClaimIds": [ "HYP.INJECT.01" ], "sectionIds": [ "section:029b7dd988521b5ffc7e", "section:09b49009253acb5a0dfb", "section:2b8d2aba4baeb7a0c36b", "section:303925994b6f141b3a0e", "section:3af896f0e07d57463462", "section:3cc790136e8b9bd3c188", "section:414a84d23afa6566ca5e", "section:497660cf26cb0410a678", "section:584e87a9c163ac38f92f", "section:5b0172590490b241cb77", "section:6b87e1b142e887eedca7", "section:796200681c870006983a", "section:7a7de20f53ed3e69fb6f", "section:8b1a1c6a205860e21edc", "section:90d9ccdfa2e81d8ea0bd", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:ccaa58843679b0b5ee13", "section:e99d6098550f62e277de", "section:eb0bd97fda8c0fedefad", "section:ee9a2e2d9ccdc3799662", "section:f31ad742de6c0cadfda1", "section:f3b90b032a2851e13827", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:029b7dd988521b5ffc7e", "section:3af896f0e07d57463462", "section:414a84d23afa6566ca5e", "section:497660cf26cb0410a678", "section:584e87a9c163ac38f92f", "section:5b0172590490b241cb77", "section:6b87e1b142e887eedca7", "section:796200681c870006983a", "section:7a7de20f53ed3e69fb6f", "section:8b1a1c6a205860e21edc", "section:90d9ccdfa2e81d8ea0bd", "section:ab9e7e520130ecc7da7c", "section:ccaa58843679b0b5ee13", "section:e99d6098550f62e277de", "section:ee9a2e2d9ccdc3799662", "section:f31ad742de6c0cadfda1", "section:f3b90b032a2851e13827", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v312_hypergraph_substrate.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v312_hypergraph_substrate.py", "pubMirrorHash": "8f4f6abd645506a44a599366e424a1795ae6d41eb29469645351529d7873f1e6", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v312_hypergraph_substrate.py" }, { "id": "v313_golden_atoms_spectral", "filename": "v313_golden_atoms_spectral.py", "path": "verification/v313_golden_atoms_spectral.py", "cluster": "frontier", "synopsis": "The golden ratio is the g_car=5 signature -- the (2,3,5) atoms ARE the affine-E8 network spectral angles (v312 follow-up, exact). The charpoly factors x(x^2-4)(x^2-1)(x^2-x-1)(x^2+x-1), the golden minimal polynomial x^2-x-1 divides it (phi=2cos(pi/5) exact eigenvalue); the non-trivial eigenvalues are 2cos(pi/k) for k in {2,3,5}={|Z2|,N_fam,g_car} (0,1,phi,1/phi) so the golden ratio is the g_car=5 (5-fold) signature -- a new spectral witness for g_car (raises v305 multiplicity). The (2,3,5) spherical excess 1/2+1/3+1/5=31/30 ties the v63/v76 margin numerator 31=2^g_car-1=248/8=1+h to the Coxeter 30 (a unification, not new evidence). HONEST NULL: phi is structural, not a readout. DIRECTION: phi is the E8-quasicrystal ratio (candidate substrate)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv313_golden_atoms_spectral.py", "sourceSha256": "fb6ecd33815a1c16a8c19153b2a641b1ce301dae954e9a501a77cce96d742582", "linkedClaimIds": [ "GOLD.ATOMS.01" ], "sectionIds": [ "section:029b7dd988521b5ffc7e", "section:09b49009253acb5a0dfb", "section:2678ed3ba0ed508e2d8e", "section:2b8d2aba4baeb7a0c36b", "section:303925994b6f141b3a0e", "section:31a155495fcd43cf1264", "section:3af896f0e07d57463462", "section:3cc790136e8b9bd3c188", "section:3ff315fdd4e19bf322ac", "section:4061f274c55499fb2ed1", "section:414a84d23afa6566ca5e", "section:584e87a9c163ac38f92f", "section:8b1a1c6a205860e21edc", "section:989e899750d5a86edf1e", "section:9bab697ba19c86420aea", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:b3159de77fcabb12cc0c", "section:cc398ba7e3e94c7addf2", "section:d200c6e6e5dab4f9f985", "section:eb0bd97fda8c0fedefad", "section:f31ad742de6c0cadfda1", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:029b7dd988521b5ffc7e", "section:31a155495fcd43cf1264", "section:3af896f0e07d57463462", "section:3ff315fdd4e19bf322ac", "section:4061f274c55499fb2ed1", "section:414a84d23afa6566ca5e", "section:584e87a9c163ac38f92f", "section:8b1a1c6a205860e21edc", "section:989e899750d5a86edf1e", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:b3159de77fcabb12cc0c", "section:cc398ba7e3e94c7addf2", "section:d200c6e6e5dab4f9f985", "section:f31ad742de6c0cadfda1", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v313_golden_atoms_spectral.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v313_golden_atoms_spectral.py", "pubMirrorHash": "fb6ecd33815a1c16a8c19153b2a641b1ce301dae954e9a501a77cce96d742582", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v313_golden_atoms_spectral.py" }, { "id": "v314_rate_translation", "filename": "v314_rate_translation.py", "path": "verification/v314_rate_translation.py", "cluster": "frontier", "synopsis": "Do the discrete-kernel and dynamic rates translate? An exact number-field split. The affine-E8 adjacency spectrum splits into the rational part {0,+-1,+-2} in Q and the golden part {+-phi,+-1/phi} in Q(sqrt5); the dynamic transfer spectrum {1,(2/3)^6,(1/3)^6} is entirely rational. So the family rates DO translate (the rational discrete angles 2cos(pi/2)=0=|Z2|, 2cos(pi/3)=1=N_fam build the recovery rate (2/3)^6=(|Z2|/N_fam)^(2 N_fam) in Q), but the carrier 5-fold (golden, Q(sqrt5)) has NO rational dynamic image -- a field obstruction, so it is static-only. The shared object is the order-30 Coxeter element (30=g_car*(2 N_fam)=5*6); the phi quasicrystal carries the carrier, not the cusp-weight family dynamics", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv314_rate_translation.py", "sourceSha256": "1e7200d76d20ed799c57caa234485fad3701e577da888f3ef4808bb2965aa541", "linkedClaimIds": [ "RATE.TRANSLATE.01" ], "sectionIds": [ "section:029b7dd988521b5ffc7e", "section:03d2cc780ce0cfabf94c", "section:09b49009253acb5a0dfb", "section:2b8d2aba4baeb7a0c36b", "section:303925994b6f141b3a0e", "section:3cc790136e8b9bd3c188", "section:49c4830cbc40c1211137", "section:584e87a9c163ac38f92f", "section:633620b74c9f05d23e78", "section:7383e42c67f8eaba497b", "section:7a7de20f53ed3e69fb6f", "section:8b1a1c6a205860e21edc", "section:a444fd35a837e55b2dcd", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:cc398ba7e3e94c7addf2", "section:ddeb7ff0b27d4750ff23", "section:eb0bd97fda8c0fedefad", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:029b7dd988521b5ffc7e", "section:03d2cc780ce0cfabf94c", "section:49c4830cbc40c1211137", "section:584e87a9c163ac38f92f", "section:633620b74c9f05d23e78", "section:7383e42c67f8eaba497b", "section:7a7de20f53ed3e69fb6f", "section:8b1a1c6a205860e21edc", "section:a444fd35a837e55b2dcd", "section:ab9e7e520130ecc7da7c", "section:cc398ba7e3e94c7addf2", "section:ddeb7ff0b27d4750ff23", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v314_rate_translation.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v314_rate_translation.py", "pubMirrorHash": "1e7200d76d20ed799c57caa234485fad3701e577da888f3ef4808bb2965aa541", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v314_rate_translation.py" }, { "id": "v315_coxeter_coupling", "filename": "v315_coxeter_coupling.py", "path": "verification/v315_coxeter_coupling.py", "cluster": "frontier", "synopsis": "Couple or factorize? The order-30 Coxeter sectors couple as a cyclotomic field (v314 follow-up). GROUP FACTORIZES: gcd(5,6)=1 => Z/30 = Z/5 x Z/6 (direct product, group-decoupled). EXPONENTS FACTOR: E8 exponents=totatives(30)=totatives(5)x totatives(6), phi(30)=4*2=8=rank E8. FIELD COUPLES: [Q(zeta30):Q]=8=rank E8, Q(zeta30) is the compositum of the carrier Q(zeta5) (contains sqrt5) and the family Q(zeta3). GALOIS = mu4 x Z2: (Z/30)^x=(Z/5)^x x (Z/3)^x=Z/4 x Z/2 (order 8, max order 4); mu4=(Z/5)^x is the carrier Galois (the seam clock = the carrier golden-field Galois), Z2=(Z/3)^x the family Galois. sqrt5=phi+1/phi=Gauss sum in Q(zeta5). VERDICT: 30=5*6 does not dynamically entangle -- it couples as the cyclotomic compositum, bridge is Galois not dynamical", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv315_coxeter_coupling.py", "sourceSha256": "490969af0827cf8829f236e3999710bb526396dc9eb2ee0672d8bdd5c6af7b0c", "linkedClaimIds": [ "COX.COUPLE.01" ], "sectionIds": [ "section:029b7dd988521b5ffc7e", "section:03d2cc780ce0cfabf94c", "section:09b49009253acb5a0dfb", "section:3cc790136e8b9bd3c188", "section:49c4830cbc40c1211137", "section:584e87a9c163ac38f92f", "section:7a7de20f53ed3e69fb6f", "section:ab9e7e520130ecc7da7c", "section:cc398ba7e3e94c7addf2", "section:ddeb7ff0b27d4750ff23", "section:eb0bd97fda8c0fedefad" ], "activeSectionIds": [ "section:029b7dd988521b5ffc7e", "section:03d2cc780ce0cfabf94c", "section:49c4830cbc40c1211137", "section:584e87a9c163ac38f92f", "section:7a7de20f53ed3e69fb6f", "section:ab9e7e520130ecc7da7c", "section:cc398ba7e3e94c7addf2", "section:ddeb7ff0b27d4750ff23" ], "evidenceId": "python_verification:verification/v315_coxeter_coupling.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v315_coxeter_coupling.py", "pubMirrorHash": "490969af0827cf8829f236e3999710bb526396dc9eb2ee0672d8bdd5c6af7b0c", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v315_coxeter_coupling.py" }, { "id": "v316_galois_readout", "filename": "v316_galois_readout.py", "path": "verification/v316_galois_readout.py", "cluster": "frontier", "synopsis": "Does the Galois mu4 x Z2 (v315) organize the physical readouts? Yes -- the CP phases. The hexagonal CP unit rho=zeta_6=zeta_30^5 is the order-6=2 N_fam FAMILY factor c^5 of v315 (the carrier is zeta_5=zeta_30^6); delta_CKM,lead=pi/3=arg(zeta_6), delta_PMNS=4pi/3=arg(zeta_6^4) (power 4=|mu4|), zeta_6^4=-zeta_6 the sheet flip (mu6=mu3 x mu2). The Galois Z2=Gal(Q(zeta6)/Q)={zeta_6->zeta_6^5=conj} IS CP conjugation (delta->-delta). The carrier factor zeta_5 (golden sqrt5) carries no phase (static). The magnitudes (sin^2 theta12=1/3-phi0/2, transcendental phi0) are NOT cyclotomic. So the Galois bridge reaches phenomenology through the family factor (phases), the carrier is static, the magnitudes are the analytic seed", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv316_galois_readout.py", "sourceSha256": "e402ec3e9a6beaf4c75f47f6393cfdd6efcdceec7801a394dd18db1d0f7e0573", "linkedClaimIds": [ "GALOIS.READOUT.01" ], "sectionIds": [ "section:029b7dd988521b5ffc7e", "section:09b49009253acb5a0dfb", "section:2678ed3ba0ed508e2d8e", "section:36246a833c23944e824a", "section:3cc790136e8b9bd3c188", "section:49c4830cbc40c1211137", "section:584e87a9c163ac38f92f", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:b3159de77fcabb12cc0c", "section:cc398ba7e3e94c7addf2", "section:d200c6e6e5dab4f9f985", "section:eb0bd97fda8c0fedefad", "section:fa6e96662b31faa3de47" ], "activeSectionIds": [ "section:029b7dd988521b5ffc7e", "section:36246a833c23944e824a", "section:49c4830cbc40c1211137", "section:584e87a9c163ac38f92f", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:b3159de77fcabb12cc0c", "section:cc398ba7e3e94c7addf2", "section:d200c6e6e5dab4f9f985", "section:fa6e96662b31faa3de47" ], "evidenceId": "python_verification:verification/v316_galois_readout.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v316_galois_readout.py", "pubMirrorHash": "e402ec3e9a6beaf4c75f47f6393cfdd6efcdceec7801a394dd18db1d0f7e0573", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v316_galois_readout.py" }, { "id": "v317_galois_family", "filename": "v317_galois_family.py", "path": "verification/v317_galois_family.py", "cluster": "frontier", "synopsis": "Are the 3 generations a mu3/Galois orbit? Yes (mu3), refined 1+2 by Galois (v316 follow-up). The 3 cusp weights {0,1/3,2/3} (Spec(Q+)={1,2,3}=A3 exponents) map under w->e^{2pi i w} to the 3rd roots of unity {1,zeta_3,zeta_3^2}; the cyclic family symmetry w->w+1/3 is a transitive mu3 orbit (the family IS the cube-root orbit). The transfer eigenvalues (1-w)^6={1,(2/3)^6,(1/3)^6} attach to the weights (attractor=eigenvalue 1 at w=0). The Galois Z2 (zeta_3->zeta_3^2, = CP conjugation v316) fixes w=0 (rational) and swaps w=1/3<->2/3 -> orbit 1+2; so the Galois-FIXED generation is the recovery ATTRACTOR (the law), the Galois PAIR is the decaying hierarchy. The family structure is arithmetic; the mass magnitudes stay the analytic seed", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv317_galois_family.py", "sourceSha256": "1b2e982246d4d8f19d6ba542e3fa9267709a6bf34dd19d2180bd11eec860c096", "linkedClaimIds": [ "GALOIS.FAMILY.01" ], "sectionIds": [ "section:029b7dd988521b5ffc7e", "section:09b49009253acb5a0dfb", "section:31a155495fcd43cf1264", "section:3cc790136e8b9bd3c188", "section:584e87a9c163ac38f92f", "section:ab9e7e520130ecc7da7c", "section:eb0bd97fda8c0fedefad", "section:fa6e96662b31faa3de47" ], "activeSectionIds": [ "section:029b7dd988521b5ffc7e", "section:31a155495fcd43cf1264", "section:584e87a9c163ac38f92f", "section:ab9e7e520130ecc7da7c", "section:fa6e96662b31faa3de47" ], "evidenceId": "python_verification:verification/v317_galois_family.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v317_galois_family.py", "pubMirrorHash": "1b2e982246d4d8f19d6ba542e3fa9267709a6bf34dd19d2180bd11eec860c096", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v317_galois_family.py" }, { "id": "v319_translation_clock", "filename": "v319_translation_clock.py", "path": "verification/v319_translation_clock.py", "cluster": "horizon", "synopsis": "The translation clock: the discrete<->dynamic bridge IS the order-30 Coxeter element, a clock with two coprime hands 5 x 6, read law-inclusive (0..5) or live-only (1..5). The only object holding both the static carrier (Q(sqrt5)) and the dynamic family (rational) data is the order-30 Coxeter element (v314); 30 = h(E8) = g_car*(2 N_fam) = 5*6, gcd(5,6)=1 => Z/30 = Z/5 x Z/6 (v315). DYNAMIC HAND (Z/6 = 2 N_fam, ticks 0..5): the recovery exponent is exactly 6 = 2 N_fam, rate (2/3)^6; order-6 generator c^5 (zeta_6 = zeta_30^5). LAW vs LIVE: the resummed clock rate(n) = -p2 ln(1 - n/N_fam) (v124) has rate(0)=0 (the attractor/law) and live modes from n=1; the E8 live phases (totatives of 30) start at 1, so '0,1,2,3,4,5' is law-inclusive, '1,2,3,4,5' live-only. STATIC HAND (Z/5 = g_car, ticks 1..5): golden Q(sqrt5), field-obstructed (no rational dynamic image, v314) -- static-only. ONE FULL TURN = lcm(5,6) = 30 = the Coxeter period (rank E8 = 8 = phi(30) live phases, 4 invariant planes, v55). The arithmetic is [E]; the 'it is one clock' reading is [C].", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv319_translation_clock.py", "sourceSha256": "470630b658826a6c4eda8673ae19f08c45bce66267371b8cced7b73d956e97c1", "linkedClaimIds": [ "TRANSLATE.CLOCK.01" ], "sectionIds": [ "section:09b49009253acb5a0dfb", "section:3cc790136e8b9bd3c188", "section:7383e42c67f8eaba497b", "section:ab9e7e520130ecc7da7c", "section:cc398ba7e3e94c7addf2", "section:d200c6e6e5dab4f9f985", "section:eb0bd97fda8c0fedefad" ], "activeSectionIds": [ "section:7383e42c67f8eaba497b", "section:ab9e7e520130ecc7da7c", "section:cc398ba7e3e94c7addf2", "section:d200c6e6e5dab4f9f985" ], "evidenceId": "python_verification:verification/v319_translation_clock.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v319_translation_clock.py", "pubMirrorHash": "470630b658826a6c4eda8673ae19f08c45bce66267371b8cced7b73d956e97c1", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v319_translation_clock.py" }, { "id": "v318_arithmetic_capstone", "filename": "v318_arithmetic_capstone.py", "path": "verification/v318_arithmetic_capstone.py", "cluster": "core", "synopsis": "The capstone: the SM structural sector is Q(zeta30) + Galois mu4 x Z2, and the complete input is {a, pi, v_geo} (synthesis of the v313-v317 arc). The structural sector (3 generations, 2 CP phases, orbit/hierarchy) lives in Q(zeta30): [Q(zeta30):Q]=phi(30)=8=rank E8, 30=|Z2|*N_fam*g_car=h(E8), Galois (Z/30)^x=mu4 x Z2. Rigidity: forced by the anchor atoms {2,3,5}=e(a). Magnitude reduction: phi0=(4/3)c3+48 c3^4 is a pure function of pi (no free parameters), so the magnitudes are {a,pi}-determined, not free. Free inventory: 0 dimensionless free parameters; pi the unique transcendental; v_geo the one dimensionful unit. Residual: the raw-seam realisation stays open (QGEO.SYM.01/SEAM.EQUIV.01)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv318_arithmetic_capstone.py", "sourceSha256": "cdeda2f4b1e14bec5e2fa3f511fde225fc077d163b868fdbd807d83315e6946b", "linkedClaimIds": [ "ARITH.CAPSTONE.01" ], "sectionIds": [ "section:029b7dd988521b5ffc7e", "section:09b49009253acb5a0dfb", "section:31a155495fcd43cf1264", "section:3cc790136e8b9bd3c188", "section:7383e42c67f8eaba497b", "section:ab9e7e520130ecc7da7c", "section:cc398ba7e3e94c7addf2", "section:eb0bd97fda8c0fedefad" ], "activeSectionIds": [ "section:029b7dd988521b5ffc7e", "section:31a155495fcd43cf1264", "section:7383e42c67f8eaba497b", "section:ab9e7e520130ecc7da7c", "section:cc398ba7e3e94c7addf2" ], "evidenceId": "python_verification:verification/v318_arithmetic_capstone.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v318_arithmetic_capstone.py", "pubMirrorHash": "cdeda2f4b1e14bec5e2fa3f511fde225fc077d163b868fdbd807d83315e6946b", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v318_arithmetic_capstone.py" }, { "id": "v320_galois_cp_relation", "filename": "v320_galois_cp_relation.py", "path": "verification/v320_galois_cp_relation.py", "cluster": "frontier", "synopsis": "A NEW falsifiable prediction from the Galois structure: the two CP phases are locked, delta_PMNS = delta_CKM,lead + pi. Both phases are powers of one hexagonal unit rho=zeta_6 (v316): delta_CKM,lead=arg(rho)=pi/3=60deg, delta_PMNS=arg(rho^4)=4pi/3=240deg, rho^4=-rho, so delta_PMNS-delta_CKM,lead=pi exactly (the Z2 sheet flip) -- the quark and lepton leading CP phases are NOT independent. Prediction of record: delta_PMNS,lead=240deg (upgrades the assigned texture to a Galois-forced relation to the measured quark phase); currently within the broad NuFIT 6.0 range; KILL TEST: delta_PMNS robustly away from 240deg (>3 sigma; DUNE/Hyper-K/JUNO) falsifies the Galois-CP organization", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv320_galois_cp_relation.py", "sourceSha256": "523ece28d6b6eb1d04e1b4deeadaa4d98baa4969e6d864c798a9de267e2b1889", "linkedClaimIds": [ "GALOIS.CP.PREDICT.01" ], "sectionIds": [ "section:029b7dd988521b5ffc7e", "section:0541834291cb75f95ce2", "section:09b49009253acb5a0dfb", "section:2678ed3ba0ed508e2d8e", "section:3cc790136e8b9bd3c188", "section:51b5da5a67a36e5155ae", "section:568b5e9acdb7b04367d3", "section:697c671889813baf24f5", "section:7383e42c67f8eaba497b", "section:77994b345651d1c08987", "section:7a7de20f53ed3e69fb6f", "section:9736dbf5091605f1747b", "section:990b0c61d0a9e705bf40", "section:9b90248eafa8cb1d0229", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:b3159de77fcabb12cc0c", "section:d200c6e6e5dab4f9f985", "section:eb0bd97fda8c0fedefad", "section:f0ac30137703825661c6", "section:f6d50ad015506eb0de3c", "section:fdf63a1d99769ab37ccb" ], "activeSectionIds": [ "section:029b7dd988521b5ffc7e", "section:697c671889813baf24f5", "section:7383e42c67f8eaba497b", "section:77994b345651d1c08987", "section:7a7de20f53ed3e69fb6f", "section:9736dbf5091605f1747b", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:b3159de77fcabb12cc0c", "section:d200c6e6e5dab4f9f985", "section:f6d50ad015506eb0de3c", "section:fdf63a1d99769ab37ccb" ], "evidenceId": "python_verification:verification/v320_galois_cp_relation.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v320_galois_cp_relation.py", "pubMirrorHash": "523ece28d6b6eb1d04e1b4deeadaa4d98baa4969e6d864c798a9de267e2b1889", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v320_galois_cp_relation.py" }, { "id": "v321_killtest_board", "filename": "v321_killtest_board.py", "path": "verification/v321_killtest_board.py", "cluster": "frontier", "synopsis": "The forward kill-test board: the decisive upcoming measurements, ranked (forward companion to v307). Each entry is locked to a freeze_file.csv kill row: #1 JUNO sin^2 theta12=0.306747 (fastest), #2 CMB-S4/LiteBIRD r (kill r>0.01), #3 DESI/Euclid w=-1, #4 DUNE/Hyper-K delta_PMNS=240deg (the new v320 Galois-CP relation), #5 DUNE/LEGEND/nEXO ordering+m_betabeta, #6 PSI n2EDM nEDM, #7 JUNO sin^2 theta13 (~2 sigma now), #8 LiteBIRD beta. Coverage locked to freeze_file; >=7 decisive tests; a forward decision ledger complementing v307, no new physics", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv321_killtest_board.py", "sourceSha256": "debba6d7a00df62cbb70dac97b6b707eb4e37c4398d2f13371c571cddc08d610", "linkedClaimIds": [ "KILL.BOARD.01" ], "sectionIds": [ "section:0541834291cb75f95ce2", "section:77994b345651d1c08987", "section:7884780b54d3f6204d24", "section:9736dbf5091605f1747b", "section:990b0c61d0a9e705bf40", "section:9b90248eafa8cb1d0229", "section:ab9e7e520130ecc7da7c", "section:b5985d0cb2d5eb8aa959", "section:ddeb7ff0b27d4750ff23" ], "activeSectionIds": [ "section:77994b345651d1c08987", "section:7884780b54d3f6204d24", "section:9736dbf5091605f1747b", "section:ab9e7e520130ecc7da7c", "section:b5985d0cb2d5eb8aa959", "section:ddeb7ff0b27d4750ff23" ], "evidenceId": "python_verification:verification/v321_killtest_board.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v321_killtest_board.py", "pubMirrorHash": "debba6d7a00df62cbb70dac97b6b707eb4e37c4398d2f13371c571cddc08d610", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v321_killtest_board.py" }, { "id": "v322_cp_lock_sharpened", "filename": "v322_cp_lock_sharpened.py", "path": "verification/v322_cp_lock_sharpened.py", "cluster": "frontier", "synopsis": "The v320 CP-lock prediction sharpened into a quantitative kill test. The leading CP phase sits on the six hexagonal nodes arg(rho^k)=k*60deg; delta_CKM,lead=60deg (node 1), delta_PMNS,lead=240deg (node 4). The node selector IS the deck order: delta_PMNS,lead=|mu4|*delta_CKM,lead=4*(pi/3)=4pi/3=delta_CKM,lead+pi (rho^4=-rho). Sub-leading budget: delta_CKM,full=pi/3+3 lambda^2 (~68.7deg); the lepton sub-leading is a separate open holonomy term bounded by ~3 lambda^2~8.7deg => band 240 +- ~9deg. Current tension: vs NuFIT 6.0 NO (delta_CP=212 +26/-41 deg) the leading 240deg sits at +1.08 sigma, band edge ~231deg at +0.74 sigma -- compatible today. Kill: the nearest wrong node is 60deg away >> budget; DUNE/Hyper-K (~5-15deg) discriminate, >3 sigma outside kills the lock. An anarchic delta_CP hits the band with p~5% and node 4 1-in-6 -- a low-prior pre-registered prediction", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv322_cp_lock_sharpened.py", "sourceSha256": "b3261e7af6d7261306c2f32f681b6b3d29bf4fbf9fc3b352182f05a710d80c71", "linkedClaimIds": [ "GALOIS.CP.SHARPEN.01" ], "sectionIds": [ "section:029b7dd988521b5ffc7e", "section:09b49009253acb5a0dfb", "section:3cc790136e8b9bd3c188", "section:7383e42c67f8eaba497b", "section:ab9e7e520130ecc7da7c", "section:eb0bd97fda8c0fedefad" ], "activeSectionIds": [ "section:029b7dd988521b5ffc7e", "section:7383e42c67f8eaba497b", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v322_cp_lock_sharpened.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v322_cp_lock_sharpened.py", "pubMirrorHash": "b3261e7af6d7261306c2f32f681b6b3d29bf4fbf9fc3b352182f05a710d80c71", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v322_cp_lock_sharpened.py" }, { "id": "v323_bw_geometric_modular", "filename": "v323_bw_geometric_modular.py", "path": "verification/v323_bw_geometric_modular.py", "cluster": "frontier", "synopsis": "The keystone pushed one step: Bisognano-Wichmann makes the seam modular flow GEOMETRIC, so the mu4 deck invariance is not an independent axiom. The clock rho=diag(i^n)=exp(i(pi/2)L) is a geometric rotation (L=diag(n) the rotation generator, rho^4=I, mu4 in U(1)_rot). For a rotation-covariant covariance C=f(L) the modular Hamiltonian K=log((1-C)/C)=g(L), so [K,L]=0 (the modular flow commutes with all rotations) and [rho,K]=[rho,C]=0 -- the clock is a modular symmetry for free. Discriminator vs v309: a period-4 curvature preserves the clock but its modular flow is NOT geometric ([K,L]!=0); BW is strictly stronger. Linked bedrock: GIVEN the seam is the (E8)_1 chiral net (v308), BW/Hislop-Longo make the vacuum modular flow geometric => QGEO.SYM.01 (omega o rho=omega) is downstream of SEAM.EQUIV.01 + a rotation-invariant vacuum. Residual: the raw collar vacuum is rotation-invariant (cleaner than v309, shared with v308)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv323_bw_geometric_modular.py", "sourceSha256": "cfef049d611a93ab594892fb78c9a0dfb2faa7f51286e3961331e7e3d1088230", "linkedClaimIds": [ "QGEO.BW.01", "FORM.QGEO.BW.01" ], "sectionIds": [ "section:01c88746fb95cc0958d7", "section:029b7dd988521b5ffc7e", "section:04b7cfb5801c917940c7", "section:136a1e576865c1424f29", "section:213a1f15f7373957fc2f", "section:2525c189f32461c9368a", "section:2585b5d786c3bdb7ddb7", "section:2cf3ee9ae0a89a313d79", "section:49790f0118ee369b917a", "section:5ff3f529ae7be4541192", "section:671808877239add5f598", "section:6a93c4dd5fe420e1990e", "section:6cd1a267e72b20619327", "section:708f3d321d2dd13c9cb9", "section:81a6dc002dc46cf7b6c5", "section:8611c18776ca96eaa8ee", "section:888628823bf71f709698", "section:8e4972dbe899b5debb90", "section:8f5691e12b337bb463ce", "section:93b8868beb643874af75", "section:9a6aaf6fc60f9b74b301", "section:9f2ef8163653328e6c3e", "section:ab9e7e520130ecc7da7c", "section:ac6f5be914309816a43d", "section:acb731fecb30c7953915", "section:b93e6ae7b00f32ee1201", "section:d90bd5e1e6d8fa41397d", "section:eb00caf29086b02d5bf5", "section:f3b90b032a2851e13827", "section:f5274c8105ff62e99dcd" ], "activeSectionIds": [ "section:01c88746fb95cc0958d7", "section:029b7dd988521b5ffc7e", "section:04b7cfb5801c917940c7", "section:213a1f15f7373957fc2f", "section:2585b5d786c3bdb7ddb7", "section:2cf3ee9ae0a89a313d79", "section:49790f0118ee369b917a", "section:5ff3f529ae7be4541192", "section:671808877239add5f598", "section:708f3d321d2dd13c9cb9", "section:81a6dc002dc46cf7b6c5", "section:8611c18776ca96eaa8ee", "section:888628823bf71f709698", "section:8e4972dbe899b5debb90", "section:8f5691e12b337bb463ce", "section:9a6aaf6fc60f9b74b301", "section:ab9e7e520130ecc7da7c", "section:ac6f5be914309816a43d", "section:acb731fecb30c7953915", "section:f3b90b032a2851e13827", "section:f5274c8105ff62e99dcd" ], "evidenceId": "python_verification:verification/v323_bw_geometric_modular.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v323_bw_geometric_modular.py", "pubMirrorHash": "cfef049d611a93ab594892fb78c9a0dfb2faa7f51286e3961331e7e3d1088230", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v323_bw_geometric_modular.py" }, { "id": "v324_hypergraph_fiber", "filename": "v324_hypergraph_fiber.py", "path": "verification/v324_hypergraph_fiber.py", "cluster": "frontier", "synopsis": "The minimal hypergraph substrate that works: a (2,3,5)-network FIBERED by a 3-fold cusp channel reproduces both the E8 skeleton and the recovery gap (the constructive v312 follow-up). Network factor (carrier/5-fold): T_net=(A+2I)/4 fixes the Kac marks (eigenvalue 1=E8 skeleton), subleading (phi+2)/4 (golden); (2/3)^6 NOT in its spectrum (v312 negative). Cusp fiber (family/3-fold): T_cusp=diag((1-w)^{2N_fam}), w in {0,1/3,2/3} (N_fam=3, v317), spectrum {1,(2/3)^6,(1/3)^6}. Fibered substrate carries both: T=T_net (x) T_cusp has top eigenvalue 1 (eigenvector marks (x) w=0 = skeleton x democratic cusp) AND (2/3)^6 as a genuine eigenvalue (network attractor x cusp subleading). Honest injection (v312): without the fiber (T_net (x) I_3) there is no (2/3)^6 -- the cusp datum is injected, not graph-spectral; substrate = network x cusp = the v315 split 30=g_car*(2 N_fam)=5*6. Minimality: the smallest fiber is the 3-node cusp (=N_fam) = order-30 (v319 clock). Verdict: a consistent fibered realization, not a derivation of 2/3 from a pure rewrite", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv324_hypergraph_fiber.py", "sourceSha256": "81b2211d35635972d9b92559f15d62660df7c9e5014693ab674eff982f2d3149", "linkedClaimIds": [ "HYP.FIBER.01" ], "sectionIds": [ "section:029b7dd988521b5ffc7e", "section:09b49009253acb5a0dfb", "section:3cc790136e8b9bd3c188", "section:497660cf26cb0410a678", "section:584e87a9c163ac38f92f", "section:ab9e7e520130ecc7da7c", "section:ac6f5be914309816a43d", "section:ccaa58843679b0b5ee13", "section:eb0bd97fda8c0fedefad", "section:f3b90b032a2851e13827" ], "activeSectionIds": [ "section:029b7dd988521b5ffc7e", "section:497660cf26cb0410a678", "section:584e87a9c163ac38f92f", "section:ab9e7e520130ecc7da7c", "section:ac6f5be914309816a43d", "section:ccaa58843679b0b5ee13", "section:f3b90b032a2851e13827" ], "evidenceId": "python_verification:verification/v324_hypergraph_fiber.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v324_hypergraph_fiber.py", "pubMirrorHash": "81b2211d35635972d9b92559f15d62660df7c9e5014693ab674eff982f2d3149", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v324_hypergraph_fiber.py" }, { "id": "v325_pillowcase_keystone", "filename": "v325_pillowcase_keystone.py", "path": "verification/v325_pillowcase_keystone.py", "cluster": "frontier", "synopsis": "The seam keystone as ONE citable theorem: the raw seam state is the flat tau=i pillowcase state, with EXACTLY ONE open lemma. IF (raw RP-collar seam state = flat tau=i pillowcase / rotation-invariant state) THEN 4 square marks + mu4 deck + omega o rho=omega + holomorphic c=8 => (E8)_1, with the carrier recovery gap as input. Pieces (all exact): n=2chi(S^2)=4 (v216); cross-ratio 2 => j=1728 (v214/v267); flat orbifold S^2(2,2,2,2), chi_orb=0 (Troyanov); DtN sub-principal at m=0 mod 4 (v201/v280); det Cartan(E8)=1 vs D8=4 (v83/v143/v308); gap 6 ln(3/2)>0 (v76/v302). The ONE open lemma -- the raw collar state IS the flat tau=i pillowcase / rotation-invariant state -- is SHARED by both bedrock IDs (QGEO.SYM.01, SEAM.EQUIV.01; v323), machine-pinned in Lean (FORM.SEAMEQUIV.01 + FORM.QGEO.BW.01). An assembly/reduction certificate (like v176/v261), not a closure.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv325_pillowcase_keystone.py", "sourceSha256": "5d8c9e2d89fc10a2a3f173e697ea87c4e39fa36d48276c020da16f586b97ecec", "linkedClaimIds": [ "QGEO.KEYSTONE.01", "FORM.CARTAN.DET.01" ], "sectionIds": [ "section:2525c189f32461c9368a", "section:2cf3ee9ae0a89a313d79", "section:6cd1a267e72b20619327", "section:888628823bf71f709698", "section:ab9e7e520130ecc7da7c", "section:b93e6ae7b00f32ee1201", "section:f3b90b032a2851e13827" ], "activeSectionIds": [ "section:2cf3ee9ae0a89a313d79", "section:888628823bf71f709698", "section:ab9e7e520130ecc7da7c", "section:f3b90b032a2851e13827" ], "evidenceId": "python_verification:verification/v325_pillowcase_keystone.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v325_pillowcase_keystone.py", "pubMirrorHash": "5d8c9e2d89fc10a2a3f173e697ea87c4e39fa36d48276c020da16f586b97ecec", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v325_pillowcase_keystone.py" }, { "id": "v326_ftransfer_suite", "filename": "v326_ftransfer_suite.py", "path": "verification/v326_ftransfer_suite.py", "cluster": "frontier", "synopsis": "The F_transfer solver suite: the four transfer readouts as ONE runnable harness, each a gapped relaxation to a unique attractor, with values + uncertainties + honest typing (productises v303). F_pole (Koide): Moebius contraction to Q*=2/3 with multiplier (2/3)^6 = the seam-clock subleading eigenvalue, unique attractor at the SEAM rate. F_Boltzmann (eta_B): washout contraction to the balance 6.1e-11, monotone (H-theorem), external thermal rate. F_relic (axion): the comoving number N=E/omega is the adiabatic invariant, the relic freezes (seed theta_i=3pi/5), cosmological rate. F_QCD (m_p/m_e): 1-loop RG with carrier b0=7 flows to the Gaussian UV fixed point, Lambda_QCD generated; standard RG. F_RareKaon (bridge): BR(K+)=9.45e-11 on NA62 2016-2024 (v202). Only F_pole has the seam rate (2/3)^6; the other four share the SHAPE with external rates honestly fenced (v187/v303) -- the suite makes the frontier measurable without claiming the external rates.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv326_ftransfer_suite.py", "sourceSha256": "06de6ee1ed756d2c187f50e9cb2de4ce3b23796db5266bb4e1f406178e55441f", "linkedClaimIds": [ "FR.SUITE.01" ], "sectionIds": [ "section:2525c189f32461c9368a", "section:2692631f31aef19d9368", "section:6cd1a267e72b20619327", "section:888628823bf71f709698", "section:ab9e7e520130ecc7da7c", "section:b93e6ae7b00f32ee1201", "section:f3b90b032a2851e13827" ], "activeSectionIds": [ "section:2692631f31aef19d9368", "section:888628823bf71f709698", "section:ab9e7e520130ecc7da7c", "section:f3b90b032a2851e13827" ], "evidenceId": "python_verification:verification/v326_ftransfer_suite.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v326_ftransfer_suite.py", "pubMirrorHash": "06de6ee1ed756d2c187f50e9cb2de4ce3b23796db5266bb4e1f406178e55441f", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v326_ftransfer_suite.py" }, { "id": "v327_hypergraph_rewrite", "filename": "v327_hypergraph_rewrite.py", "path": "verification/v327_hypergraph_rewrite.py", "cluster": "frontier", "synopsis": "Deriving the cusp weight 2/3 from a minimal rewrite (sharpening v324/v312). A minimal local rule -- a family channel with N_fam=3 slots, one absorbing attractor (w=0) and |Z2|=2 surviving -- supplies the cusp fiber. M=[[1,0,0],[0,1/3,1/3],[0,1/3,1/3]] has spectrum {1,2/3,0}; 2/3=(N_fam-1)/N_fam=|Z2|/N_fam EMERGES from the rule arity, not injected. Over the order-6=2 N_fam hand the rate is (2/3)^6=64/729 = the recovery gap (v76/v324), derived. NON-GRAPH-SPECTRAL (proof, sharpening v312): 2/3 is NOT a root of the affine-E8 charpoly (p(2/3)=-3520/19683 != 0), so the recovery rate cannot be an adjacency eigenvalue. The absorbing state (eigenvalue 1) is the democratic w=0 law (v317). Honest residual: the arity {2,3} (the anchor atoms) is still the input (P2) -- v324's injected datum reduced to the anchor arity. Substrate = (2,3,5)-adjacency (carrier) x this minimal branching rule (family).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv327_hypergraph_rewrite.py", "sourceSha256": "5c55ee1d7e13a18f71e984a713b13ab7db0ae5618dc11b590c7e889c0acf1cb7", "linkedClaimIds": [ "HYP.REWRITE.01" ], "sectionIds": [ "section:09b49009253acb5a0dfb", "section:3cc790136e8b9bd3c188", "section:3d01f167d55724948536", "section:497660cf26cb0410a678", "section:4d7b24e6cd695cd3409f", "section:584e87a9c163ac38f92f", "section:7ef5c3edcea8d045b5b2", "section:8ac4310a6a4cf6c449f1", "section:ab9e7e520130ecc7da7c", "section:ccaa58843679b0b5ee13", "section:eb0ad9c39f3387e3dcf3", "section:eb0bd97fda8c0fedefad", "section:f3b90b032a2851e13827" ], "activeSectionIds": [ "section:3d01f167d55724948536", "section:497660cf26cb0410a678", "section:4d7b24e6cd695cd3409f", "section:584e87a9c163ac38f92f", "section:7ef5c3edcea8d045b5b2", "section:8ac4310a6a4cf6c449f1", "section:ab9e7e520130ecc7da7c", "section:ccaa58843679b0b5ee13", "section:eb0ad9c39f3387e3dcf3", "section:f3b90b032a2851e13827" ], "evidenceId": "python_verification:verification/v327_hypergraph_rewrite.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v327_hypergraph_rewrite.py", "pubMirrorHash": "5c55ee1d7e13a18f71e984a713b13ab7db0ae5618dc11b590c7e889c0acf1cb7", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v327_hypergraph_rewrite.py" }, { "id": "v328_theta13_pressure", "filename": "v328_theta13_pressure.py", "path": "verification/v328_theta13_pressure.py", "cluster": "neutrinos", "synopsis": "The theta13 pressure point: the honest weak spot, quantified and pre-registered. sin^2 theta13 = phi0 e^{-5/6} = 0.023108 vs NuFIT 6.0 NO (0.02195 +- 0.00058) is +2.0 sigma -- the most-tensioned CORE prediction (v62/v307). theta13 is the carrier hypercharge trace (exponent gamma=tr_E Y^2=5/6 EXACT, v268), NOT the seesaw mu-tau breaking that sets theta12 -- distinct channels (a theta13 pull does not move theta12). No cheap relief: the back-solved seed phi0(theta13)=0.0505 is ~5% below the axiom, PMNS theta13 RG running is <1% (NO) so cannot close it, and 5/6 is exact -- the prediction stays frozen (REG.FREEZE.01). Pre-registered kill: a stable sin^2 theta13 away from 0.023108 at >3 sigma (JUNO/global) flags the carrier-trace/seed-grammar reading. Exactly the v306 seed-hyperplane outlier -- one honest pressure point, not a pattern of failures.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv328_theta13_pressure.py", "sourceSha256": "a38930faff62d47871c9ea7986ae0940c7faf80d48c9332b999b3cdea1855276", "linkedClaimIds": [ "FLAV.TH13.PRESSURE.01" ], "sectionIds": [ "section:239f008e8aa92b407eb9", "section:3317d161dfba545d677a", "section:51b5da5a67a36e5155ae", "section:697c671889813baf24f5", "section:7a7de20f53ed3e69fb6f", "section:ab9e7e520130ecc7da7c", "section:cfd99b18e189abbc1f87", "section:f3b90b032a2851e13827" ], "activeSectionIds": [ "section:239f008e8aa92b407eb9", "section:3317d161dfba545d677a", "section:697c671889813baf24f5", "section:7a7de20f53ed3e69fb6f", "section:ab9e7e520130ecc7da7c", "section:cfd99b18e189abbc1f87", "section:f3b90b032a2851e13827" ], "evidenceId": "python_verification:verification/v328_theta13_pressure.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v328_theta13_pressure.py", "pubMirrorHash": "a38930faff62d47871c9ea7986ae0940c7faf80d48c9332b999b3cdea1855276", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v328_theta13_pressure.py" }, { "id": "v329_os_gap_reduction", "filename": "v329_os_gap_reduction.py", "path": "verification/v329_os_gap_reduction.py", "cluster": "frontier", "synopsis": "Closing the OS step: the bulk gap IS the transfer gap (second quantization), and assembling the single sufficient premise of the whole bedrock. [E] OS GAP = TRANSFER GAP: the OS/Euclidean many-body Hamiltonian dGamma(-log T) has spectrum = sums of single-mode energies, so the many-body (bulk) gap = the smallest positive single-mode energy = 6 ln(3/2), INDEPENDENT of system size -- exactly 'OS bulk gap = transfer gap' (the v308 open input), discharged at the many-body level. [E] H => omega o rho = omega: under H the covariance is rotation-covariant C=f(L), K=g(L) commutes with rho=exp(i(pi/2)L) (v201/v309/v323). [E] H => SRE => (E8)_1: det Cartan(E8)=1 vs D8=4 (v237/v308). [E] both bedrock IDs follow from the ONE premise H = 'raw collar = rotation-invariant flat tau=i pillowcase state' (Lean-pinned FORM.SEAMEQUIV.01 + FORM.QGEO.BW.01). [O] residual: the NECESSITY of H on the raw collar. Sharpens v240/v308/v323/v325; does NOT close the bedrock.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv329_os_gap_reduction.py", "sourceSha256": "12aea00b54a7c6bb79daf32b8c3f7471f9b8ec82561f25e71cc97135da3e7166", "linkedClaimIds": [ "QGEO.OSGAP.01" ], "sectionIds": [ "section:2525c189f32461c9368a", "section:2cf3ee9ae0a89a313d79", "section:5ff3f529ae7be4541192", "section:6cd1a267e72b20619327", "section:7d4bb4b4aaeb1717e77f", "section:8611c18776ca96eaa8ee", "section:888628823bf71f709698", "section:93b8868beb643874af75", "section:ab9e7e520130ecc7da7c", "section:acb731fecb30c7953915", "section:b93e6ae7b00f32ee1201", "section:eb00caf29086b02d5bf5" ], "activeSectionIds": [ "section:2cf3ee9ae0a89a313d79", "section:5ff3f529ae7be4541192", "section:7d4bb4b4aaeb1717e77f", "section:8611c18776ca96eaa8ee", "section:888628823bf71f709698", "section:ab9e7e520130ecc7da7c", "section:acb731fecb30c7953915" ], "evidenceId": "python_verification:verification/v329_os_gap_reduction.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v329_os_gap_reduction.py", "pubMirrorHash": "12aea00b54a7c6bb79daf32b8c3f7471f9b8ec82561f25e71cc97135da3e7166", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v329_os_gap_reduction.py" }, { "id": "v330_qgamb_admissible_measure", "filename": "v330_qgamb_admissible_measure.py", "path": "verification/v330_qgamb_admissible_measure.py", "cluster": "frontier", "synopsis": "Constructing the ambient measure on the gap-decoupled admissible sector as a bona fide Osterwalder-Schrader object (with the honest fence). [E] REFLECTION POSITIVITY: the seam transfer T (v221/v311; spectrum {1,(2/3)^6,(1/3)^6}) is symmetric PSD => the finite-volume measures are RP. [E] EXPONENTIAL CLUSTERING: C(n)/C(n-1) -> lambda_2=(2/3)^6 (xi=1/Delta, Delta=6 ln(3/2)). [E] TIGHTNESS => PROJECTIVE LIMIT: chi=sum_n C(n)=729/665 finite, so Var(S_L)/L -> chi => uniform tightness (Prokhorov) => the projective limit mu=lim mu_Lambda EXISTS on the admissible sector. [E] OS RECONSTRUCTION: H_OS=-log T>=0, unique vacuum, gap 6 ln(3/2) (v240) -- mu is a genuine OS measure on the admissible sector. [E] NEG: an ungapped transfer (lambda_2->1) sends chi->inf, tightness FAILS. [O] THE FULL AMBIENT MEASURE: the non-admissible (metric) sector is NOT built; by the gap margin Delta-31/(4pi^2)~1.648>0 (v76/v275) physical readouts do not need it, but QG.AMB.01 stays open. A genuine PARTIAL construction, NOT a closure.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv330_qgamb_admissible_measure.py", "sourceSha256": "21cbeb2b96d9ee581da3a9c45be400d77d232730ba37bbb19cb4cec07fb5e5be", "linkedClaimIds": [ "QGAMB.MEASURE.01" ], "sectionIds": [ "section:213a1f15f7373957fc2f", "section:2525c189f32461c9368a", "section:2cf3ee9ae0a89a313d79", "section:4a157afd200102fcaaee", "section:5ff3f529ae7be4541192", "section:6cd1a267e72b20619327", "section:7d4bb4b4aaeb1717e77f", "section:8611c18776ca96eaa8ee", "section:888628823bf71f709698", "section:93b8868beb643874af75", "section:ab9e7e520130ecc7da7c", "section:b93e6ae7b00f32ee1201", "section:cfd99b18e189abbc1f87", "section:ea84c12b5f6b31caebb5", "section:eb00caf29086b02d5bf5" ], "activeSectionIds": [ "section:213a1f15f7373957fc2f", "section:2cf3ee9ae0a89a313d79", "section:4a157afd200102fcaaee", "section:5ff3f529ae7be4541192", "section:7d4bb4b4aaeb1717e77f", "section:8611c18776ca96eaa8ee", "section:888628823bf71f709698", "section:ab9e7e520130ecc7da7c", "section:cfd99b18e189abbc1f87", "section:ea84c12b5f6b31caebb5" ], "evidenceId": "python_verification:verification/v330_qgamb_admissible_measure.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v330_qgamb_admissible_measure.py", "pubMirrorHash": "21cbeb2b96d9ee581da3a9c45be400d77d232730ba37bbb19cb4cec07fb5e5be", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v330_qgamb_admissible_measure.py" }, { "id": "v331_necessity_of_H", "filename": "v331_necessity_of_H.py", "path": "verification/v331_necessity_of_H.py", "cluster": "frontier", "synopsis": "The NECESSITY of H reduced: rotation-invariance of the seam DtN is EQUIVALENT to the four marks at the square (tau=i), so the one open lemma is exactly the order-4 CM selection (the necessity companion to v329's sufficiency). [E] SQUARE => [rho,Lambda]=0: marks at {0,pi/2,pi,3pi/2} make the curvature Z4-symmetric (Fourier support 0 mod 4), M_f couples only modes differing by 4Z (the v201/v210 sufficiency as a DtN |k|+M_f operator). [E] NECESSITY: a mark off the square breaks Z4 and gives [rho,Lambda]!=0 -- equivalence, not just implication. [E] ORDER-4 CM: cross-ratio(1,i,-1,-i)=2 => j=1728, the unique 4-config with an order-4 automorphism (v214/v267); H <=> square <=> mu4. [E] NEG: a Z2 mark set commutes with rho^2 but not rho. [O] residual: the dynamical SELECTION of the square (the 4 marks forced by v216, the square the unique order-4 CM) is the irreducible postulate. Does NOT close the bedrock.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv331_necessity_of_H.py", "sourceSha256": "5dee9560ad3ca3a6b19984e251bcdbba65b8b645d188f1f0296bfe7a182e041b", "linkedClaimIds": [ "QGEO.NECESS.01", "FORM.MU4COMM.01" ], "sectionIds": [ "section:2525c189f32461c9368a", "section:2b8d2aba4baeb7a0c36b", "section:303925994b6f141b3a0e", "section:6cd1a267e72b20619327", "section:8611c18776ca96eaa8ee", "section:888628823bf71f709698", "section:9800e2e20cb3dc2e280a", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:b93e6ae7b00f32ee1201", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:8611c18776ca96eaa8ee", "section:888628823bf71f709698", "section:9800e2e20cb3dc2e280a", "section:ab9e7e520130ecc7da7c", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v331_necessity_of_H.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v331_necessity_of_H.py", "pubMirrorHash": "5dee9560ad3ca3a6b19984e251bcdbba65b8b645d188f1f0296bfe7a182e041b", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v331_necessity_of_H.py" }, { "id": "v332_qgamb_metric_sector", "filename": "v332_qgamb_metric_sector.py", "path": "verification/v332_qgamb_metric_sector.py", "cluster": "frontier", "synopsis": "The metric sector of QG.AMB.01 characterized: the obstruction is exactly the conformal-mode (Gibbons-Hawking-Perry) problem, the physical sector is gap-insulated, and the only route is the conditional IDG taming (makes v330's metric-sector fence precise). [E] CONFORMAL-MODE WRONG SIGN: c_conf(D)=-(D-1)(D-2)/4 is NEGATIVE for D>=3 (c_conf(4)=-3/2) while the TT coefficient is positive -- the conformal-factor problem. [E] MEASURE OBSTRUCTION: the kinetic form is indefinite (one negative eigenvalue), so exp(-S) diverges over the conformal mode; the bare metric-sector measure is not directly definable. [E] PHYSICAL SECTOR INSULATED: the obstruction is in the conformal/gauge direction, not the admissible sector (positive+gapped, v330), margin Delta-31/(4pi^2)~1.648>0 (v76). [C] IDG CONDITIONAL ROUTE: the entire form factor e^{z/M^2} (v259/v304) dresses the conformal propagator with no extra pole. [E] NEG: a polynomial (R+R^2) truncation crosses zero (the Stelle ghost, v304/v278). [O] METRIC SECTOR OPEN: the full QG.AMB.01 needs the conformal mode resolved nonperturbatively (GHP rotation / IDG), gap-decoupled but NOT constructed. A precise characterization, NOT a closure.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv332_qgamb_metric_sector.py", "sourceSha256": "f27418f3602bf809b2249593d1c306f8f3441719e9b081bb7233d930e0f5d2fd", "linkedClaimIds": [ "QGAMB.METRIC.01" ], "sectionIds": [ "section:213a1f15f7373957fc2f", "section:2525c189f32461c9368a", "section:2cf3ee9ae0a89a313d79", "section:6cd1a267e72b20619327", "section:8611c18776ca96eaa8ee", "section:888628823bf71f709698", "section:ab9e7e520130ecc7da7c", "section:acb731fecb30c7953915", "section:b08e66805b3affcf9678", "section:b93e6ae7b00f32ee1201", "section:cfd99b18e189abbc1f87", "section:f5274c8105ff62e99dcd" ], "activeSectionIds": [ "section:213a1f15f7373957fc2f", "section:2cf3ee9ae0a89a313d79", "section:8611c18776ca96eaa8ee", "section:888628823bf71f709698", "section:ab9e7e520130ecc7da7c", "section:acb731fecb30c7953915", "section:b08e66805b3affcf9678", "section:cfd99b18e189abbc1f87", "section:f5274c8105ff62e99dcd" ], "evidenceId": "python_verification:verification/v332_qgamb_metric_sector.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v332_qgamb_metric_sector.py", "pubMirrorHash": "f27418f3602bf809b2249593d1c306f8f3441719e9b081bb7233d930e0f5d2fd", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v332_qgamb_metric_sector.py" }, { "id": "v333_cm_selection", "filename": "v333_cm_selection.py", "path": "verification/v333_cm_selection.py", "cluster": "frontier", "synopsis": "The CM-selection mechanism: tau=i (the square) is the UNIQUE order-4 modulus and the attractor of mark-equilibration, so the last keystone residual is 'the deck acts geometrically', not 'why the square' (the v331 follow-up). [E] ORDER-4 MODULAR ELEMENT: S=[[0,-1],[1,0]] in SL(2,Z) has S^2=-I, S^4=I and fixes tau=i; the unique order-4 elliptic point of PSL(2,Z) (the other, rho, is order 3). [E] DECK ORDER -> CM POINT: order-4 -> cross-ratio 2 -> j=1728 -> tau=i (square); order-3 -> j=0 -> tau=rho (hexagon); |mu4|=4 selects tau=i. [E] MARK-EQUILIBRATION ATTRACTOR: 4 points minimizing the log-energy (Fekete) converge to equal spacing (gaps pi/2 = the square); the square beats random perturbations -- the unique (mod rotation) attractor. [E] NEG: an order-3 deck selects rho not the square. [O] residual: only 'the deck acts GEOMETRICALLY (= QGEO.SYM.01) vs an abstract Z4 on labels' stays open -- the residual sharpens from 'why the square' to 'the deck acts geometrically'. NOT a closure.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv333_cm_selection.py", "sourceSha256": "b260ecc9c2971311fd00d7d429f58f99e0abac47ecf9969f70e2b109cc12671d", "linkedClaimIds": [ "QGEO.CMSELECT.01" ], "sectionIds": [ "section:2525c189f32461c9368a", "section:2cf3ee9ae0a89a313d79", "section:6cd1a267e72b20619327", "section:888628823bf71f709698", "section:8b1a1c6a205860e21edc", "section:ab9e7e520130ecc7da7c", "section:b93e6ae7b00f32ee1201", "section:ee232865bdd19669d0cd", "section:f1054498b80cd7df6676" ], "activeSectionIds": [ "section:2cf3ee9ae0a89a313d79", "section:888628823bf71f709698", "section:8b1a1c6a205860e21edc", "section:ab9e7e520130ecc7da7c", "section:ee232865bdd19669d0cd", "section:f1054498b80cd7df6676" ], "evidenceId": "python_verification:verification/v333_cm_selection.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v333_cm_selection.py", "pubMirrorHash": "b260ecc9c2971311fd00d7d429f58f99e0abac47ecf9969f70e2b109cc12671d", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v333_cm_selection.py" }, { "id": "v334_conformal_resolution", "filename": "v334_conformal_resolution.py", "path": "verification/v334_conformal_resolution.py", "cluster": "frontier", "synopsis": "The conformal-mode resolution: the Gibbons-Hawking-Perry contour rotation (IR sign) + the infinite-derivative (IDG) dressing (UV pole) give a CONDITIONALLY convergent metric-sector measure; the residual is the nonperturbative validity of the contour (the v332 follow-up). [E] THE OBSTRUCTION: c_conf(4)=-3/2<0, the unrotated conformal Gaussian diverges. [E] GHP CONTOUR ROTATION: phi->i phi flips the sign, int(exp(-|c|phi^2))=sqrt(pi/|c|) FINITE (GHP 1978). [E] IDG UV DRESSING: the entire form factor exp(p^2/M^2)>0 (no ghost pole, v304), dressed per-mode action positive post-GHP and UV-suppressed. [E] NEG: a polynomial truncation crosses zero (the Stelle ghost, v304/v278). [C] CONDITIONAL CONSTRUCTION: GHP+IDG give a convergent metric-sector Gaussian mode-by-mode (conditional on the contour + entire analyticity). [O] residual: whether the GHP-rotated IDG-dressed measure is the CORRECT nonperturbative QG.AMB measure (the contour's nonperturbative validity); gap-decoupled (v76), blocks no test. NOT a closure.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv334_conformal_resolution.py", "sourceSha256": "1426cf457992731d332706f2303552d3bd59770c101ea0ecd3d88b4d525eefd3", "linkedClaimIds": [ "QGAMB.CONFORMAL.01" ], "sectionIds": [ "section:213a1f15f7373957fc2f", "section:2525c189f32461c9368a", "section:2b8d2aba4baeb7a0c36b", "section:303925994b6f141b3a0e", "section:4a157afd200102fcaaee", "section:4dcf513f2ae74de8645b", "section:5ff3f529ae7be4541192", "section:6cd1a267e72b20619327", "section:888628823bf71f709698", "section:93b8868beb643874af75", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:acb731fecb30c7953915", "section:b08e66805b3affcf9678", "section:b93e6ae7b00f32ee1201", "section:c00f76407fefd9782fd7", "section:eb00caf29086b02d5bf5", "section:ee232865bdd19669d0cd", "section:f5274c8105ff62e99dcd", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:213a1f15f7373957fc2f", "section:4a157afd200102fcaaee", "section:4dcf513f2ae74de8645b", "section:5ff3f529ae7be4541192", "section:888628823bf71f709698", "section:ab9e7e520130ecc7da7c", "section:acb731fecb30c7953915", "section:b08e66805b3affcf9678", "section:c00f76407fefd9782fd7", "section:ee232865bdd19669d0cd", "section:f5274c8105ff62e99dcd", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v334_conformal_resolution.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v334_conformal_resolution.py", "pubMirrorHash": "1426cf457992731d332706f2303552d3bd59770c101ea0ecd3d88b4d525eefd3", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v334_conformal_resolution.py" }, { "id": "v335_seam_equiv_unify", "filename": "v335_seam_equiv_unify.py", "path": "verification/v335_seam_equiv_unify.py", "cluster": "core", "synopsis": "The keystone unification: there is ONE open theorem (SEAM.EQUIV.01), QGEO.SYM.01 is its COROLLARY (a conformal-net axiom), and QG.AMB.01 is a decoupled general QG problem, NOT a TFPT gate. [E] QGEO.SYM.01 = COROLLARY: a chiral conformal net has a Moebius-covariant vacuum (the unique invariant positive-energy vector, a NET AXIOM); rotations U(1) < Moebius => rotation-invariant vacuum; the mu4 clock = rotation by pi/2 fixes it => omega o rho = omega. So SEAM.EQUIV.01 => QGEO.SYM.01 with NO extra premise (the v323 'rotation-invariant vacuum' is a net axiom); the two bedrock items collapse to ONE. [E] THE ONE KEYSTONE THEOREM: SEAM.EQUIV.01 = a construction theorem (c=8, det Cartan E8=1, gap 6 ln(3/2)>0 derived) with EXACTLY 1 open continuum lemma. [E] QG.AMB.01 DECOUPLED: margin Delta-31/(4pi^2)~1.648>0 => no TFPT prediction depends on it; the general Euclidean-QG conformal-factor problem (GHP 1978), inherited not TFPT-specific. [E] COLLAPSED STATUS: structural items 2->1; live residual = v_geo + G_net(=SEAM.EQUIV.01) + F_transfer. [O] the one residual = SEAM.EQUIV.01's continuum OS reconstruction (Lean-pinned). A synthesis/inventory; does NOT close SEAM.EQUIV.01.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv335_seam_equiv_unify.py", "sourceSha256": "04854b5445a8c31f8c38e2d376dc2b4b0fae623cec9fc5b734a76c205732517c", "linkedClaimIds": [ "SEAM.EQUIV.UNIFY.01" ], "sectionIds": [ "section:04b7cfb5801c917940c7", "section:213a1f15f7373957fc2f", "section:2525c189f32461c9368a", "section:2585b5d786c3bdb7ddb7", "section:2b8d2aba4baeb7a0c36b", "section:2cf3ee9ae0a89a313d79", "section:303925994b6f141b3a0e", "section:4dcf513f2ae74de8645b", "section:6a93c4dd5fe420e1990e", "section:6cd1a267e72b20619327", "section:75d473d613aba16a08b8", "section:81a6dc002dc46cf7b6c5", "section:888628823bf71f709698", "section:8e4972dbe899b5debb90", "section:a153934887244824336d", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:b93e6ae7b00f32ee1201", "section:c00f76407fefd9782fd7", "section:cfd99b18e189abbc1f87", "section:d90bd5e1e6d8fa41397d", "section:ea84c12b5f6b31caebb5", "section:f5274c8105ff62e99dcd", "section:f68163cf343646a0f102", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:04b7cfb5801c917940c7", "section:213a1f15f7373957fc2f", "section:2585b5d786c3bdb7ddb7", "section:2cf3ee9ae0a89a313d79", "section:4dcf513f2ae74de8645b", "section:75d473d613aba16a08b8", "section:81a6dc002dc46cf7b6c5", "section:888628823bf71f709698", "section:8e4972dbe899b5debb90", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:c00f76407fefd9782fd7", "section:cfd99b18e189abbc1f87", "section:ea84c12b5f6b31caebb5", "section:f5274c8105ff62e99dcd", "section:f68163cf343646a0f102", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v335_seam_equiv_unify.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v335_seam_equiv_unify.py", "pubMirrorHash": "04854b5445a8c31f8c38e2d376dc2b4b0fae623cec9fc5b734a76c205732517c", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v335_seam_equiv_unify.py" }, { "id": "v336_continuum_limit", "filename": "v336_continuum_limit.py", "path": "verification/v336_continuum_limit.py", "cluster": "core", "synopsis": "The ONE open lemma of SEAM.EQUIV.01, stated precisely and mapped to the recent rigorous literature: the continuum-limit and OS-reconstruction legs are now CITABLE, the genuinely-open residual narrows. [C] CONTINUUM LEG: Osborne-Stottmeister (CFT from Lattice Fermions, CMP 398 (2023) 219; legacy internal token MMST, on the MMST/Morinelli-Morsella-Stottmeister-Tanimoto OAR framework, arXiv:2010.11121) give the chiral-CFT scaling limit of free lattice fermions (Koo-Saleur -> Virasoro); WZW range rank<=c<=D. (E8)_1: c=8, rank 8, D=16 Majoranas (SO(16)_1 -> (E8)_1), 8<=8<=16 in range; the collar is gapped quasi-free (CAR). [C] OS LEG: Adamo-Moriwaki-Tanimoto (arXiv:2407.18222) prove the conformal OS axioms for unitary VOAs incl. lattice VOAs; (E8)_1 is the even self-dual rank-8 lattice VOA. [C] CONSTRUCTION + COVARIANCE (Adamo-Giorgetti-Tanimoto): arXiv:2506.01008 builds the 2d conformal net of an even lattice and classifies the 2d Heisenberg-net extensions as lattice nets (the lattice IS a conformal net), and arXiv:2508.07109 shows every DHR rep of such a net is automatically positive-energy + diffeomorphism-covariant (covariance is a consequence, not an input; defuses the v215 BW circularity). [E] TARGET PINNED: c=g_car+N_fam=8, det Cartan E8=1, the D=16 Majorana SO(16)_1 IS the carrier-16 and the mu4 extension IS the seam glue. [O] OPEN RESIDUAL: c=8 alone does NOT pin the net (SO(16)_1 also c=8, det 4), so the open lemma = the holomorphy discriminator det K=1. 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"verification/v337_decoupling_theorem.py", "cluster": "frontier", "synopsis": "THE DECOUPLING THEOREM (consolidated, citable): every TFPT dimensionless readout factors through the gapped admissible sector and is INDEPENDENT of the ambient QG measure -- the theorem that makes the QG.AMB.01 reclassification (v335) honest. [E] GAP MARGIN: Delta - 2*dim(E8)*c3^2 = 6 ln(3/2) - 31/(4 pi^2) ~ 1.648 > 0. [E] FACTORIZATION: every readout (mass ratios, mixings, alpha^-1, R+R^2) is a function of the admissible gapped transfer spectrum {1,(2/3)^6,(1/3)^6} + the discrete kernel alone. [E] THE THEOREM: margin>0 => exponential clustering (lambda_2=(2/3)^6), finite susceptibility chi=729/665, so the ambient contribution is gap-suppressed => no readout depends on the ambient measure => QG.AMB.01 decoupled. [E] NEG CONTROL: gap closed => chi diverges => fails (non-vacuous). [E] COROLLARY: zero frozen kill tests depend on the ambient measure. 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[N] SK-DEPENDENT TENSION: sin^2 theta13 = phi0 e^{-5/6} = 0.023108 is +2.0 sigma vs the no-SK central (0.02195) and +1.7 sigma vs the with-SK NO best fit (0.02215) -- NOT a clean 2 sigma. [E] WITHIN 3 SIGMA: 0.023108 < the with-SK 3 sigma upper 0.02388 (not falsified). [N] BUDGET: moving to the central needs -4.1%; RG < 1% and the exponent 5/6 is exact => no freeze-respecting relief (v328). [X] JUNO DECIDES: sub-1% precision turns 1.7-2.0 sigma into ~6 sigma -- near-term pre-registered kill/confirm. 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Both NO, with the exact reason per residual, classified into FOUR kinds. [E] v_geo/M_Planck FORBIDDEN BY THEOREM (No-Unit, v153): a mass is dimension 1 while every TFPT datum is dimension 0, so no dimensionless map outputs a scale; over-determined (gravity = dark energy to 0.11%, v274); every RATIO is derived, only the unit is not. [E] m_p/m_e structure in place (v262): carrier b3=-7 + closed electron; 2 external inputs: alpha_s(M_Z) and the lattice C_p~2.83. [X] alpha_s external BECAUSE OF A TENSION: SM content does NOT unify (spread ~8.8 at 2e16, v246). [N] C_p parameter-free but lattice-only (v35). [C] eta_B/axion = cosmological initial conditions; Koide Q=2/3 structural [E]. [A] FOUR kinds: forbidden-by-theorem / external-parameter-free / external-tensioned / cosmological. A boundary audit, NOT a solution.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv339_firstprinciples_boundary.py", "sourceSha256": "f6f1bbe5cdc094c7fe32aac5bd92be22833121f41b611aab374836d11685573b", "linkedClaimIds": [ "FIRSTPRINCIPLES.BOUNDARY.01" ], "sectionIds": [ "section:2805350687457d7649bf", "section:a850fdd649c27ed35b89", "section:ab9e7e520130ecc7da7c" ], "activeSectionIds": [ "section:2805350687457d7649bf", "section:a850fdd649c27ed35b89", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v339_firstprinciples_boundary.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v339_firstprinciples_boundary.py", "pubMirrorHash": "f6f1bbe5cdc094c7fe32aac5bd92be22833121f41b611aab374836d11685573b", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v339_firstprinciples_boundary.py" }, { "id": "v340_As_reconcile", "filename": "v340_As_reconcile.py", "path": "verification/v340_As_reconcile.py", "cluster": "frontier", "synopsis": "A_s is predicted (not missing), is DIMENSIONLESS (so it does NOT define an absolute mass), and the apparent -11 sigma tension is a reheating-channel question -- reconciled with the archived old derivation (TFPT v4.5/v4.6). [E] A_s = N_star^2 (M_scal/Mbar)^2/(24 pi^2) = N_star^2 c3^7/(24 pi^2) (v86); M_scal/Mbar = c3^{7/2} = 1.2565e-5 is a PURE RATIO, so A_s carries NO absolute scale -- it pins N_star, NOT M_bar => A_s does NOT define mass (No-Unit v153 stands). [N] the -11 sigma is the slow-vs-fast reheating dichotomy (slow Higgs N_star=51.44 -> A_s=1.764e-9; A_s-preferred N_star=56.2). [P] ARCHIVE: old v4.5/v4.6 used the algebraic N_star=3/phi0-1=55.42 and reported A_s=2.124e-9; at that N_star the current normalisation gives 2.047e-9 (-1.9 sigma). [E] nothing lost: the current theory DERIVES N_star (record band [50,60], v84). [X] decisive test: fast preheating or slow reheating confirmed.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv340_As_reconcile.py", "sourceSha256": "e42af560ef291569e5427c8f8f908f4af16daa12dc8cc8ac1cf4826834b05792", "linkedClaimIds": [ "AS.RECONCILE.01" ], "sectionIds": [ "section:30f11b5d5f7a7088ac58", "section:3bd0d82163305ccd4d89", "section:8586f27d7589c2e3d5c5", "section:ab9e7e520130ecc7da7c", "section:b8644b20b70a62943387", "section:cc0b991cf89028331b90" ], "activeSectionIds": [ "section:3bd0d82163305ccd4d89", "section:ab9e7e520130ecc7da7c", "section:b8644b20b70a62943387" ], "evidenceId": "python_verification:verification/v340_As_reconcile.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v340_As_reconcile.py", "pubMirrorHash": "e42af560ef291569e5427c8f8f908f4af16daa12dc8cc8ac1cf4826834b05792", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v340_As_reconcile.py" }, { "id": "v351_continuum_realisation_sharpened", "filename": "v351_continuum_realisation_sharpened.py", "path": "verification/v351_continuum_realisation_sharpened.py", "cluster": "core", "synopsis": "The continuum realisation sharpened -- the 'c=8 ambiguity' flagged open in v277/v344 (E8 vs SO(16) both have c=8) is RESOLVED, non-circularly, by the seam's ORDER-4 mu4 clock. [E] E8 (det 1, holomorphic) vs D8=SO(16) (det 4). [E] the order-4 clock (the four Gauss-Bonnet marks, |mu4|=4=h(A3), v216): index-4 extension D5(+)A3 = E8 (v154), index-2 = SO(16); so order-4 selects E8 (16->4->1) not SO(16) (16->4) -- the order (4 not 2) is the discriminator. [E] bootstrap agrees: h(E8)=30 (max prime 5) vs h(D8)=14 (max prime 7). [E] which-net ambiguity RESOLVED (det K=1 is then a consequence). [O] residual = PURELY the chiral-edge/scaling-limit existence (bulk-edge, v336), net+holomorphy pinned. 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The No-Unit Theorem (v153) showed the dimensionless compiler cannot output a scale (v_geo a forced unit). SHARPENING after the parameter-free gravity (v358/v359/v361): the gravity sector adds NO new scale either -- 1/c3=8pi and the Lambda prefactor (8pi)^2*48c3^4=3/(4pi^2) are dimensionless, so 1/G~v_geo^2 and Lambda~(dimensionless)*v_geo^4 reduce to v_geo times atoms. [E] FINAL TALLY: every dimensionful quantity = (dimensionless ratio)*(power of v_geo); free content = {v_geo, pi}, ZERO dimensionless dials, vs the SM's ~26. [O] v_geo irreducibly primitive (No-Unit; 1/G UV-sensitive Sakharov v68). 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[E] the carrier's gravitational anomaly is FORCED: c_-=8 (16 Majoranas=dim S+=2^(g_car-1); chiral central charge 16/2=8=g_car+N_fam, the same c_- as v358). [E] the backreaction is FINITE -> Lambda from alpha: the matter vacuum energy through G_ab=(1/c3)T_ab is gap-suppressed (Decoupling Thm v337) to rho_Lambda/Mbar^4=(3/(4 pi^2))e^{-2 alpha^-1} (v60), 123 orders = 119.03+3.92 -- NOT the M_Pl^4 catastrophe; the loop (v359+v60+carrier vacuum) closes. [E] J3 explicit (v358): delta=(8 pi^2 R^4/15) delta, carrier T_ab=the SM's (v159). [C] SM trace anomaly reproduced (content=SM). [O] DECLINE: no new atom-forced read-out of individual SM quantum numbers beyond c_-=8 and Lambda -> per v354/v355 declined. Finite & consistent backreaction, no new dial.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv361_grav_backreaction.py", "sourceSha256": "c412314a87a2018a1fe9aadb098ad4d25fd1e5cadd1cbce513b9d31660648dd4", "linkedClaimIds": [ "GRAV.BACKREACT.01" ], "sectionIds": [ "section:761d5a6c7853cbe93148", "section:93b8868beb643874af75", "section:9a6aaf6fc60f9b74b301", "section:ab9e7e520130ecc7da7c", "section:b0eabbf91a1894618a3d", "section:eb00caf29086b02d5bf5", "section:f5274c8105ff62e99dcd" ], "activeSectionIds": [ "section:761d5a6c7853cbe93148", "section:9a6aaf6fc60f9b74b301", "section:ab9e7e520130ecc7da7c", "section:b0eabbf91a1894618a3d", "section:f5274c8105ff62e99dcd" ], "evidenceId": "python_verification:verification/v361_grav_backreaction.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v361_grav_backreaction.py", "pubMirrorHash": "c412314a87a2018a1fe9aadb098ad4d25fd1e5cadd1cbce513b9d31660648dd4", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v361_grav_backreaction.py" }, { "id": "v360_grav_gap_corrections", "filename": "v360_grav_gap_corrections.py", "path": "verification/v360_grav_gap_corrections.py", "cluster": "core", "synopsis": "Direction 2: the gap-induced higher-curvature correction to GR -- the disciplined result. Does the seam transfer gap give a NEW forced near-term GR-deviation beyond the known R^2 scalaron? With the v354/v355 discriminator: NO. [E] the leading higher-curvature term IS the R^2 scalaron (a4=R^2/72 v36; M_scal^2/Mbar^2=c3^7, exp 7=g+N-1) -- already in TFPT, already falsifiable via n_s=1-2/N*, r=12/N*^2 (CMB-S4). [C] it is the entanglement-equilibrium next order (Wald first law -> f(R)=R+R^2, v28/v359). [E] the gap Delta=6 ln(3/2) is dimensionless, so a distinct gap term sits at xi*v_geo ~ seam/Planck scale, not near-term observable. [O] DECLINE: a new dimensionless coefficient is not atom-forced (needs heat-kernel/Wald data; exp 7 vs 6, c3^7 vs (2/3)^6 unrelated) -> per v354/v355 declined. No new near-term forced prediction; the answer is the scalaron.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv360_grav_gap_corrections.py", "sourceSha256": "2d2ba9d18b8856e5b7b1dd34aceffd08fb17badd9f64cdfb7be5039e3119fa69", "linkedClaimIds": [ "GRAV.GAPCORR.01" ], "sectionIds": [ "section:72b43011ac4fb932c47a", "section:ab9e7e520130ecc7da7c", "section:b9e3cb43b2bc303303e6", "section:f5274c8105ff62e99dcd" ], "activeSectionIds": [ "section:72b43011ac4fb932c47a", "section:ab9e7e520130ecc7da7c", "section:b9e3cb43b2bc303303e6", "section:f5274c8105ff62e99dcd" ], "evidenceId": "python_verification:verification/v360_grav_gap_corrections.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v360_grav_gap_corrections.py", "pubMirrorHash": "2d2ba9d18b8856e5b7b1dd34aceffd08fb17badd9f64cdfb7be5039e3119fa69", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v360_grav_gap_corrections.py" }, { "id": "v359_grav_nonlinear_einstein", "filename": "v359_grav_nonlinear_einstein.py", "path": "verification/v359_grav_nonlinear_einstein.py", "cluster": "core", "synopsis": "The FULL covariant Einstein equation, parameter-free (Direction 1, extends v358). The Jacobson-2015 fixed-VOLUME entanglement equilibrium brings in the EINSTEIN TENSOR G_ab (not just R_ab) -- the unique divergence-free metric tensor (Lovelock) -- so equilibrium yields the full covariant G_ab + Lambda g_ab = (1/c3) T_ab with conservation built in. [C/E] fixed-volume -> Einstein tensor (trace=-R in d=4). [E] Lovelock => nabla^a T_ab=0 is an output. [E] coeff 1: 8pi=1/c3 fixed (v358). [E] coeff 2: Lambda from alpha -- rho_Lambda/Mbar^4=(3/(4pi^2))e^{-2 alpha^-1}, prefactor (8pi)^2*48c3^4=3/(4pi^2) (v60); BOTH coefficients TFPT-fixed. RESULT: the original B6 full covariant field equation is now parameter-free at the LOCAL level. [O] residual: the equation-of-state status + the global ambient measure (C7).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv359_grav_nonlinear_einstein.py", "sourceSha256": "607d1ed5742664fd809c40ec53e1b473c230663b2e5949c8bee5aa7ae4ceb98a", "linkedClaimIds": [ "GRAV.NONLINEAR.01" ], "sectionIds": [ "section:01c88746fb95cc0958d7", "section:08b2bae94061036431b4", "section:0c131301948f5acf50d5", "section:136a1e576865c1424f29", "section:17538bc5f76786fa0bbe", "section:213a1f15f7373957fc2f", "section:2b8d2aba4baeb7a0c36b", "section:2db6bd35ce5c578613f3", "section:2e4923f3fd42adc44e3d", "section:2ffaaee2ce19180008ab", "section:303925994b6f141b3a0e", "section:307c4c95a7c84b5efc0b", "section:33f8ca97d5f5599b425b", "section:3bfc0afca092b381dee1", "section:3c0ef7a887cebe028f40", "section:3ef64d782ddc411f1754", "section:40ced8641cc307aac43a", "section:49790f0118ee369b917a", "section:4a157afd200102fcaaee", "section:4e5537e69e05316e0599", "section:56ca118419000d5423f4", "section:5ff3f529ae7be4541192", "section:65138c298db225aabbae", "section:6a93c4dd5fe420e1990e", "section:6c9d1c3b370b8f366d55", "section:701d23928f8e38ea7d4b", "section:72b43011ac4fb932c47a", "section:75d473d613aba16a08b8", "section:761d5a6c7853cbe93148", "section:7df526709d9eeccd2491", "section:81a6dc002dc46cf7b6c5", "section:840d8edcd2db5226531d", "section:89a96ea40df8ee1ce3c8", "section:8b1a1c6a205860e21edc", "section:8f5691e12b337bb463ce", "section:8f73277edff787de34d0", "section:91c49cb4658c6aa96d2e", "section:93b8868beb643874af75", "section:94fabfd63333427d7867", "section:9a6aaf6fc60f9b74b301", "section:9d6c7d63f5df5a4df579", "section:9f2ef8163653328e6c3e", "section:a153934887244824336d", "section:a5afdfe2d50d9975d56b", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:b0eabbf91a1894618a3d", "section:b191b0a66e5bacdc1a0e", "section:b3146d55cec712d485d5", "section:b6f6bed3bead3afd28d6", "section:b9e3cb43b2bc303303e6", "section:be245dd6a6eb1776e773", "section:c80612b5b357f44d318a", "section:d90bd5e1e6d8fa41397d", "section:e4bb9a238c9f340ff5d1", "section:e7b2d5a6deafa57401db", "section:ea84c12b5f6b31caebb5", "section:eb00caf29086b02d5bf5", "section:f5274c8105ff62e99dcd", "section:f55a4eb54f833ae02970", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:01c88746fb95cc0958d7", "section:08b2bae94061036431b4", "section:17538bc5f76786fa0bbe", "section:213a1f15f7373957fc2f", "section:3c0ef7a887cebe028f40", "section:40ced8641cc307aac43a", "section:49790f0118ee369b917a", "section:4a157afd200102fcaaee", "section:56ca118419000d5423f4", "section:5ff3f529ae7be4541192", "section:65138c298db225aabbae", "section:6c9d1c3b370b8f366d55", "section:72b43011ac4fb932c47a", "section:75d473d613aba16a08b8", "section:761d5a6c7853cbe93148", "section:7df526709d9eeccd2491", "section:81a6dc002dc46cf7b6c5", "section:89a96ea40df8ee1ce3c8", "section:8b1a1c6a205860e21edc", "section:8f5691e12b337bb463ce", "section:8f73277edff787de34d0", "section:94fabfd63333427d7867", "section:9a6aaf6fc60f9b74b301", "section:9d6c7d63f5df5a4df579", "section:a153934887244824336d", "section:a5afdfe2d50d9975d56b", "section:ab9e7e520130ecc7da7c", "section:b0eabbf91a1894618a3d", "section:b3146d55cec712d485d5", "section:b6f6bed3bead3afd28d6", "section:b9e3cb43b2bc303303e6", "section:be245dd6a6eb1776e773", "section:e7b2d5a6deafa57401db", "section:ea84c12b5f6b31caebb5", "section:f5274c8105ff62e99dcd", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v359_grav_nonlinear_einstein.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v359_grav_nonlinear_einstein.py", "pubMirrorHash": "607d1ed5742664fd809c40ec53e1b473c230663b2e5949c8bee5aa7ae4ceb98a", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v359_grav_nonlinear_einstein.py" }, { "id": "v358_grav_entropy_equilibrium", "filename": "v358_grav_entropy_equilibrium.py", "path": "verification/v358_grav_entropy_equilibrium.py", "cluster": "core", "synopsis": "The entanglement-equilibrium derivation (Jacobson 2015 / Faulkner et al., delta S = delta) with TFPT's atoms -> the LINEARISED Einstein equation falls out PARAMETER-FREE, and the two formerly-open pieces are closed. [E] parameter-free Einstein coeff G_ab=(1/c3)T_ab, 1/c3=8pi fixed (Unruh 1/(2pi)=4c3, EH 1/(16pi)=c3/2, Einstein 8pi=1/c3, Bekenstein 1/4=1/|mu4|). [E] THERMO=GEO coincidence (new): the first law's 2pi/eta = the geometric |Z2|2pi chi iff |mu4|=|Z2|chi=4 -- the thermodynamic and geometric origins of c3 are ONE. [C] J3 solved: the CHM ball modular Hamiltonian (boost via BW v323) gives the matter flux delta=8pi^2 R^4/15 delta. [E] entropy density atom-fixed: 1/4=1/|mu4| + central charge c=g_car+N_fam=8 (form v59). [O] residual: the equation-of-state status + the global ambient measure (C7) + the v_geo unit (v359 closes the FULL covariant equation); no free dimensionless gravity dial remains.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv358_grav_entropy_equilibrium.py", "sourceSha256": "f5f0beb9178b8fffcde3b5b9458d75c025b3c1f7f2affffd24b8d7c938ca4ce2", "linkedClaimIds": [ "GRAV.ENTROPY.EQUILIBRIUM.01" ], "sectionIds": [ "section:01c88746fb95cc0958d7", "section:08b2bae94061036431b4", "section:0c131301948f5acf50d5", "section:136a1e576865c1424f29", "section:17538bc5f76786fa0bbe", "section:213a1f15f7373957fc2f", "section:2b8d2aba4baeb7a0c36b", "section:2db6bd35ce5c578613f3", "section:2e4923f3fd42adc44e3d", "section:2ffaaee2ce19180008ab", "section:303925994b6f141b3a0e", "section:307c4c95a7c84b5efc0b", "section:33f8ca97d5f5599b425b", "section:3bfc0afca092b381dee1", "section:3ef64d782ddc411f1754", "section:40ced8641cc307aac43a", "section:49790f0118ee369b917a", "section:4a157afd200102fcaaee", "section:4e5537e69e05316e0599", "section:56ca118419000d5423f4", "section:5ff3f529ae7be4541192", "section:65138c298db225aabbae", "section:671808877239add5f598", "section:6a93c4dd5fe420e1990e", "section:6c9d1c3b370b8f366d55", "section:701d23928f8e38ea7d4b", "section:708f3d321d2dd13c9cb9", "section:72b43011ac4fb932c47a", "section:75d473d613aba16a08b8", "section:761d5a6c7853cbe93148", "section:7df526709d9eeccd2491", "section:81a6dc002dc46cf7b6c5", "section:840d8edcd2db5226531d", "section:89a96ea40df8ee1ce3c8", "section:8b1a1c6a205860e21edc", "section:8f5691e12b337bb463ce", "section:91c49cb4658c6aa96d2e", "section:93b8868beb643874af75", "section:94fabfd63333427d7867", "section:9a6aaf6fc60f9b74b301", "section:9d6c7d63f5df5a4df579", "section:9f2ef8163653328e6c3e", "section:a153934887244824336d", "section:a5afdfe2d50d9975d56b", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:b0eabbf91a1894618a3d", "section:b191b0a66e5bacdc1a0e", "section:b3146d55cec712d485d5", "section:b6f6bed3bead3afd28d6", "section:be245dd6a6eb1776e773", "section:c80612b5b357f44d318a", "section:d90bd5e1e6d8fa41397d", "section:e4bb9a238c9f340ff5d1", "section:e7b2d5a6deafa57401db", "section:e99d6098550f62e277de", "section:ea84c12b5f6b31caebb5", "section:eb00caf29086b02d5bf5", "section:f5274c8105ff62e99dcd", "section:f55a4eb54f833ae02970", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:01c88746fb95cc0958d7", "section:08b2bae94061036431b4", "section:17538bc5f76786fa0bbe", "section:213a1f15f7373957fc2f", "section:40ced8641cc307aac43a", "section:49790f0118ee369b917a", "section:4a157afd200102fcaaee", "section:56ca118419000d5423f4", "section:5ff3f529ae7be4541192", "section:65138c298db225aabbae", "section:671808877239add5f598", "section:6c9d1c3b370b8f366d55", "section:708f3d321d2dd13c9cb9", "section:72b43011ac4fb932c47a", "section:75d473d613aba16a08b8", "section:761d5a6c7853cbe93148", "section:7df526709d9eeccd2491", "section:81a6dc002dc46cf7b6c5", "section:89a96ea40df8ee1ce3c8", "section:8b1a1c6a205860e21edc", "section:8f5691e12b337bb463ce", "section:94fabfd63333427d7867", "section:9a6aaf6fc60f9b74b301", "section:9d6c7d63f5df5a4df579", "section:a153934887244824336d", "section:a5afdfe2d50d9975d56b", "section:ab9e7e520130ecc7da7c", "section:b0eabbf91a1894618a3d", "section:b3146d55cec712d485d5", "section:b6f6bed3bead3afd28d6", "section:be245dd6a6eb1776e773", "section:e7b2d5a6deafa57401db", "section:e99d6098550f62e277de", "section:ea84c12b5f6b31caebb5", "section:f5274c8105ff62e99dcd", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v358_grav_entropy_equilibrium.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v358_grav_entropy_equilibrium.py", "pubMirrorHash": "f5f0beb9178b8fffcde3b5b9458d75c025b3c1f7f2affffd24b8d7c938ca4ce2", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v358_grav_entropy_equilibrium.py" }, { "id": "v356_continuum_mmst_applicability", "filename": "v356_continuum_mmst_applicability.py", "path": "verification/v356_continuum_mmst_applicability.py", "cluster": "core", "synopsis": "Direction A: the continuum chain of SEAM.EQUIV.01 assembled theorem-by-theorem, residual reduced to ONE lattice-realization input tied to the seam's one-sidedness. Chain: gapped (v302) quasi-free 16-Majorana collar (v155/v160) -> invertible (Kitaev, v301) -> the NONTRIVIAL invertible phase (c_-=8) -> a non-gappable anomalous chiral edge (anomaly inflow: edge EXISTENCE follows, reducing the v336/v351 'does the edge exist?' residual) -> chiral-CFT scaling limit (MMST v336, 8<=8<=16) -> order-4 mu4 clock + AQFT stack pin (E8)_1 (v351/v297). The only non-theorem link is the seam one-sidedness = the c3 origin (c_-!=0 = one-sided = the |Z2| oint K = 8 of c3=1/(8pi), v58). [C]/[E]/[O]; ADVANCES SEAM.EQUIV.01 to one realization input, does not close. (Direction B was found already closed by v40.)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv356_continuum_mmst_applicability.py", "sourceSha256": "4d076d55ef31ac0a7336e06af2e47b2f73428c080d634c496446d572dcbb6450", "linkedClaimIds": [ "SEAM.EQUIV.CONTINUUM.03" ], "sectionIds": [ "section:03b9058ca08ba4829ac7", "section:1a6d16256ec9d6226d97", "section:4a157afd200102fcaaee", "section:5f8b87dd447560390c4e", "section:6a93c4dd5fe420e1990e", "section:7144b70a605254dfecbc", "section:8e4972dbe899b5debb90", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d", "section:f97072f658fe6bcec8d8", "section:fd15b9954fc0175fba1b" ], "activeSectionIds": [ "section:1a6d16256ec9d6226d97", "section:4a157afd200102fcaaee", "section:5f8b87dd447560390c4e", "section:7144b70a605254dfecbc", "section:8e4972dbe899b5debb90", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:f97072f658fe6bcec8d8" ], "evidenceId": "python_verification:verification/v356_continuum_mmst_applicability.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v356_continuum_mmst_applicability.py", "pubMirrorHash": "4d076d55ef31ac0a7336e06af2e47b2f73428c080d634c496446d572dcbb6450", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v356_continuum_mmst_applicability.py" }, { "id": "v355_e8_unmapped_bandwidth", "filename": "v355_e8_unmapped_bandwidth.py", "path": "verification/v355_e8_unmapped_bandwidth.py", "cluster": "registry", "synopsis": "A disciplined bandwidth search of the unmapped E8 region (next step after v354), run with a STRICT discriminator: a candidate counts only if it is a FORCED identity (a theorem about E8), never a numerical coincidence -- because mining a rich object for matches is the numerology temptation. [E] FORCED SET-LEVEL (the real collective content): sum(degrees)=128=dim S+ the spinor half of 248=120+128; sum(exponents)=120=#pos roots; product(degrees)=|W(E8)|; exponents = the phi(30)=8 totatives of 30 (v223); max(degree)=30=h(E8). [C] SUGGESTIVE not forced: 12=h(E6),18=h(E7),30=h(E8) (the McKay ladder v219), but 'deg(E8) contains subalgebra Coxeter numbers' is not a theorem -- flagged. [O] DECLINED: the per-degree atom matches (14=dim G2, 20=det L, 24=|W(A3)|, 12=|R(A3)|, 18=p4(a); v66 flagged 12,18 fittable) each admit multiple readings, and the |W| prime 7='scalaron exponent' is one of many -- declined. [E] RECONCILES v66 (degrees=atoms) and v354 (only 2,8,30 primary): NO new forced physical hit; the disciplined decline IS the anti-numerology result.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv355_e8_unmapped_bandwidth.py", "sourceSha256": "11d7a248be3d51240d264e91bd22746af2169f425c07a9622ec6f53567c34d2e", "linkedClaimIds": [ "E8.UNMAPPED.BANDWIDTH.01" ], "sectionIds": [ "section:25a3a7ca87e0691a61b8", "section:44fb2c4f56d2211a1e7f", "section:4d7b24e6cd695cd3409f", "section:51b5da5a67a36e5155ae", "section:671808877239add5f598", "section:697c671889813baf24f5", "section:7a7de20f53ed3e69fb6f", "section:90d9ccdfa2e81d8ea0bd", "section:93b8868beb643874af75", "section:99fa7c49f30373d04fa1", "section:9a6aaf6fc60f9b74b301", "section:ab9e7e520130ecc7da7c", "section:b08e66805b3affcf9678", "section:b0eabbf91a1894618a3d", "section:b37031f13445096fcccf", "section:b9e3cb43b2bc303303e6", "section:db9b59159ab5489cccfa", "section:e99d6098550f62e277de", "section:eb00caf29086b02d5bf5", "section:f5274c8105ff62e99dcd", "section:f9ed8e942e9df8db94c7" ], "activeSectionIds": [ "section:25a3a7ca87e0691a61b8", "section:44fb2c4f56d2211a1e7f", "section:4d7b24e6cd695cd3409f", "section:671808877239add5f598", "section:697c671889813baf24f5", "section:7a7de20f53ed3e69fb6f", "section:90d9ccdfa2e81d8ea0bd", "section:99fa7c49f30373d04fa1", "section:9a6aaf6fc60f9b74b301", "section:ab9e7e520130ecc7da7c", "section:b08e66805b3affcf9678", "section:b0eabbf91a1894618a3d", "section:b37031f13445096fcccf", "section:b9e3cb43b2bc303303e6", "section:db9b59159ab5489cccfa", "section:e99d6098550f62e277de", "section:f5274c8105ff62e99dcd", "section:f9ed8e942e9df8db94c7" ], "evidenceId": "python_verification:verification/v355_e8_unmapped_bandwidth.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v355_e8_unmapped_bandwidth.py", "pubMirrorHash": "11d7a248be3d51240d264e91bd22746af2169f425c07a9622ec6f53567c34d2e", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v355_e8_unmapped_bandwidth.py" }, { "id": "v354_e8_reverse_audit", "filename": "v354_e8_reverse_audit.py", "path": "verification/v354_e8_reverse_audit.py", "cluster": "registry", "synopsis": "The REVERSE numerology audit + what the golden ratio means. The forward rule (v305) is one-directional (every readout must map onto E8); the reverse question: how much E8 structure maps onto NOTHING? [E] E8 has 8 Casimir invariant degrees {2,8,12,14,18,20,24,30}; THREE feed a readout (2 metric, 8 rank->c3, 30 Coxeter->g_car) and FIVE are UNMAPPED {12,14,18,20,24} -- 3/8 load-bearing, 5/8 not. [E] ECONOMY, NOT PROMISCUITY: a small fixed set (rank 8, h=30, det 1, D5(+)A3, 16-spinor) generates ALL readouts; the higher Casimirs are never reached into to fit -- the anti-numerology signature (economy + a large untouched remainder). [E] the golden ratio is UNMAPPED (the affine-E8 attractor eigenvalue v312, the icosian lattice v348; no FROZEN readout is phi -- the sole [C] exception, cos(theta_i=3pi/5)=-1/(2phi) on the axion spine branch, refined in v429) -> NOT numerology (which needs a number fitted to an observation); phi is the algebraic signature of the 5-fold h=30=2*3*5, the carrier announcing it is icosahedral. [O] the 5/8 unmapped is the HULL OVERHEAD (E8 = minimal unimodular hull, not the world group); where future readouts could live, or over-capacity. The reverse complement of v305.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv354_e8_reverse_audit.py", "sourceSha256": "aeacc858d379d929440e50030e77ab775a5b52949b04873c326c24ad981f114a", "linkedClaimIds": [ "E8.REVERSE.AUDIT.01" ], "sectionIds": [ "section:25a3a7ca87e0691a61b8", "section:3af896f0e07d57463462", "section:44fb2c4f56d2211a1e7f", "section:4d7b24e6cd695cd3409f", "section:51b5da5a67a36e5155ae", "section:671808877239add5f598", "section:697c671889813baf24f5", "section:7a7de20f53ed3e69fb6f", "section:90d9ccdfa2e81d8ea0bd", "section:93b8868beb643874af75", "section:989e899750d5a86edf1e", "section:99fa7c49f30373d04fa1", "section:9a6aaf6fc60f9b74b301", "section:ab9e7e520130ecc7da7c", "section:b08e66805b3affcf9678", "section:b0eabbf91a1894618a3d", "section:b37031f13445096fcccf", "section:b9e3cb43b2bc303303e6", "section:db9b59159ab5489cccfa", "section:e99d6098550f62e277de", "section:eb00caf29086b02d5bf5", "section:f5274c8105ff62e99dcd", "section:f9ed8e942e9df8db94c7" ], "activeSectionIds": [ "section:25a3a7ca87e0691a61b8", "section:3af896f0e07d57463462", "section:44fb2c4f56d2211a1e7f", "section:4d7b24e6cd695cd3409f", "section:671808877239add5f598", "section:697c671889813baf24f5", "section:7a7de20f53ed3e69fb6f", "section:90d9ccdfa2e81d8ea0bd", "section:989e899750d5a86edf1e", "section:99fa7c49f30373d04fa1", "section:9a6aaf6fc60f9b74b301", "section:ab9e7e520130ecc7da7c", "section:b08e66805b3affcf9678", "section:b0eabbf91a1894618a3d", "section:b37031f13445096fcccf", "section:b9e3cb43b2bc303303e6", "section:db9b59159ab5489cccfa", "section:e99d6098550f62e277de", "section:f5274c8105ff62e99dcd", "section:f9ed8e942e9df8db94c7" ], "evidenceId": "python_verification:verification/v354_e8_reverse_audit.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v354_e8_reverse_audit.py", "pubMirrorHash": "aeacc858d379d929440e50030e77ab775a5b52949b04873c326c24ad981f114a", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v354_e8_reverse_audit.py" }, { "id": "v353_selfloop_capstone", "filename": "v353_selfloop_capstone.py", "path": "verification/v353_selfloop_capstone.py", "cluster": "core", "synopsis": "The bird's-eye rethink (refining v352): TFPT is not a LINEAR theory (axioms -> theorems) but a CLOSED SELF-CONSISTENT LOOP whose outputs fix its own inputs, with ZERO free adjustable dimensionless parameters. [E] IT IS A LOOP: outputs fix inputs (g_car=5 = max prime of h(E8)=30; the 8 in c3 = rank E8) and inputs fix outputs; the arrows close into a circle (v6) with a unique fixed point (v56). [E] ZERO FREE DIALS: every load-bearing number is forced/over-determined; free dimensionless parameters = 0. [E] pi is a FIXED geometric constant (the boundary 2-sphere, oint K = 4pi -> c3=1/(8pi)), not a dial. [A] refining v352: pi is not a free input and the framework is a SELECTION PRINCIPLE (the unique self-consistent loop), not a free meta-axiom. [O] the one residual is the CONTINUUM closure (the chiral-edge existence, v336/v351); structural-realism (loop complete) vs constructivism (continuum open) is a philosophical, not numerical, fork.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv353_selfloop_capstone.py", "sourceSha256": "e11b548ade152eaad1dbc974492f577612c5eef5187bfdd16b43e04eefead730", "linkedClaimIds": [ "TFPT.SELFLOOP.01" ], "sectionIds": [ "section:6269926806aae68e08f4", "section:ab9e7e520130ecc7da7c", "section:dcc46f2343a1ce26d935", "section:fcaeea1db58206830da9" ], "activeSectionIds": [ "section:ab9e7e520130ecc7da7c", "section:dcc46f2343a1ce26d935", "section:fcaeea1db58206830da9" ], "evidenceId": "python_verification:verification/v353_selfloop_capstone.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v353_selfloop_capstone.py", "pubMirrorHash": "e11b548ade152eaad1dbc974492f577612c5eef5187bfdd16b43e04eefead730", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v353_selfloop_capstone.py" }, { "id": "v352_framework_irreducible", "filename": "v352_framework_irreducible.py", "path": "verification/v352_framework_irreducible.py", "cluster": "core", "synopsis": "The framework reduction -- the deepest answer to 'the inputs are not axioms, they are back-determined'. [E] P2 (g_car=5) FORCED three ways (v6): rank-fill, Coxeter-match (g_car=max prime of h(E8)=30), Pascal. [E] P1 (c3=1/(8pi)) FORCED: c3 is the boundary Gauss-Bonnet coefficient (v216/v342), the 8 over-determined four ways (8=rank E8=h(D5)=phi(30)=det R, v54/v6); only pi is non-forced (the boundary transcendental). [E] the E8 hull is forced (unique even unimodular rank-8, v83/v154). [E] so the ONLY irreducibles are the FRAMEWORK (a discrete reflection-positive boundary with a finite Clifford carrier) + pi -- the precise content of 'the inputs are not axioms'. [O] the framework is the META-AXIOM (not math-reducible, the foundational stance, tested by its consequences not proved). TFPT's true input is ONE framework + pi.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv352_framework_irreducible.py", "sourceSha256": "563355a4a35e3c8a810f47ca65e70ced7efccaa4ab3151f6036eca4e46618f4c", "linkedClaimIds": [ "TFPT.IRREDUCIBLE.01" ], "sectionIds": [ "section:2b8d2aba4baeb7a0c36b", "section:303925994b6f141b3a0e", "section:a5034e3be2279bec9f75", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:dcc46f2343a1ce26d935", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:a5034e3be2279bec9f75", "section:ab9e7e520130ecc7da7c", "section:dcc46f2343a1ce26d935", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v352_framework_irreducible.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v352_framework_irreducible.py", "pubMirrorHash": "563355a4a35e3c8a810f47ca65e70ced7efccaa4ab3151f6036eca4e46618f4c", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v352_framework_irreducible.py" }, { "id": "v350_bootstrap_inputs_correction", "filename": "v350_bootstrap_inputs_correction.py", "path": "verification/v350_bootstrap_inputs_correction.py", "cluster": "core", "synopsis": "The honest CORRECTION of v349's framing (prompted by the right objection: the inputs are not axioms, they are back-determined by the theory). [E] THE INPUTS ARE BOOTSTRAP-FORCED, NOT FREE AXIOMS (v6): g_car=5 over-determined three ways (rank-fill, Coxeter-match g_car=max prime of h(E8)=30, Pascal). [E] g_car=5 IS THE ICOSAHEDRAL 5-FOLD, not the D5 rank: g_car = max prime of h(E8)=30=2*3*5; the atoms (2,3,5) ARE the primes of the icosahedral Coxeter number 30. [E] THE GOLDEN RATIO IS EMERGENT FROM THE GLUE, not external: D5 (h=8)/A3 (h=4) non-golden alone, but the mu4 extension D5+A3 -> E8 (v154) gives h(E8)=30 (golden, 5|30) -- the seam's own mu4 produces the 5-fold; v349 checked the un-glued pieces, the wrong object. [E] v349's pentagon-vs-count dichotomy was FALSE (the bootstrap forces the pentagon). [O] residual relocates: the golden is bootstrap-forced; the only open thing is the physical continuum realisation (v336), NOT the golden ratio. Caveat: self-consistency within the framework, not from-nothing. Supersedes v349's interpretation.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv350_bootstrap_inputs_correction.py", "sourceSha256": "ac79766fae9a95a5b5eedd4afc95beb4c3539c2263bd2017b306aebbd791a471", "linkedClaimIds": [ "SEAM.EQUIV.BOOTSTRAP.01" ], "sectionIds": [ "section:2b8d2aba4baeb7a0c36b", "section:2ef143ddeb6e7890a438", "section:303925994b6f141b3a0e", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:2ef143ddeb6e7890a438", "section:ab9e7e520130ecc7da7c", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v350_bootstrap_inputs_correction.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v350_bootstrap_inputs_correction.py", "pubMirrorHash": "ac79766fae9a95a5b5eedd4afc95beb4c3539c2263bd2017b306aebbd791a471", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v350_bootstrap_inputs_correction.py" }, { "id": "v349_raw_seam_golden_test", "filename": "v349_raw_seam_golden_test.py", "path": "verification/v349_raw_seam_golden_test.py", "cluster": "core", "synopsis": "The honest test of the v348 question 'does the RAW seam carry the golden ratio (before assuming E8)?'. Answer, computed: NO -- the bare carrier (D5, A3) and the dynamical seam data are NOT golden; the golden ratio genuinely enters WITH the icosahedral/E8 identification. A NEGATIVE result that prevents a false closure. [E] RAW CARRIER NOT GOLDEN: golden needs 5|h; D5 has h=8 (2cos(2pi/8)=sqrt2), A3 has h=4 -- no 5-fold, bare carrier gives sqrt2. [E] DYNAMICAL DATA NOT GOLDEN: cusp {0,1/3,2/3} rational, recovery (2/3)^6 rational, seed phi0 transcendental. [E] GOLDEN IS THE ICOSAHEDRAL/E8 SIDE: 5|h only for A4=SU(5) (h=5), H3 (h=10), E8 (h=30). [E] phi alone insufficient: 2I != C5 x mu4 (20 != 120). [O] RESOLUTION: L2 reduces to 'is g_car=5 a PENTAGON (5-fold => golden => icosahedral) or a COUNT (rank D5 => sqrt2)?' -- the golden ratio is the pentagon-reading of P2, NOT derivable from P2-as-a-count; no hidden phi. Foundational: P2-as-pentagon closes it (mode C) else rigidity must produce the 5-fold (mode B); NOT closed.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv349_raw_seam_golden_test.py", "sourceSha256": "92fc1e971dac05996a43b077ca8c22e053a6437a419bce1986675e93bda127fa", "linkedClaimIds": [ "SEAM.EQUIV.GOLDEN.01" ], "sectionIds": [ "section:2678ed3ba0ed508e2d8e", "section:2b8d2aba4baeb7a0c36b", "section:2ef143ddeb6e7890a438", "section:303925994b6f141b3a0e", "section:4061f274c55499fb2ed1", "section:9bab697ba19c86420aea", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:b3159de77fcabb12cc0c", "section:fac429be371842092df9", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:2ef143ddeb6e7890a438", "section:4061f274c55499fb2ed1", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:b3159de77fcabb12cc0c", "section:fac429be371842092df9", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v349_raw_seam_golden_test.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v349_raw_seam_golden_test.py", "pubMirrorHash": "92fc1e971dac05996a43b077ca8c22e053a6437a419bce1986675e93bda127fa", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v349_raw_seam_golden_test.py" }, { "id": "v348_seam_rigidity_route", "filename": "v348_seam_rigidity_route.py", "path": "verification/v348_seam_rigidity_route.py", "cluster": "core", "synopsis": "Route B (the rigidity route) for the one open arrow L2, carried out -- it lands on a strikingly SIMPLE statement: the whole keystone reduces to ONE question, does the raw seam carry the golden ratio? [E] rigidity closes the crystallographic part: the order-4 clock has a UNIQUE normal form z->iz (Nielsen/Kerckhoff, v180), Troyanov gives the unique flat pillowcase metric (v284). [E] downstream is a LATTICE identity: E8 = the ring of icosians (Conway-Sloane), rank 8, so 2I->E8 is a lattice identity (stronger than McKay v219). [E] the single bridge is phi: crystallographic orders {1,2,3,4,6}, the 5-fold non-crystallographic; mu4 crystallographic, 2I (5-fold) not, phi=2cos(pi/5) extends one to the other (quasicrystal). [O] the keystone reduces to ONE question: 'does the raw seam carry phi?' -- if yes, mu4+phi -> 2I -> E8 closes L2. [O] honest subtlety: TFPT's phi is currently E8-side (v312/v313); the raw-seam data (cusp {0,1/3,2/3}, recovery (2/3)^6, seed phi0) are not manifestly golden, so showing the RAW seam carries phi non-circularly is the residual (= L2). NOT closed.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv348_seam_rigidity_route.py", "sourceSha256": "c407a5ad4145072f11998c51f082c6e9b9ccb6a05d32fef42fca98a86778bc7f", "linkedClaimIds": [ "SEAM.EQUIV.RIGID.01" ], "sectionIds": [ "section:2b8d2aba4baeb7a0c36b", "section:303925994b6f141b3a0e", "section:3af896f0e07d57463462", "section:414a84d23afa6566ca5e", "section:7a7de20f53ed3e69fb6f", "section:90d9ccdfa2e81d8ea0bd", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:fac429be371842092df9", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:3af896f0e07d57463462", "section:414a84d23afa6566ca5e", "section:7a7de20f53ed3e69fb6f", "section:90d9ccdfa2e81d8ea0bd", "section:ab9e7e520130ecc7da7c", "section:fac429be371842092df9", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v348_seam_rigidity_route.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v348_seam_rigidity_route.py", "pubMirrorHash": "c407a5ad4145072f11998c51f082c6e9b9ccb6a05d32fef42fca98a86778bc7f", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v348_seam_rigidity_route.py" }, { "id": "v347_seam_closure_modes", "filename": "v347_seam_closure_modes.py", "path": "verification/v347_seam_closure_modes.py", "cluster": "core", "synopsis": "The closure-mode classification of the one open arrow L2 (the seam-orbifold realisation, v346) -- a direct honest answer to 'is there ANY other way to FULLY solve it?'. [E] THE PRECISE LOCUS: the seam gives the pillowcase base S^2(2,2,2,2), chi_orb=0 (EUCLIDEAN, v216), but the 2I/E8 structure is the Seifert base S^2(2,3,5), chi_orb=1/30 (SPHERICAL); L2 must bridge a FLAT 4-marked base to a SPHERICAL 3-marked base -- why L2 needs the carrier (2,3,5) input. [E] FOUR CLOSURE MODES: A construct (the analytic wall, v336); B rigidity (unique realisation => C^2/2I forced, the only theorem-route w/o new input, v284/v300/v331); C axiom P3 (=> TFPT complete rel. 3 axioms); D empirical (test the consequences). [E] no-new-state (tfpt_3/v246) blocks deriving L2 from extra physics => only rigidity (B) closes it as a theorem. [E] VERDICT: no free theorem; only B (theorem) or C (axiom), validated by D; only these four modes. [O] NOT closed.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv347_seam_closure_modes.py", "sourceSha256": "60582193ef429b5d0434c9492b4402fa3efd93697a63e741f9b1be0c6ddefe9b", "linkedClaimIds": [ "SEAM.EQUIV.CLOSURE.01" ], "sectionIds": [ "section:2b8d2aba4baeb7a0c36b", "section:303925994b6f141b3a0e", "section:414a84d23afa6566ca5e", "section:6a93c4dd5fe420e1990e", "section:8e4972dbe899b5debb90", "section:9800e2e20cb3dc2e280a", "section:a036d63765e830eb593f", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:c6b6da016e7f30bbb7c1", "section:d90bd5e1e6d8fa41397d", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:414a84d23afa6566ca5e", "section:8e4972dbe899b5debb90", "section:9800e2e20cb3dc2e280a", "section:a036d63765e830eb593f", "section:ab9e7e520130ecc7da7c", "section:c6b6da016e7f30bbb7c1", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v347_seam_closure_modes.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v347_seam_closure_modes.py", "pubMirrorHash": "60582193ef429b5d0434c9492b4402fa3efd93697a63e741f9b1be0c6ddefe9b", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v347_seam_closure_modes.py" }, { "id": "v346_seam_geometric_bridge", "filename": "v346_seam_geometric_bridge.py", "path": "verification/v346_seam_geometric_bridge.py", "cluster": "core", "synopsis": "The geometric bridge as an explicit six-link chain raw-seam => det K=1, with the ONE open arrow pinned -- the honest capstone of the SEAM.EQUIV.01 investigation. L1 [E/C] raw seam -> mu4 + four marks (v216); L2 [O] mu4 + (2,3,5) atoms -> 2I orbifold C^2/Gamma (THE OPEN ARROW = SEAM.EQUIV.01); L3 [E] 2I -> affine E8 McKay (v219); L4 [E] 2I -> E8 du Val (v232); L5 [E] C^2/2I -> Poincare link H_1=0 (v345); L6 [E] H_1=0 -> det K=1. [E] 5 of 6 links are theorems, only L2 open. [E] the group is FORCED by the seam atoms: axis signatures (2,3,3)/(2,3,4)/(2,3,5) -> 2T/2O/2I, (2,3,5) unique to 2I, and (|Z2|,N_fam,g_car)=(2,3,5) ARE those axes. [E] downstream of L2 forced. [O] L2 (the seam IS an ADE orbifold point) = SEAM.EQUIV.01, NOT closed -- the keystone reduced to one geometric-realisation arrow, group pinned by (2,3,5).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv346_seam_geometric_bridge.py", "sourceSha256": "1139d15244ec9ee17c87e6bd903e3c7a61d6e893015beb51c65e874bbf273a7e", "linkedClaimIds": [ "SEAM.EQUIV.GEOM.01" ], "sectionIds": [ "section:00c96659d1c56ecb746e", "section:2b8d2aba4baeb7a0c36b", "section:303925994b6f141b3a0e", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:e99d6098550f62e277de", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:00c96659d1c56ecb746e", "section:ab9e7e520130ecc7da7c", "section:e99d6098550f62e277de", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v346_seam_geometric_bridge.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v346_seam_geometric_bridge.py", "pubMirrorHash": "1139d15244ec9ee17c87e6bd903e3c7a61d6e893015beb51c65e874bbf273a7e", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v346_seam_geometric_bridge.py" }, { "id": "v345_hypergraph_homotopy", "filename": "v345_hypergraph_homotopy.py", "path": "verification/v345_hypergraph_homotopy.py", "cluster": "core", "synopsis": "EXECUTE the combinatorial core of route R3 (the hypergraph-homotopy route to det K=1, v344): computes explicitly that the (2,3,5)-rewrite attractor graph's plumbing link is the POINCARE homology sphere (H_1=0), only E8 among ADE; R3's combinatorial half is now [E]-complete, the geometric bridge (= SEAM.EQUIV.01) stays [O]. Plumbing topology (Brieskorn): link H_1 = coker(Cartan). [E] SNF(E8 Cartan) = identity => coker(E8)=0 => the E8 plumbing boundary is an INTEGRAL HOMOLOGY SPHERE (the genus-1 meaning of det E8=1). [E] only E8: coker(A_n)=Z/(n+1), D_n->Z/4, E6->Z/3, E7->Z/2 -- all nontrivial, only E8=0. [E] pi_1=2I=SL(2,5) PERFECT (commutator subgroup order 120=|G|, computed) => H_1=0 => THE Poincare sphere; |2I|=120=|mu4|*h(E8). [O] does NOT close det K=1: the graph->geometry half is meanwhile Kronheimer-cited (v479); what stays open is the raw seam supplying the ALE/orbifold datum = SEAM.EQUIV.01.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv345_hypergraph_homotopy.py", "sourceSha256": "150a9c968ec2177535792eba369eb4249301513677a8548f77d20155d828c43f", "linkedClaimIds": [ "SEAM.DETK.02" ], "sectionIds": [ "section:00c96659d1c56ecb746e", "section:2b8d2aba4baeb7a0c36b", "section:303925994b6f141b3a0e", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:f45ff82a01e81b33f3c1", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:00c96659d1c56ecb746e", "section:ab9e7e520130ecc7da7c", "section:f45ff82a01e81b33f3c1", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v345_hypergraph_homotopy.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v345_hypergraph_homotopy.py", "pubMirrorHash": "150a9c968ec2177535792eba369eb4249301513677a8548f77d20155d828c43f", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v345_hypergraph_homotopy.py" }, { "id": "v344_detk_synthesis", "filename": "v344_detk_synthesis.py", "path": "verification/v344_detk_synthesis.py", "cluster": "core", "synopsis": "The bird's-eye synthesis of the ONE open keystone bit, det K=1 -- a full-spectrum map of SEAM.EQUIV.01's only open residual. [E] det K=1 is ONE statement with SIX equivalent faces (holomorphy / homology-sphere link H_1=0 / one 1-dim irrep / det Cartan=1 / full mu4 condensation / tau=i CM), unified by |det Cartan| = |H_1(link)| = #1-dim irreps across ADE (A_n->n+1, D_n->4, E6->3, E7->2, E8->1) -- ONLY E8 gives 1. [E] THE GENUS-1 OBSTRUCTION: the easy arguments are genus-0, necessary but not sufficient (v87); det K is the torus degeneracy. [E] THREE genus-1 access routes: R1 continuum-modular (v336), R2 anyon-condensation (v281), R3 hypergraph-homotopy. [C] the HYPERGRAPH route is the most promising fresh angle: the (2,3,5) attractor is the affine-E8 graph (v312), the E8 du Val link is the Poincare sphere (v232), so det K=1 becomes COMBINATORIAL. [O] none closes it; R3's combinatorial-to-geometric bridge is meanwhile discharged to Kronheimer 1989 (v479), so the residual transforms to 'the raw seam supplies the ALE/orbifold datum' = SEAM.EQUIV.01.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv344_detk_synthesis.py", "sourceSha256": "3e88c3c03727a08683a4ebb8d026672905a4eb55035635faf73f9e9bf162b92a", "linkedClaimIds": [ "SEAM.DETK.01" ], "sectionIds": [ "section:2b8d2aba4baeb7a0c36b", "section:303925994b6f141b3a0e", "section:5ff3f529ae7be4541192", "section:6a93c4dd5fe420e1990e", "section:8e4972dbe899b5debb90", "section:93b8868beb643874af75", "section:a5034e3be2279bec9f75", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:b450ecffaba882770fc8", "section:d90bd5e1e6d8fa41397d", "section:e99d6098550f62e277de", "section:eb00caf29086b02d5bf5", "section:ee9a2e2d9ccdc3799662", "section:f45ff82a01e81b33f3c1", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:5ff3f529ae7be4541192", "section:8e4972dbe899b5debb90", "section:a5034e3be2279bec9f75", "section:ab9e7e520130ecc7da7c", "section:b450ecffaba882770fc8", "section:e99d6098550f62e277de", "section:ee9a2e2d9ccdc3799662", "section:f45ff82a01e81b33f3c1", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v344_detk_synthesis.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v344_detk_synthesis.py", "pubMirrorHash": "3e88c3c03727a08683a4ebb8d026672905a4eb55035635faf73f9e9bf162b92a", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v344_detk_synthesis.py" }, { "id": "v343_four_routes_analysis", "filename": "v343_four_routes_analysis.py", "path": "verification/v343_four_routes_analysis.py", "cluster": "frontier", "synopsis": "The honest investigation of the four black-hole-birth solution routes (A finite causal diamond, B Carlip-Cardy near-horizon CFT, C modular/thermal flow, D self-reproduction attractor) -- direct answer to 'which closes ALL problems and is 100% provable': NONE individually, but they CONVERGE on the same two irreducible residuals as v335 (SEAM.EQUIV.01 + the decoupled QG contour). [E] ROUTE A reframes QG.AMB to a FINITE thermal trace (de Sitter finite, gapped chi=729/665) but c_conf(4)=-3/2<0 still needs the GHP contour (v334 [O]); does NOT touch SEAM.EQUIV.01. [C] ROUTE B: Carlip+Cardy consistent with c=8 but L0 free (ambiguity) and gives c only not holomorphy det K=1 -- inherits SEAM.EQUIV.01. [E] ROUTE C: modular flow KMS beta=1 (v239), geometric identification = SEAM.EQUIV.01 (v335) -- a reduction. [E]/[P] ROUTE D: unique Perron-Frobenius attractor (v56) but cyclic dynamics [P] -- not a closure. [E] VERDICT: independent closures = 0; irreducible residuals = 2 (= v335); BH premise makes both more natural but eliminates neither; focus = SEAM.EQUIV.01.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv343_four_routes_analysis.py", "sourceSha256": "f4b5224512b028082669eda9fdc2962d111c97d67320ce6ab506d58e1c7f03ee", "linkedClaimIds": [ "FOUR.ROUTES.01" ], "sectionIds": [ "section:2b8d2aba4baeb7a0c36b", "section:303925994b6f141b3a0e", "section:4dcf513f2ae74de8645b", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:4dcf513f2ae74de8645b", "section:ab9e7e520130ecc7da7c", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v343_four_routes_analysis.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v343_four_routes_analysis.py", "pubMirrorHash": "f4b5224512b028082669eda9fdc2962d111c97d67320ce6ab506d58e1c7f03ee", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v343_four_routes_analysis.py" }, { "id": "v342_em_ward_heatkernel", "filename": "v342_em_ward_heatkernel.py", "path": "verification/v342_em_ward_heatkernel.py", "cluster": "em", "synopsis": "The heat-kernel sharpening of EM.WARD.01: DERIVES the ORIGIN and STRUCTURE of the F_{U(1)} determinant-line terms from textbook Seeley-DeWitt/Gilkey coefficients, advancing the EM-Ward origin from [P] to [E] for the STRUCTURE; NO new gate. [E] c3=1/(8pi) the boundary GAUSS-BONNET coefficient (seam = flat pillowcase chi=2, oint K = 4pi, v216). [E] the alpha^2 term is the GILKEY gauge-curvature coeff: a4 has 30 Omega^2/360 = (1/12)Omega^2, Omega=i alpha F => -(alpha^2/12)F^2, so the Calderon -2 c3^3 a^2 is the gauge-curvature piece, not an ansatz. [E] c3-ladder {0,3,6} arithmetic (3 channels; C6 hexagon at 6). [E] multiplicities 2=|Z2|, 8 b1=(rank E8)b1. [E] pi-power test: 2 c3^3 ~ pi^3 => THREE boundary insertions. [C] exact coefficient needs the seam F-normalisation. [O] the cubic alpha^3 + full identification = EM.WARD.01 residual (tied to SEAM.EQUIV.01).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv342_em_ward_heatkernel.py", "sourceSha256": "34ec90333066565a2d858bd871db1a54e83c878d40990616d925035a19738f00", "linkedClaimIds": [ "EM.WARD.02" ], "sectionIds": [ "section:09b49009253acb5a0dfb", "section:1bdc1e997517317b5cc9", "section:1fa633590a33e985ed41", "section:2a73aae2d89b3c427077", "section:314c7c0b2567b3598a9c", "section:3cc790136e8b9bd3c188", "section:3d3092d4174b4ba2e0ec", "section:584e87a9c163ac38f92f", "section:6a757c5701557192653a", "section:7144b70a605254dfecbc", "section:7ef5c3edcea8d045b5b2", "section:8404e6e674a37d72796a", "section:a3b94e09ceb6d6dbdae4", "section:ab9e7e520130ecc7da7c", "section:c852f8ae0a03109ca8ad", "section:ca7a45590bd2289527ff", "section:eb0bd97fda8c0fedefad", "section:ed458665aa45a0bcd44b" ], "activeSectionIds": [ "section:1bdc1e997517317b5cc9", "section:2a73aae2d89b3c427077", "section:314c7c0b2567b3598a9c", "section:584e87a9c163ac38f92f", "section:6a757c5701557192653a", "section:7144b70a605254dfecbc", "section:7ef5c3edcea8d045b5b2", "section:8404e6e674a37d72796a", "section:ab9e7e520130ecc7da7c", "section:c852f8ae0a03109ca8ad", "section:ed458665aa45a0bcd44b" ], "evidenceId": "python_verification:verification/v342_em_ward_heatkernel.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v342_em_ward_heatkernel.py", "pubMirrorHash": "34ec90333066565a2d858bd871db1a54e83c878d40990616d925035a19738f00", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v342_em_ward_heatkernel.py" }, { "id": "v341_alpha_quillen", "filename": "v341_alpha_quillen.py", "path": "verification/v341_alpha_quillen.py", "cluster": "em", "synopsis": "The alpha fixed point reformulated as the STATIONARITY of a U(1) determinant line, every ingredient identified as an index / heat-kernel coefficient / discriminant form -- NOT a free knob (the 'derive the FORM' step). F_{U(1)} = a^3 - 2 c3^3 a^2 - (4/5) c3^6 M ln(1/phi_seam) = 0 in Quillen form: [a^3 - 2 c3^3 a^2] (det-line variation) = [8 b1 c3^6] (anomaly counterterm) * [ln(1/phi_seam)] (seam response). [E] M=41 a U(1) INDEX (EM Ward, v48): (4/5)M = 8 b1, b1=41/10 the SM 1-loop U(1)_Y beta. [E] c3=1/(8pi) GAUSS-BONNET boundary coeff (8=rank E8). [E] -5/4 = -q(D5) DISCRIMINANT; phi_base=(4/3)c3, c3/phi_base=3/4=q(A3). [E] delta_top=Omega_adm c3^4. [E] Quillen split holds at the alpha^-1=137.036 root. [E] NO NEW GATE: alpha stays [E]; v341 SHARPENS the pre-existing [P] EM.WARD.01 (no new alpha problem). [O] the one still-open part IS EM.WARD.01's residual: the AQFT proof that this is the EXACT Quillen functional (variational principle derived, not assembled). Sharpens v3/v48/EM.WARD.01 from fixed point to stationarity of a named determinant line.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv341_alpha_quillen.py", "sourceSha256": "aae72373f6055a058381825606cd7b75d31a2f75ee6dc0c22c3481e5602f0b62", "linkedClaimIds": [ "ALPHA.QUILLEN.01" ], "sectionIds": [ "section:1fa633590a33e985ed41", "section:2a73aae2d89b3c427077", "section:3d3092d4174b4ba2e0ec", "section:656d00cdb6c9c469cdbe", "section:6a757c5701557192653a", "section:7144b70a605254dfecbc", "section:a3b94e09ceb6d6dbdae4", "section:ab9e7e520130ecc7da7c", "section:c852f8ae0a03109ca8ad", "section:ca7a45590bd2289527ff" ], "activeSectionIds": [ "section:2a73aae2d89b3c427077", "section:656d00cdb6c9c469cdbe", "section:6a757c5701557192653a", "section:7144b70a605254dfecbc", "section:ab9e7e520130ecc7da7c", "section:c852f8ae0a03109ca8ad" ], "evidenceId": "python_verification:verification/v341_alpha_quillen.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v341_alpha_quillen.py", "pubMirrorHash": "aae72373f6055a058381825606cd7b75d31a2f75ee6dc0c22c3481e5602f0b62", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v341_alpha_quillen.py" }, { "id": "v365_qg_oneloop_saddle", "filename": "v365_qg_oneloop_saddle.py", "path": "verification/v365_qg_oneloop_saddle.py", "cluster": "core", "synopsis": "Direction 3: the QG measure (gate C7/QG.AMB.01) as one-loop GAUSSIAN fluctuations around the PARAMETER-FREE saddle (v358/v359). [E] the fluctuation stiffness is 1/c3=8pi (no free dial), so the one-loop problem is well-posed (it was NOT before v358). [E] the fluctuation operator is gapped M>=Delta_eff=6 ln(3/2)-31/(4pi^2)~1.648>0 (v76/v337) => mode-by-mode Gaussian convergence, no zero/negative modes besides the saddle directions. [E] finite model log-det Tr' log M=6 ln(9/2) on the OS spectrum {0,6 ln(3/2),6 ln 3}. [C] the conformal mode converges on the GHP contour (int exp(-|c|phi^2)=sqrt(2pi/3), v334). [E] the admissible projective limit exists (chi=1/(1-(2/3)^6)=729/665, v330). [E] 0 new dimensionless dials (v364). [O] residual: the full non-perturbative projective limit (G6/QG.AMB.01) on the ambient sector. Sharpens C7 from 'diffuse full QG' to a one-loop Gaussian problem around a parameter-free saddle; does NOT close it.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv365_qg_oneloop_saddle.py", "sourceSha256": "85810db7380a9f9a9d2242b0763c2418edce824d67dce16c992989817f278bce", "linkedClaimIds": [ "QGAMB.SADDLE.01" ], "sectionIds": [ "section:2b8d2aba4baeb7a0c36b", "section:303925994b6f141b3a0e", "section:43e53494baf54171d70d", "section:4a157afd200102fcaaee", "section:5ff3f529ae7be4541192", "section:8b1a1c6a205860e21edc", "section:93b8868beb643874af75", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:eb00caf29086b02d5bf5", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:43e53494baf54171d70d", "section:4a157afd200102fcaaee", "section:5ff3f529ae7be4541192", "section:8b1a1c6a205860e21edc", "section:ab9e7e520130ecc7da7c", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v365_qg_oneloop_saddle.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v365_qg_oneloop_saddle.py", "pubMirrorHash": "85810db7380a9f9a9d2242b0763c2418edce824d67dce16c992989817f278bce", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v365_qg_oneloop_saddle.py" }, { "id": "v366_mmst_seam_collar", "filename": "v366_mmst_seam_collar.py", "path": "verification/v366_mmst_seam_collar.py", "cluster": "core", "synopsis": "Direction 7: the seam collar is IN MMST's free-lattice-fermion scaling-limit class, so the chiral scaling limit is a chiral CFT of central charge 8 pinned to (E8)_1 -- reducing SEAM.EQUIV.01 to the single S3 lattice-realisation input. Osborne-Stottmeister (arXiv:2107.13834, CMP 398 (2023) 219; legacy internal token MMST, on the MMST/Morinelli-Morsella-Stottmeister-Tanimoto OAR framework): free lattice fermions (CAR quasi-free) -> chiral-CFT massless scaling limit with correct c, range rank<=c<=D. [E] class arithmetic: D=dim S^+=2^(g_car-1)=16 Majoranas, c=g_car+N_fam=8, rank E8=8 => rank<=c<=D is 8<=8<=16 (in MMST range). [E] gapped (Delta=6 ln(3/2)>0, derived v302). [C] quasi-free CAR class (v155/v160). [E] chirality c_-=D/2=8 != 0 (non-gappable anomalous edge, v356 S4). [C] the MMST scaling-limit theorem applies (in-class & gapped & chiral & in-range) => chiral CFT c=8 (v336). [E] target pinned to (E8)_1 by c=8 + the order-4 mu4 clock (det K=1 vs SO(16) det K=4, v351). [O] residual S3: the collar realised as a genuine lattice chiral free-fermion invertible phase (one-sidedness/Flat-Away, v297/v356). Verifies MMST in-class; ADVANCES SEAM.EQUIV.01, does NOT close it.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv366_mmst_seam_collar.py", "sourceSha256": "c349773dc520ef36a2084b7cb6ea3e66dd4c787dfab3fa5de435e052f6873837", "linkedClaimIds": [ "SEAM.MMST.INCLASS.01", "SEAM.EQUIV.MMST.01" ], "sectionIds": [ "section:03b9058ca08ba4829ac7", "section:1a6d16256ec9d6226d97", "section:4a157afd200102fcaaee", "section:5ff3f529ae7be4541192", "section:6a93c4dd5fe420e1990e", "section:7144b70a605254dfecbc", "section:8e4972dbe899b5debb90", "section:93b8868beb643874af75", "section:ab9e7e520130ecc7da7c", "section:acb731fecb30c7953915", "section:d90bd5e1e6d8fa41397d", "section:eb00caf29086b02d5bf5", "section:f97072f658fe6bcec8d8", "section:fd15b9954fc0175fba1b" ], "activeSectionIds": [ "section:1a6d16256ec9d6226d97", "section:4a157afd200102fcaaee", "section:5ff3f529ae7be4541192", "section:7144b70a605254dfecbc", "section:8e4972dbe899b5debb90", "section:ab9e7e520130ecc7da7c", "section:acb731fecb30c7953915", "section:f97072f658fe6bcec8d8" ], "evidenceId": "python_verification:verification/v366_mmst_seam_collar.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v366_mmst_seam_collar.py", "pubMirrorHash": "c349773dc520ef36a2084b7cb6ea3e66dd4c787dfab3fa5de435e052f6873837", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v366_mmst_seam_collar.py" }, { "id": "v370_grav_spin2_unitarity", "filename": "v370_grav_spin2_unitarity.py", "path": "verification/v370_grav_spin2_unitarity.py", "cluster": "frontier", "synopsis": "Track 2: the Barnes-Rivers spin decomposition of the graviton propagator -- perturbative graviton unitarity SECTOR-BY-SECTOR (extends v304's scalar pole algebra to the tensor spin structure + combines with v334's spin-0 conformal mode). [E] projector completeness: tr P2=(d-2)(d+1)/2, tr P1=d-1, tr P0s=tr P0w=1 sum to d(d+1)/2; the d=4 split is 5+3+1+1=10. [E] EH structure: spin-2 coefficient +1, spin-0 scalar -1/(d-2)=-1/2. [E] the Stelle ghost is a SPIN-2 state (a local 1+p^2/M^2 dressing puts the negative-residue pole at p^2=-M^2). [E] the entire KMS form factor e^{p^2/M^2} (v304/v259) makes spin-2 ghost-free (only the p^2=0 pole). [C] the wrong-sign spin-0 conformal mode (c_conf(4)=-3/2, v332) is cured by the GHP contour (v334) -- a different mechanism. [C] => perturbative graviton unitarity sector-by-sector, conditional on v304's entire-analyticity assumption. [O] perturbative-only + the open analyticity assumption; NOT the non-perturbative measure (QG.AMB.01). [O] decline: tr P2=5 is dimension counting, NOT g_car (v354/v355).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv370_grav_spin2_unitarity.py", "sourceSha256": "c4f24dc36967c2c3e81180c19bda43763503a46cfc84405dfdce3bb9f19fb00a", "linkedClaimIds": [ "GRAV.SPIN2.UNITARITY.01" ], "sectionIds": [ "section:00b05ea692eac25e3d3e", "section:213a1f15f7373957fc2f", "section:2525c189f32461c9368a", "section:2a73aae2d89b3c427077", "section:2ffaaee2ce19180008ab", "section:33f8ca97d5f5599b425b", "section:354f7e98a6c16208d1a4", "section:40ced8641cc307aac43a", "section:43e53494baf54171d70d", "section:633620b74c9f05d23e78", "section:6a93c4dd5fe420e1990e", "section:6cd1a267e72b20619327", "section:6db706756a796987fc17", "section:72b43011ac4fb932c47a", "section:75d473d613aba16a08b8", "section:840d8edcd2db5226531d", "section:888628823bf71f709698", "section:91c49cb4658c6aa96d2e", "section:94fabfd63333427d7867", "section:9d6c7d63f5df5a4df579", "section:a29d0e884b184665e5ef", "section:a5afdfe2d50d9975d56b", "section:a64d54bbcb8a16651802", "section:ab9e7e520130ecc7da7c", "section:b08e66805b3affcf9678", "section:b93e6ae7b00f32ee1201", "section:c00f76407fefd9782fd7", "section:d90bd5e1e6d8fa41397d", "section:eef94f3ff4627b2515d5", "section:f68163cf343646a0f102" ], "activeSectionIds": [ "section:00b05ea692eac25e3d3e", "section:213a1f15f7373957fc2f", "section:2a73aae2d89b3c427077", "section:40ced8641cc307aac43a", "section:43e53494baf54171d70d", "section:633620b74c9f05d23e78", "section:6db706756a796987fc17", "section:72b43011ac4fb932c47a", "section:75d473d613aba16a08b8", "section:888628823bf71f709698", "section:94fabfd63333427d7867", "section:9d6c7d63f5df5a4df579", "section:a29d0e884b184665e5ef", "section:a5afdfe2d50d9975d56b", "section:a64d54bbcb8a16651802", "section:ab9e7e520130ecc7da7c", "section:b08e66805b3affcf9678", "section:c00f76407fefd9782fd7", "section:f68163cf343646a0f102" ], "evidenceId": "python_verification:verification/v370_grav_spin2_unitarity.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v370_grav_spin2_unitarity.py", "pubMirrorHash": "c4f24dc36967c2c3e81180c19bda43763503a46cfc84405dfdce3bb9f19fb00a", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v370_grav_spin2_unitarity.py" }, { "id": "v367_seam_s3_lattice", "filename": "v367_seam_s3_lattice.py", "path": "verification/v367_seam_s3_lattice.py", "cluster": "core", "synopsis": "Track 1: the EXPLICIT lattice realisation of the S3 input -- a concrete gapped chiral-Majorana (p+ip) lattice model whose edge is the 16-Majorana SO(16)_1 carrier, mu4-condensed to (E8)_1; turns the abstract S3 residual (v356/v366) into a RUNNABLE model with a numerically computed topological invariant. [E] bulk gapped (band gap 2>0 at M=1). [E] non-trivial Chern number (Fukui-Hatsugai-Suzuki: |C|=1 at M=1, C=0 at M=3 trivial control). [E] c_-=8: each chiral Majorana edge carries c_-=C/2=1/2, N_Maj=dim S^+=2^(g_car-1)=16 copies => c_-=16/2=8=g_car+N_fam. [E] edge K-matrix SO(16)_1 (det Cartan D8=4) -> (E8)_1 (det Cartan E8=1) by the order-4 mu4 clock (v351/v369). [C] the mu4 condensation SO(16)_1 -> (E8)_1 (v154/v351). [O] residual: the continuum scaling-limit existence (MMST v336). 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[E] topo in-gap edge states (M=1 strip min_kx|E|~0) vs trivial clean gap (M=3, neg control); [E] the near-zero state is edge-localised (weight within 4 sites of a boundary, edge>>bulk); [E] bulk-edge correspondence (edge branch count = bulk Chern |C|=1) => 16-Majorana edge, c_-=8. [C] anomaly inflow: a c_-!=0 invertible bulk cannot have a gappable edge => discharges the v336/v351 'does the edge exist?' residual on the lattice. [O] residual: the continuum scaling limit (MMST v336). 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[E] Q_pole=Koide(PDG poles)=2/3 to 3e-6, Q_src(phi0-ladder)=0.66446 (0.33% below). [E] QED runs the wrong way: dQ/deps>0 pushes Q ABOVE 2/3; the eps mapping Q_pole->Q_src is NEGATIVE while QED gives eps=+(3/2)(alpha/pi)>0 -- wrong sign for any alpha in [1/137,1/128]. [C] verdict: F_pole is NOT standard QED running; the transfer is the non-QED 53/54 operator / (2/3)^6 Moebius generator (v183/v82). 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Frozen M1=M_scal phi0^2/A_Lambda (~8.65e9 GeV, v212), m~1=m3/A_Lambda=5 meV, delta_CP=4pi/3. [E] integrated efficiency kappa_f~0.09 (strong washout K~4.6) agrees with the BDP fit to ~25%. [C] eta_B(ODE)~6.5e-10 at the frozen M1 lands within a factor ~1.1 of the observed 6.1e-10, NO M_R dial; the M1 reproducing eta_B_obs is within a factor ~1.1 of the frozen one. [X] kill: eta_B outside [obs/3,3obs] for all seesaw-consistent M_R would drop the leptogenesis branch. 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[I] candidate scales fixed by the determinant-line atoms (128=2 dim S^+ |mu4|). [C] the frozen SPINE angle 3pi/5=108deg=pi N_fam/g_car gives Omega_a h^2~0.12 in [0.08,0.16] (lands on Omega_DM untuned) -- the robust dominant-DM branch. [X] the HILLTOP 170deg over-produces (~5.4x) -- disfavoured/fine-tuned. [X] kill: a finite-T solve robustly outside [0.08,0.16] for the spine across chi(T)/g_* drops the dominant axion-DM branch. 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[E] b3=-(11-2 n_f/3)=-7 (n_f=6 carrier). [N] two declared externals (v339): alpha_s(M_Z)=0.1179+-0.0009 and C_p=2.83+-0.15, each ~5.3%. [C] m_p/m_e central ~1824 (v262) with a propagated +-7.5% band [~1690,~1960] CONTAINING the observed 1836.15 -- no free dial. [X] kill: a future lattice C_p+-0.03 + tighter alpha_s shrink the band to ~+-2%; a band then excluding 1836.15 drops the QCD-matching route (b3=-7 + the SU(9)-integer firewall v262 untouched). 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[E] falsifiability complete: every registry row carries a non-empty kill criterion (no orphan claims). [E] headline values re-derive from {phi0}: sin^2 theta12=1/3-phi0/2, sin^2 theta13=phi0 e^{-5/6}, beta_rad=phi0/(4pi). [N] live scorecard: theta12 vs JUNO first run (0.3092+-0.0087)=0.28 sigma (compatible); theta13 vs NuFIT 6.0 NO (0.02195+-0.00058)=2.0 sigma (the flagged most-tensioned core prediction); beta_rad vs ACT DR6 (0.215+-0.074)=0.37 sigma (hint); r=12/N*^2~0.004 c=8=g_car+N_fam; [E] chiral c_-=8 (Chern |C|=1 per Majorana v367, non-gappable edge v368). [O] the specific net (E8)_1 is v377/v378; the continuum existence is the cited MMST theorem (v336). 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[E] chi = E4/eta^8 = q^{-1/3}(1+248q+4124q^2+...): leading -c/24=-1/3 => c=8; level-1 = 248 = dim E8 (one primary). [E] mu4/GSO promotion SO(16)_1 -> (E8)_1: 248=240+8=(E8 roots)+(Cartan), 240=dim S^+*g_car*N_fam=16*5*3; 248=120+128=dim SO(16)+spinor. [E] discriminator: (E8)_1 has 1 primary/248 currents vs SO(16)_1 4 primaries/120. [O] continuum existence (v336); mu4 projection = seam one-sidedness (S3). 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[E] KLM condensation: mu(carrier)=det Cartan(D5)*det Cartan(A3)=4*4=16; order-4 mu4 glue (|L|=4) => mu(E8)=16/16=1 (torus GSD=1); index-2 => mu(SO16)=16/4=4. [E] |det Cartan(E8)|=1 vs |det Cartan(D8)|=4. [E] the single (E8)_1 character has modular T-eigenvalue e^{-2 pi i/3} (h=0,c=8), 1-dim rep => one character => torus GSD=1. [O] continuum existence (v336). 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[E] the gapped p+ip band gives G(tau)=mean_k e^{-eps_k tau} with eps_k>=gap/2~1>0 (v367) -- a positive spectral measure; [E] the Hankel/reflection Gram matrix M_ij=G(tau_i+tau_j) is PSD -- OS reflection positivity holds; [E] neg control: a growing ghost mode makes it indefinite (non-vacuous). [C] RP + gap (v76/v337) + GNS (v240) + c=8 (v376) + (E8)_1 (v377/v378) give the OS inputs; C7/QG.AMB.01 is then DISCHARGED by the redundancy theorem v369, not built. 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[E] the seam KMS cutoff f(u)=e^{-u} (v259) gives the dressed spin-2 propagator e^{-p^2/M^2}/p^2 = 1/(p^2 a) with a(u)=e^u entire & nowhere zero => only the p^2=0 pole (no ghost). [E] each finite truncation carries the ghost: the R+R^2 order T_1=1+u has the Stelle zero u=-1, the Weyl^2 order T_2=1+u+u^2/2 the pair -1+-i; the entire a has none. [E] the ghost DECOUPLES: |nearest zero| of T_n grows monotonically with n (1,1.41,...,3.07 for n=1..8) -> infinity, so 'entire' = 'do not truncate'. [C] => perturbative graviton unitarity. [O] the exact off-shell curved-space Hessian identification is the cited heat-kernel resummation; perturbative-only, not the non-perturbative measure.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv380_grav_kms_hessian.py", "sourceSha256": "ac34423c37a537bd807361b7c677c81cfd938daee02dc9b4c2e2e76be75922f0", "linkedClaimIds": [ "GRAV.KMS.HESSIAN.01" ], "sectionIds": [ "section:00b05ea692eac25e3d3e", "section:213a1f15f7373957fc2f", "section:2525c189f32461c9368a", "section:2a73aae2d89b3c427077", "section:2ffaaee2ce19180008ab", "section:33f8ca97d5f5599b425b", "section:354f7e98a6c16208d1a4", "section:40ced8641cc307aac43a", "section:43e53494baf54171d70d", "section:633620b74c9f05d23e78", "section:6a93c4dd5fe420e1990e", "section:6cd1a267e72b20619327", "section:6db706756a796987fc17", "section:72b43011ac4fb932c47a", "section:75d473d613aba16a08b8", "section:840d8edcd2db5226531d", "section:888628823bf71f709698", "section:91c49cb4658c6aa96d2e", "section:94fabfd63333427d7867", "section:9d6c7d63f5df5a4df579", "section:a29d0e884b184665e5ef", "section:a5afdfe2d50d9975d56b", "section:a64d54bbcb8a16651802", "section:ab9e7e520130ecc7da7c", "section:b93e6ae7b00f32ee1201", "section:c00f76407fefd9782fd7", "section:d90bd5e1e6d8fa41397d", "section:eef94f3ff4627b2515d5", "section:f68163cf343646a0f102" ], "activeSectionIds": [ "section:00b05ea692eac25e3d3e", "section:213a1f15f7373957fc2f", "section:2a73aae2d89b3c427077", "section:40ced8641cc307aac43a", "section:43e53494baf54171d70d", "section:633620b74c9f05d23e78", "section:6db706756a796987fc17", "section:72b43011ac4fb932c47a", "section:75d473d613aba16a08b8", "section:888628823bf71f709698", "section:94fabfd63333427d7867", "section:9d6c7d63f5df5a4df579", "section:a29d0e884b184665e5ef", "section:a5afdfe2d50d9975d56b", "section:a64d54bbcb8a16651802", "section:ab9e7e520130ecc7da7c", "section:c00f76407fefd9782fd7", "section:f68163cf343646a0f102" ], "evidenceId": "python_verification:verification/v380_grav_kms_hessian.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v380_grav_kms_hessian.py", "pubMirrorHash": "ac34423c37a537bd807361b7c677c81cfd938daee02dc9b4c2e2e76be75922f0", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v380_grav_kms_hessian.py" }, { "id": "v369_qgamb_redundancy", "filename": "v369_qgamb_redundancy.py", "path": "verification/v369_qgamb_redundancy.py", "cluster": "frontier", "synopsis": "Track 2 (next-plan v2): the AMBIENT REDUNDANCY statement -- the holographic route to Gravity-complete that SIDESTEPS building the general Euclidean QG measure (C7/QG.AMB.01). Instead of constructing the non-perturbative ambient measure (the conformal-factor swamp, v332/v334), assemble the established discriminators that prove the ambient sector carries NO physical d.o.f. relative to the holomorphic boundary algebra, so QG.AMB.01 is a non-fundamental CERTIFICATION object (like a coordinate choice in GR), not missing dynamics. [E] HOLOMORPHIC => DHR=Vec: #DHR primaries = |det Cartan| = 1 for E8 (ONE primary = vacuum) vs 4 for SO(16)/D8 -- no nontrivial superselection charges => no hidden boundary sector a bulk could carry invisibly. [E] NO TORUS GSD: ground-state degeneracy on T^2 = #anyons = |det K| = 1 for E8 => unique ground state => no topologically protected invisible bulk d.o.f. (the genus-1 obstruction of v344). [E] FINITE PETZ RECOVERY: deviation subspace contracts at (2/3)^6=64/729<1 (v221) => Rec_Sigma bounded. [E] GAP-DECOUPLING MARGIN: Delta_eff=6 ln(3/2)-31/(4 pi^2)~1.648>0 (v76/v337) => ambient sector energetically separated. [C] RECONSTRUCTION MAP: Bisognano-Wichmann gives the modular boost (v258/v309/v323) => Rec_Sigma: (bulk)->A_Sigma^{mu4}. [C] THE REDUNDANCY STATEMENT: under SEAM.EQUIV.01 + BW, O_phys^bulk/Diff ~= A_Sigma^{mu4} => QG.AMB.01 carries no extra physical d.o.f. [O] residual: the two premises -- SEAM.EQUIV.01 (S3 lattice input, v366) + BW intrinsicality (v329); provides the ALTERNATIVE route, does NOT construct the measure. 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Types the standard causal-perturbation-theory closure for the TFPT finite interaction class; does NOT build a path integral and is NOT a new mechanism. [E] POWER-COUNTING: every gauge+matter vertex (Yang-Mills + Dirac-Yukawa + Higgs + ghost) is a mass-dimension-4 marginal operator => the EG singular order omega<=4 => a FINITE counterterm space at every order (power-counting renormalisable). [E] BRST NILPOTENCY s^2=0 verified via the Jacobi identity for su(2) (residual 0) and su(3) (1e-16), the carrier weak+colour gauge content. [E] the seam gap Delta=6 ln(3/2)>0 (v302) gives the IR-safe adiabatic limit g->1. [C] imported: T_n exists to all orders by causal factorisation (Epstein-Glaser 1973 / Brunetti-Fredenhagen). [C] imported: all-order BRST invariance (Piguet-Sorella / Kugo-Ojima) => Slavnov-Taylor to all orders. [E] scope fence: matter+gauge ONLY -- the R^2/Weyl^2 gravity sub-sector is v304/v370/v380, not a local EG vertex; S_pert is not the ambient measure QG.AMB.01 (a [C] redundancy v369). NET [C] (imported EG+BRST on the TFPT dim-4 class + gap), prerequisites [E]; NOT [E], NOT a path integral. 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[E] the Quillen split holds at the root a^3-2 c3^3 a^2 = 8 b1 c3^6 ln(1/phi_seam) at alpha^-1=137.0359992 (F_U(1)=0 IS the stationarity of the U(1) determinant line, v341). [E] every coefficient a named atom: 8 b1=(4/5)*41 a U(1) index, c3=1/(8 pi) the Gauss-Bonnet boundary coeff (c3^3,c3^6 heat-kernel powers), q(D5)+q(A3)=2 discriminant forms (v341/v48/v216). [E] the value alpha^-1=137.0359992168 stays closed (unique root+ablation, v3) -- only 'why this functional' is open. [O] THE TARGET: the from-first-principles AQFT/zeta proof that F_U(1) is the EXACT Quillen functional. [C] a FACE of SEAM.EQUIV.01 (v336): the seam U(1) determinant line lives on the same holomorphic seam net, so once the net is (E8)_1 its U(1) sub-determinant is fixed -- not a second independent gate, it names/tracks the pre-existing EM.WARD.01 residual (v341/v342). No new number (reuses v341, Wolfram-mirrored).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv382_alpha_quillen_exact.py", "sourceSha256": "22e404abe44cca4c9384a5f9efa9afdeb06229ccb0020abd8d81fd3cbb586deb", "linkedClaimIds": [ "ALPHA.QUILLEN.EXACT.01" ], "sectionIds": [ "section:0534241ef38a39dcc3cc", "section:1bdc1e997517317b5cc9", "section:1fa633590a33e985ed41", "section:2a73aae2d89b3c427077", "section:314c7c0b2567b3598a9c", "section:3d3092d4174b4ba2e0ec", "section:6a757c5701557192653a", "section:7144b70a605254dfecbc", "section:7486a840eb74d5da4e47", "section:7ee581db787f8ddbcb4a", "section:8404e6e674a37d72796a", "section:8b1a1c6a205860e21edc", "section:8d1e955857da6655fadd", "section:a3b94e09ceb6d6dbdae4", "section:ab9e7e520130ecc7da7c", "section:b37031f13445096fcccf", "section:c519f45910c30ff3c0ae", "section:c852f8ae0a03109ca8ad", "section:ca7a45590bd2289527ff", "section:ce5afee193d0ce1ea07e", "section:d1b557c6c16fcdfd5e58" ], "activeSectionIds": [ "section:0534241ef38a39dcc3cc", "section:1bdc1e997517317b5cc9", "section:2a73aae2d89b3c427077", "section:314c7c0b2567b3598a9c", "section:6a757c5701557192653a", "section:7144b70a605254dfecbc", "section:7486a840eb74d5da4e47", "section:8404e6e674a37d72796a", "section:8b1a1c6a205860e21edc", "section:8d1e955857da6655fadd", "section:ab9e7e520130ecc7da7c", "section:b37031f13445096fcccf", "section:c852f8ae0a03109ca8ad", "section:ce5afee193d0ce1ea07e", "section:d1b557c6c16fcdfd5e58" ], "evidenceId": "python_verification:verification/v382_alpha_quillen_exact.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v382_alpha_quillen_exact.py", "pubMirrorHash": "22e404abe44cca4c9384a5f9efa9afdeb06229ccb0020abd8d81fd3cbb586deb", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v382_alpha_quillen_exact.py" }, { "id": "v383_dynamics_universal", "filename": "v383_dynamics_universal.py", "path": "verification/v383_dynamics_universal.py", "cluster": "frontier", "synopsis": "DYNAMICS.UNIVERSAL.01: the UNIVERSAL spectral-gap / Perron-Frobenius principle -- every TFPT sector is the SAME object (a gapped operator with a UNIQUE leading attractor = the physics, a spectral gap = the reason there is no free parameter), extending v303 from F_transfer to the whole theory. [E] FLAVOR (computed): the cusp transfer spectrum {1,(2/3)^6,(1/3)^6} has a simple Perron leading 1 and gap 6 ln(3/2)>0 (v56/v82). [E] DISCRETE COMPILER (computed): the affine-E8 adjacency has Perron eigenvalue 2 (Kac marks, v312/v313) and subleading 2cos(pi/5)=phi, gap 2-phi=1/phi^2>0. [E] DECOUPLING MARGIN: Delta_eff=6 ln(3/2)-31/(4 pi^2)~1.648>0 (v76/v337). [E] TWO NUMBER-FIELD FACETS (v314): golden phi in Q(sqrt5) (carrier-5, static) and (2/3)^6 in Q (family-3, dynamic) are the prime-5 and prime-3 facets of the order-30 Coxeter clock 30=2*3*5=h(E8) -- a factorisation, not an equality. [C] the other sectors are the same structure: gravity (v358/v359), QG saddle (v365), RG fixed point (v157/v158), all-order S-matrix (v381), recovery (v221), F_transfer (v303), tau=i (v333). [C] META-THEOREM: gapped => unique attractor => parameter-free, theory-wide. A synthesis, no new number.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv383_dynamics_universal.py", "sourceSha256": "b91230af4915e41bef8ecfab5fefe1f8386ae8182e6a9954b433e5cbcb2b2c07", "linkedClaimIds": [ "DYNAMICS.UNIVERSAL.01" ], "sectionIds": [ "section:2b8d2aba4baeb7a0c36b", "section:303925994b6f141b3a0e", "section:48dc2c7b5335aebad935", "section:568b5e9acdb7b04367d3", "section:5b0172590490b241cb77", "section:633620b74c9f05d23e78", "section:6b87e1b142e887eedca7", "section:7ee581db787f8ddbcb4a", "section:8b1a1c6a205860e21edc", "section:8d1e955857da6655fadd", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:c519f45910c30ff3c0ae", "section:f0ac30137703825661c6", "section:f1054498b80cd7df6676", "section:f6d50ad015506eb0de3c", "section:fb4cf64c8cbaeb3f6d74", "section:fddca2e76a3d11b710e6", "section:fdf63a1d99769ab37ccb" ], "activeSectionIds": [ "section:48dc2c7b5335aebad935", "section:5b0172590490b241cb77", "section:633620b74c9f05d23e78", "section:6b87e1b142e887eedca7", "section:8b1a1c6a205860e21edc", "section:8d1e955857da6655fadd", "section:ab9e7e520130ecc7da7c", "section:f1054498b80cd7df6676", "section:f6d50ad015506eb0de3c", "section:fb4cf64c8cbaeb3f6d74", "section:fddca2e76a3d11b710e6", "section:fdf63a1d99769ab37ccb" ], "evidenceId": "python_verification:verification/v383_dynamics_universal.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v383_dynamics_universal.py", "pubMirrorHash": "b91230af4915e41bef8ecfab5fefe1f8386ae8182e6a9954b433e5cbcb2b2c07", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v383_dynamics_universal.py" }, { "id": "v384_residual_certification", "filename": "v384_residual_certification.py", "path": "verification/v384_residual_certification.py", "cluster": "frontier", "synopsis": "RESIDUAL.CERTIFICATION.01 (historical compiler scope; corrected 2026-09-05): the then-listed compiler residual is CERTIFICATION, not CONSTRUCTION -- after v369/v381/v382 there is NO open TFPT physics MECHANISM left; every residual is an external CERTIFICATE of already-determined structure, of three kinds: (A) external math proof, (B) theorem-forbidden, (C) external physics. A ledger-CI audit. [E] LEDGER CI: every residual claim id is present (no orphan). [E] NO-UNIT (B): c3=1/(8 pi) and g_car=5 are mass-dim 0, so by No-Unit (v153/v364) no dimensionless compiler outputs an absolute scale => v_geo is forbidden by theorem, not a gap. [E] GAP-DECOUPLED (A): Delta_eff~1.648>0 (v76/v337) => every readout is independent of the ambient measure (QG.AMB.01 a [C] redundancy, v369). [E] CLASSIFICATION COMPLETE: SEAM.EQUIV.01 (continuum existence=cited MMST/Adamo v336)->A, ALPHA.QUILLEN.EXACT.01 (v382)->A, QG.AMB.01 (v369)->A, v_geo->B, F_transfer (v371-v374, firewall v187)->C; ZERO open internal mechanisms within that scoped compiler list. This audit does not classify the physical completeness gates T1-T8; those and a shared 3+1D parent remain open. [C] CONVERGENCE applies only to the historical compiler residual. An audit, no new number.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv384_residual_certification.py", "sourceSha256": "b25d08fbed044c7ce7cb6be753e46788d3cace23fd3a396401d59244291a122c", "linkedClaimIds": [ "RESIDUAL.CERTIFICATION.01" ], "sectionIds": [ "section:1bdc1e997517317b5cc9", "section:1fa633590a33e985ed41", "section:2ee299d2f97d03685885", "section:314c7c0b2567b3598a9c", "section:37d6ecba160419b2f272", "section:3d3092d4174b4ba2e0ec", "section:5b0172590490b241cb77", "section:6a757c5701557192653a", "section:6a93c4dd5fe420e1990e", "section:6b87e1b142e887eedca7", "section:7486a840eb74d5da4e47", "section:75d473d613aba16a08b8", "section:7ee581db787f8ddbcb4a", "section:8404e6e674a37d72796a", "section:8b1a1c6a205860e21edc", "section:8d1e955857da6655fadd", "section:a153934887244824336d", "section:a3b94e09ceb6d6dbdae4", "section:ab9e7e520130ecc7da7c", "section:c519f45910c30ff3c0ae", "section:c852f8ae0a03109ca8ad", "section:ca7a45590bd2289527ff", "section:d59ca752d5e1a51b75b5", "section:d90bd5e1e6d8fa41397d" ], "activeSectionIds": [ "section:1bdc1e997517317b5cc9", "section:2ee299d2f97d03685885", "section:314c7c0b2567b3598a9c", "section:37d6ecba160419b2f272", "section:5b0172590490b241cb77", "section:6a757c5701557192653a", "section:6b87e1b142e887eedca7", "section:7486a840eb74d5da4e47", "section:75d473d613aba16a08b8", "section:8404e6e674a37d72796a", "section:8b1a1c6a205860e21edc", "section:8d1e955857da6655fadd", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:c852f8ae0a03109ca8ad", "section:d59ca752d5e1a51b75b5" ], "evidenceId": "python_verification:verification/v384_residual_certification.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v384_residual_certification.py", "pubMirrorHash": "b25d08fbed044c7ce7cb6be753e46788d3cace23fd3a396401d59244291a122c", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v384_residual_certification.py" }, { "id": "v385_uvbranch_killtest", "filename": "v385_uvbranch_killtest.py", "path": "verification/v385_uvbranch_killtest.py", "cluster": "registry", "synopsis": "UVBRANCH.KILLTEST.01: the optional carrier-Pati-Salam UV branch on the ALL-ORDER footing -- a single citable kill-test surface with the proton-decay SAFETY hierarchy computed (not a fake tau_p window). A consolidation (does NOT re-run the RGE v246 nor re-derive the PS scale v249/v253). [E] carrier content = SM (b=(41/10,-19/6,-7), v159/v246, no new states) and S_pert closes to all orders (v381) => the SM-non-unification is all-order-robust. [X] plain-SM 4D-GUT killed (sin^2 thW=3/8 vs 0.231; v246). [C] optional carrier-PS branch: M_PS=kappa M_scal, M_scal=c3^{7/2}Mbar~3.06e13 GeV, kappa in [1.0,1.2] (v253), content {1,10,16,45} no 126 (v247/v248), not default (v265). [E] proton-decay SAFETY hierarchy: minimal PS gauge bosons are SU(4) leptoquarks (B-L-conserving q<->l, rare LFV K_L->mu e), NOT the p->e+ pi0 dim-6 operator (needs SO(10)/SU(5) diquark, absent); binding bound M_PS>~1e6 GeV cleared by M_PS/M_bound~1e7>>1. [X] frozen kill tests (v265): kappa leaving O(1) / a forbidden rep / a new gauge-charged state / a rare-LFV signal below the bound; no fake tau_p. A consolidation, no new number.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv385_uvbranch_killtest.py", "sourceSha256": "9daa1fde6c6f2952721e4b88e919380936ca2892542a7e9ec44a972d1067bf98", "linkedClaimIds": [ "UVBRANCH.KILLTEST.01" ], "sectionIds": [ "section:633620b74c9f05d23e78", "section:ab9e7e520130ecc7da7c", "section:c00f76407fefd9782fd7" ], "activeSectionIds": [ "section:633620b74c9f05d23e78", "section:ab9e7e520130ecc7da7c", "section:c00f76407fefd9782fd7" ], "evidenceId": "python_verification:verification/v385_uvbranch_killtest.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v385_uvbranch_killtest.py", "pubMirrorHash": "9daa1fde6c6f2952721e4b88e919380936ca2892542a7e9ec44a972d1067bf98", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v385_uvbranch_killtest.py" }, { "id": "v386_grav_amplitude", "filename": "v386_grav_amplitude.py", "path": "verification/v386_grav_amplitude.py", "cluster": "frontier", "synopsis": "GRAV.AMPLITUDE.01: the entire-form-factor graviton-exchange AMPLITUDE is finite, UV-softened and tree-unitary -- perturbative gravity as an explicit scattering problem, extending v304/v370/v380 from the propagator to the amplitude. The dressed spin-2 propagator P=e^{-p^2/M^2}/p^2=1/(p^2 a), a(u)=e^u, M=M_scal. [E] one pole, ghost-free: a entire & nowhere zero (v380) => only pole at p^2=0, residue e^0=1>0. [E] UV-softened: ratio e^{-u} at u=1,5,10,20=0.37,6.7e-3,4.5e-5,2.1e-9 (faster than any power). [E] low-energy = GR + a calculable -p^2/M^2 correction (M=M_scal=c3^{7/2}Mbar, v253). [C] tree unitarity: a single positive-residue pole, no negative-norm states (v370/v380). [C] the amplitude A=(kappa^2/2)(T.P2.T')e^{-p^2/M^2}/p^2 is GR at low energy, softened in the UV (perturbative-only; QG.AMB.01 a [C] redundancy v369). No new number.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv386_grav_amplitude.py", "sourceSha256": "56955b04acb03b2e45278a82e278b440e4a2b9e2d2d812e21efaecdd634ed42a", "linkedClaimIds": [ "GRAV.AMPLITUDE.01" ], "sectionIds": [ "section:633620b74c9f05d23e78", "section:6b87e1b142e887eedca7", "section:75d473d613aba16a08b8", "section:a5afdfe2d50d9975d56b", "section:a64d54bbcb8a16651802", "section:ab9e7e520130ecc7da7c" ], "activeSectionIds": [ "section:633620b74c9f05d23e78", "section:6b87e1b142e887eedca7", "section:75d473d613aba16a08b8", "section:a5afdfe2d50d9975d56b", "section:a64d54bbcb8a16651802", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v386_grav_amplitude.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v386_grav_amplitude.py", "pubMirrorHash": "56955b04acb03b2e45278a82e278b440e4a2b9e2d2d812e21efaecdd634ed42a", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v386_grav_amplitude.py" }, { "id": "v387_corrections_gap", "filename": "v387_corrections_gap.py", "path": "verification/v387_corrections_gap.py", "cluster": "frontier", "synopsis": "CORRECTIONS.GAP.01: the practical harvest of v383 -- the same spectral gap that makes each sector parameter-free ALSO sets the SIZE of its first correction (correction_n ~ (lambda_2/lambda_1)^n). [E] FLAVOR: lambda_2=(2/3)^6=64/729 => first Koide correction ~0.088 (v56/v82). [E] RECOVERY: the same (2/3)^6 Petz rate (v221). [E] QG: capped by chi=1/(1-(2/3)^6)=729/665 (v337). [E] DISCRETE COMPILER: the update (A+2I)/4 fixes the Kac marks (lambda_1=1) and decays at the golden (phi+2)/4~0.905 (carrier-5 facet, v303/v312). [E] the rates split into the (2/3)^6 family (family-3, in Q) and the golden family (carrier-5, in Q(sqrt5)) -- the two facets of v314/v383. [C] the correction calculus: the gap does double duty (WHY no free parameter AND HOW BIG the first correction), so sub-leading magnitudes are organised, not free. No new number.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv387_corrections_gap.py", "sourceSha256": "096ad87c6f565e7cd7dd2525dd2e7d0ff21f415acf1b805c910e63e56cf03e05", "linkedClaimIds": [ "CORRECTIONS.GAP.01" ], "sectionIds": [ "section:2b8d2aba4baeb7a0c36b", "section:303925994b6f141b3a0e", "section:5b0172590490b241cb77", "section:633620b74c9f05d23e78", "section:6b87e1b142e887eedca7", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:f1054498b80cd7df6676", "section:fb4cf64c8cbaeb3f6d74", "section:fddca2e76a3d11b710e6" ], "activeSectionIds": [ "section:5b0172590490b241cb77", "section:633620b74c9f05d23e78", "section:6b87e1b142e887eedca7", "section:ab9e7e520130ecc7da7c", "section:f1054498b80cd7df6676", "section:fb4cf64c8cbaeb3f6d74", "section:fddca2e76a3d11b710e6" ], "evidenceId": "python_verification:verification/v387_corrections_gap.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v387_corrections_gap.py", "pubMirrorHash": "096ad87c6f565e7cd7dd2525dd2e7d0ff21f415acf1b805c910e63e56cf03e05", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v387_corrections_gap.py" }, { "id": "v388_corrections_budget", "filename": "v388_corrections_budget.py", "path": "verification/v388_corrections_budget.py", "cluster": "frontier", "synopsis": "CORRECTIONS.BUDGET.01: the gap correction (v387) is a TYPED budget, NOT a uniform band on every prediction -- the (lambda_2/lambda_1)^n size is a property of the distance from a gapped operator's leading eigenvector, so it is only defined where lambda_2 exists. The prediction surface splits into four correction classes (already implied by v303). [E] SEAM-GAPPED: Koide (F_pole v303), recovery (v221), the QG bound (capped by chi=729/665, v337) carry (2/3)^6; the discrete compiler decays at the golden (phi+2)/4 (v312). [E] KOIDE FIRST CORRECTION (door #2): F_pole is the ONE seam-gapped prediction, rate (2/3)^6~0.0878 (v371), source quotient 0.33% below 2/3 -- the rate is the suppression SCALE, not the residual. [E] EXACT-IDENTITY class (det R=8, N_Phi=1, theta_eff=0, sin^2 theta13): no lambda_2 => correction 0 STRUCTURALLY (a band would contradict [E]). [E] EXTERNAL-RATE class (eta_B/axion/m_p,m_e): the gapped shape with external rates (only F_pole has the seam rate, v303), firewalled (v187). [E] FIXED-POINT class: the texture is already explicit (theta12 eps=c3+36 c3^4). [C] a uniform band on all predictions is WRONG; the size is keyed to the mechanism class. A typing of v387, no new number.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv388_corrections_budget.py", "sourceSha256": "df4cecb3ffe6fa8da01b5c8046603c63bcbe498e5146c3ad02f59ecd266aadfe", "linkedClaimIds": [ "CORRECTIONS.BUDGET.01" ], "sectionIds": [ "section:2b8d2aba4baeb7a0c36b", "section:303925994b6f141b3a0e", "section:5b0172590490b241cb77", "section:6b87e1b142e887eedca7", "section:9a49b0a6b8928419303b", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:5b0172590490b241cb77", "section:6b87e1b142e887eedca7", "section:9a49b0a6b8928419303b", "section:ab9e7e520130ecc7da7c", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v388_corrections_budget.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v388_corrections_budget.py", "pubMirrorHash": "df4cecb3ffe6fa8da01b5c8046603c63bcbe498e5146c3ad02f59ecd266aadfe", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v388_corrections_budget.py" }, { "id": "v389_grav_loop_finiteness", "filename": "v389_grav_loop_finiteness.py", "path": "verification/v389_grav_loop_finiteness.py", "cluster": "frontier", "synopsis": "GRAV.LOOP.FINITE.01: the entire-form-factor graviton is UV-finite at the LOOP level by power counting -- the honest next step past v386 (tree). Extends v304/v370/v380/v386 from the propagator to the superficial degree of divergence of loop graphs. HONEST SCOPE: the standard infinite-derivative/nonlocal-gravity finiteness statement (Tomboulis; Biswas-Mazumdar-Siegel; Modesto), NOT a full proof of perturbative QG. [E] super-polynomial falloff p^k e^{-p^2/M^2}->0 for every k. [E] one dressed line turns a quadratic divergence into the finite (M^2/2)e^{-p0^2/M^2}; GR int p^3/p^2 dp diverges quadratically. [E] superficial degree -> -infinity at every loop order (dressed cutoff-ratio ->1 vs GR ->4). [E] the regulator is the SEAM scale M=M_scal=c3^{7/2}Mbar (v253/v259), not a dial. [C]/[O] loop UNITARITY of the nonlocal form factor (Lorentzian continuation/macro-causality) stays the honest open point -- tree unitarity is v386; NOT claimed solved. No new number.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv389_grav_loop_finiteness.py", "sourceSha256": "24486ef2555ebde94803e26da09d7ed0dda3df693e13427fd5aee1eb95d1a6c7", "linkedClaimIds": [ "GRAV.LOOP.FINITE.01" ], "sectionIds": [ "section:6b87e1b142e887eedca7", "section:a5afdfe2d50d9975d56b", "section:a64d54bbcb8a16651802", "section:ab9e7e520130ecc7da7c" ], "activeSectionIds": [ "section:6b87e1b142e887eedca7", "section:a5afdfe2d50d9975d56b", "section:a64d54bbcb8a16651802", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v389_grav_loop_finiteness.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v389_grav_loop_finiteness.py", "pubMirrorHash": "24486ef2555ebde94803e26da09d7ed0dda3df693e13427fd5aee1eb95d1a6c7", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v389_grav_loop_finiteness.py" }, { "id": "v390_prime2_facet", "filename": "v390_prime2_facet.py", "path": "verification/v390_prime2_facet.py", "cluster": "frontier", "synopsis": "COXETER.PRIME2.01: the prime-2 facet of the order-30 Coxeter clock, completing v383. The clock 30=2*3*5=h(E8) had two named number-field facets (golden phi in Q(sqrt5), prime-5/carrier; (2/3)^6 in Q, prime-3/family); this names the prime-2 facet, identified with the Gaussian field Q(i) -- tau=i and the order-4 mu4=Z/4 square seam deck (v282/v288/v333), structure already in the theory. [E] h(E8)=30 factors into exactly three primes. [E] one quadratic facet field per prime, each ramified at its prime: disc Q(i)=-4, disc Q(sqrt-3)=-3, disc Q(sqrt5)=5; ramified primes {2,3,5}, product=30. [E] prime-2 Gaussian facet: min poly x^2+1, tau=i, j(i)=1728=12^3, |mu4|=4=2^2 (the static seam-orientation facet). [E] prime-5 golden (v383): 2cos(pi/5)=phi (pentagon). [E] prime-3 family (v383/v220): (2/3)^6 + Eisenstein zeta_3 (hexagonal CP pi/3). [C] completion: each prime carries a facet (square/hexagon/pentagon = seam/CP/carrier), the prime set forced by h(E8). A synthesis, no new number.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv390_prime2_facet.py", "sourceSha256": "47f82143277cd91b33c9016ec197a646d7706adb881b26e90779ac21eb8a4403", "linkedClaimIds": [ "COXETER.PRIME2.01" ], "sectionIds": [ "section:2b8d2aba4baeb7a0c36b", "section:303925994b6f141b3a0e", "section:7ee581db787f8ddbcb4a", "section:8d1e955857da6655fadd", "section:8e3e6d08d3c102a09298", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:c519f45910c30ff3c0ae", "section:f1054498b80cd7df6676", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:8d1e955857da6655fadd", "section:8e3e6d08d3c102a09298", "section:ab9e7e520130ecc7da7c", "section:f1054498b80cd7df6676", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v390_prime2_facet.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v390_prime2_facet.py", "pubMirrorHash": "47f82143277cd91b33c9016ec197a646d7706adb881b26e90779ac21eb8a4403", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v390_prime2_facet.py" }, { "id": "v391_alpha_quillen_progress", "filename": "v391_alpha_quillen_progress.py", "path": "verification/v391_alpha_quillen_progress.py", "cluster": "em", "synopsis": "ALPHA.QUILLEN.PROGRESS.01: an HONEST attempt at the external target ALPHA.QUILLEN.EXACT.01 (v382) -- it REDUCES the open step to a sharper named sub-target via a solvable model but does NOT close it; ALPHA.QUILLEN.EXACT.01 stays [O] (external math, type A, v384). [E] solvable model: det_zeta(-d^2/dtau^2+m^2) on a circle = (2 sinh(beta m/2))^2, m-variation beta*coth(beta m/2) = 2/m + (beta^2/6)m - (beta^4/360)m^3+... a closed heat-kernel/Laurent series (m^3 coeff -1/360 verified). [E] a zeta-det variation is structured heat-kernel data, so v382's 8 b1 c3^6 counterterm (Gauss-Bonnet heat-kernel power) is the right KIND of object. [E] the v382 split re-verified at alpha^-1=137.0359992. [E] reduction: the open step reduces to the named sub-target 'seam Seeley-DeWitt coefficient = 8 b1 c3^6'. [O] NOT CLOSED: the actual seam zeta-det proof stays open, SEAM.EQUIV.01 continuum existence (v336) the other external [O]; alpha^-1 stays [E]. An attempt that reduces, does not close.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv391_alpha_quillen_progress.py", "sourceSha256": "9da74d256db2e5155c970ede1bcd3ca0e1f8491aa188ffc5af57b8d06264b384", "linkedClaimIds": [ "ALPHA.QUILLEN.PROGRESS.01" ], "sectionIds": [ "section:09b49009253acb5a0dfb", "section:1bdc1e997517317b5cc9", "section:1fa633590a33e985ed41", "section:3cc790136e8b9bd3c188", "section:3d3092d4174b4ba2e0ec", "section:584e87a9c163ac38f92f", "section:6a757c5701557192653a", "section:6b87e1b142e887eedca7", "section:7144b70a605254dfecbc", "section:7486a840eb74d5da4e47", "section:a3b94e09ceb6d6dbdae4", "section:ab9e7e520130ecc7da7c", "section:c852f8ae0a03109ca8ad", "section:ca7a45590bd2289527ff", "section:eb0bd97fda8c0fedefad" ], "activeSectionIds": [ "section:1bdc1e997517317b5cc9", "section:584e87a9c163ac38f92f", "section:6a757c5701557192653a", "section:6b87e1b142e887eedca7", "section:7144b70a605254dfecbc", "section:7486a840eb74d5da4e47", "section:ab9e7e520130ecc7da7c", "section:c852f8ae0a03109ca8ad" ], "evidenceId": "python_verification:verification/v391_alpha_quillen_progress.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v391_alpha_quillen_progress.py", "pubMirrorHash": "9da74d256db2e5155c970ede1bcd3ca0e1f8491aa188ffc5af57b8d06264b384", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v391_alpha_quillen_progress.py" }, { "id": "v433_alpha_quillen_heatkernel", "filename": "v433_alpha_quillen_heatkernel.py", "path": "verification/v433_alpha_quillen_heatkernel.py", "cluster": "em", "synopsis": "ALPHA.QUILLEN.PROGRESS.02: a SECOND honest step on the external target ALPHA.QUILLEN.EXACT.01 (v382) -- it GROUNDS and CONNECTS, it does NOT close it; ALPHA.QUILLEN.EXACT.01 stays [O] (external math, type A, v384), alpha^-1 stays [E]. [E] a solvable 4D model (flat Delta=-d^2+m^2 on T^4) reaches the a_4 (t^0) conformal-anomaly order: a_4=V m^4/(2(4pi)^2) NON-ZERO -- the order v391's 1D circle toy (a_0,a_1 only) could not reach. [E] it is the order v342 grounds (Gilkey a_4 gauge-curvature 30/360=1/12), unifying v391 (a zeta-det variation IS heat-kernel data) with v342 (the term IS the Gilkey a_4). [E] (4pi)^-2 = 4 c3^2 is c3-built. [E] the v382 split re-verified at alpha^-1=137.0359992. [O] NOT CLOSED: the actual seam a_4 (=8 b1 c3^6) and the cubic a^3 Chern moment stay open (v384); the exact seam F-normalisation stays [C] (v342). Grounds/connects, does not close.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv433_alpha_quillen_heatkernel.py", "sourceSha256": "d02949a3a409daa9366de7db943cfe4f785ea8199c1fcecbbc4ac6438458dafb", "linkedClaimIds": [ "ALPHA.QUILLEN.PROGRESS.02" ], "sectionIds": [ "section:1bdc1e997517317b5cc9", "section:1fa633590a33e985ed41", "section:314c7c0b2567b3598a9c", "section:3d3092d4174b4ba2e0ec", "section:6a757c5701557192653a", "section:7144b70a605254dfecbc", "section:8404e6e674a37d72796a", "section:a3b94e09ceb6d6dbdae4", "section:ab9e7e520130ecc7da7c", "section:c852f8ae0a03109ca8ad", "section:ca7a45590bd2289527ff", "section:ce5afee193d0ce1ea07e" ], "activeSectionIds": [ "section:1bdc1e997517317b5cc9", "section:314c7c0b2567b3598a9c", "section:6a757c5701557192653a", "section:7144b70a605254dfecbc", "section:8404e6e674a37d72796a", "section:ab9e7e520130ecc7da7c", "section:c852f8ae0a03109ca8ad", "section:ce5afee193d0ce1ea07e" ], "evidenceId": "python_verification:verification/v433_alpha_quillen_heatkernel.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v433_alpha_quillen_heatkernel.py", "pubMirrorHash": "d02949a3a409daa9366de7db943cfe4f785ea8199c1fcecbbc4ac6438458dafb", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v433_alpha_quillen_heatkernel.py" }, { "id": "v434_alpha_quillen_betafunction", "filename": "v434_alpha_quillen_betafunction.py", "path": "verification/v434_alpha_quillen_betafunction.py", "cluster": "em", "synopsis": "ALPHA.QUILLEN.PROGRESS.03: a THIRD honest step on ALPHA.QUILLEN.EXACT.01 (v382) -- it settles the three residuals named after v433 and shows they are NOT three independent problems; the target stays [O], alpha^-1 stays [E]. [E] b1 IS THE U(1) a_4 HEAT-KERNEL COEFFICIENT (beta=a_4 theorem): from the carrier hypercharge content with spin weights (2/3 Weyl, 1/3 complex scalar), sum (2/3)Y_f^2+(1/3)Y_s^2 = 41/6 (SM), (3/5)*that = 41/10 = b1 (GUT) -- the b1 in 8 b1 c3^6 is the a_4 content coefficient, not a fitted multiplicity (same number as the beta, v159/v246; same KIND as the alpha^2 Calderon a_4, v342). [E] 8 b1 c3^6 = b1*(rank E8)*c3^6 (rank 8 = chi=2 boundary, v216; c3^6 = six insertions, v342). [C] residual (1) 'exact a_4 = 8 b1 c3^6' == residual (3) 'seam F-normalisation' -- ONE obligation. [E] residual (2) located: a^3-2c3^3 a^2 = a^2(a-2c3^3), so a^3 = the first moment of the Chern density (a level, order c3^0); origin stays [O]. [E] net reduction: the EM-Ward residual is 1[C]+1[O], not three. [O] NOT CLOSED; alpha^-1 stays [E]. Python-only.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv434_alpha_quillen_betafunction.py", "sourceSha256": "cfd5067a23236a66d698d88b3fcf3d243bcf57d6f13159555aecac6e87991b52", "linkedClaimIds": [ "ALPHA.QUILLEN.PROGRESS.03" ], "sectionIds": [ "section:1fa633590a33e985ed41", "section:314c7c0b2567b3598a9c", "section:3d3092d4174b4ba2e0ec", "section:6a757c5701557192653a", "section:7144b70a605254dfecbc", "section:8404e6e674a37d72796a", "section:a3b94e09ceb6d6dbdae4", "section:ab9e7e520130ecc7da7c", "section:c852f8ae0a03109ca8ad", "section:ca7a45590bd2289527ff", "section:ce5afee193d0ce1ea07e" ], "activeSectionIds": [ "section:314c7c0b2567b3598a9c", "section:6a757c5701557192653a", "section:7144b70a605254dfecbc", "section:8404e6e674a37d72796a", "section:ab9e7e520130ecc7da7c", "section:c852f8ae0a03109ca8ad", "section:ce5afee193d0ce1ea07e" ], "evidenceId": "python_verification:verification/v434_alpha_quillen_betafunction.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v434_alpha_quillen_betafunction.py", "pubMirrorHash": "cfd5067a23236a66d698d88b3fcf3d243bcf57d6f13159555aecac6e87991b52", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v434_alpha_quillen_betafunction.py" }, { "id": "v435_alpha_quillen_chernlevel", "filename": "v435_alpha_quillen_chernlevel.py", "path": "verification/v435_alpha_quillen_chernlevel.py", "cluster": "em", "synopsis": "ALPHA.QUILLEN.PROGRESS.04: a FOURTH honest step on ALPHA.QUILLEN.EXACT.01 (v382) -- it attacks the SINGLE remaining [O] after v434 (residual (2), the cubic alpha^3 Chern level) and SHARPENS it, it does NOT close it; the target stays [O], alpha^-1 stays [E]. [E] pi-POWER / METRIC-INDEPENDENCE TEST: the three closure coefficients carry pi-powers exactly {0,3,6}=c3-orders (k0=1 -> pi^0; -2c3^3=-1/(256 pi^3) -> pi^3; -8 b1 c3^6=-41/(327680 pi^6) -> pi^6), so the Maxwell a^3 is the UNIQUE pi^0/c3^0 (metric-INDEPENDENT) term -- the signature of a topological level (a heat-kernel boundary coeff always carries the (4pi)^{-d/2} measure; a level carries none). The test partitions the closure into ONE topological level (a^3) + TWO heat-kernel boundary terms, confirming v342/v434's 'a^3 is a level, not a curvature integral' from a test. [C] conditional on the CS/eta reading (EM1, v48), large-gauge invariance forces the level in Z and k0=1 is the unit (minimal) level -- an integer, not a free real. [O] NOT CLOSED: the EM1 CS-boundary derivation stays external (type A, v384); seam F-norm stays the one [C] (v434); alpha^-1 stays [E].", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv435_alpha_quillen_chernlevel.py", "sourceSha256": "489f7a43b07f2b687eb6e180fd62a08082c3a38a1c2faf0a9774e7be715439c9", "linkedClaimIds": [ "ALPHA.QUILLEN.PROGRESS.04" ], "sectionIds": [ "section:1fa633590a33e985ed41", "section:3d3092d4174b4ba2e0ec", "section:6a757c5701557192653a", "section:7144b70a605254dfecbc", "section:8404e6e674a37d72796a", "section:a3b94e09ceb6d6dbdae4", "section:ab9e7e520130ecc7da7c", "section:c852f8ae0a03109ca8ad", "section:ca7a45590bd2289527ff", "section:ce5afee193d0ce1ea07e", "section:e7cdfe28203ecac9114d" ], "activeSectionIds": [ "section:6a757c5701557192653a", "section:7144b70a605254dfecbc", "section:8404e6e674a37d72796a", "section:ab9e7e520130ecc7da7c", "section:c852f8ae0a03109ca8ad", "section:ce5afee193d0ce1ea07e", "section:e7cdfe28203ecac9114d" ], "evidenceId": "python_verification:verification/v435_alpha_quillen_chernlevel.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v435_alpha_quillen_chernlevel.py", "pubMirrorHash": "489f7a43b07f2b687eb6e180fd62a08082c3a38a1c2faf0a9774e7be715439c9", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v435_alpha_quillen_chernlevel.py" }, { "id": "v392_seam_s3_scalinglimit", "filename": "v392_seam_s3_scalinglimit.py", "path": "verification/v392_seam_s3_scalinglimit.py", "cluster": "core", "synopsis": "SEAM.S3.SCALINGLIMIT.01: an HONEST attack on the one open lemma of SEAM.EQUIV.01 (the continuum scaling-limit existence, v336) -- does NOT close it (the abstract existence is the cited MMST theorem); STRENGTHENS the case with the existence-relevant observable v376 did not test: that the finite-size data CONVERGE. [E] the Calabrese-Cardy EE slope c1(L) at L=66..514 is a monotone Cauchy-like sequence approaching 1 (|c1(L)-1| strictly decreasing). [E] a 1/L Richardson fit gives c1(inf)~1.000 so the 16-Majorana collar c=8*c1~8.00 = g_car+N_fam is reached IN the limit. [E] the successive differences are strictly decreasing (numerical Cauchy, necessary for existence). [O] convergent data are evidence, not a proof of existence (MMST v336), and do not pin (E8)_1 vs SO(16)_1 (holomorphy v377/v378). Strengthens the residual, does NOT close it.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv392_seam_s3_scalinglimit.py", "sourceSha256": "4bfe8820d78bf8b17714320f06325429500c5597ad7fe5ba7a46eb0fdd552baa", "linkedClaimIds": [ "SEAM.S3.SCALINGLIMIT.01" ], "sectionIds": [ "section:6a93c4dd5fe420e1990e", "section:8e4972dbe899b5debb90", "section:a553d00a39600c2d24cd", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d" ], "activeSectionIds": [ "section:8e4972dbe899b5debb90", "section:a553d00a39600c2d24cd", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v392_seam_s3_scalinglimit.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v392_seam_s3_scalinglimit.py", "pubMirrorHash": "4bfe8820d78bf8b17714320f06325429500c5597ad7fe5ba7a46eb0fdd552baa", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v392_seam_s3_scalinglimit.py" }, { "id": "v393_corrections_numeric", "filename": "v393_corrections_numeric.py", "path": "verification/v393_corrections_numeric.py", "cluster": "frontier", "synopsis": "CORRECTIONS.NUMERIC.01: the typed correction budget (v388) turned into ACTUAL first-correction magnitudes -- a computed theoretical-uncertainty surface, the short-term testable harvest of v388. [E] FIXED-POINT band (theta12/theta13/lambda_C/beta_rad) = the explicit phi0 puncture term 36 c3^4/c3 = 9/(128 pi^3) ~ 0.227% (exact; = theta12's epsilon first-correction). [E] SEAM-GAPPED band (Koide/recovery) = (2/3)^6 ~ 8.78%; QG bound capped by chi-1 = 64/665 ~ 9.62% (v337). [E] EXACT-IDENTITY band = 0 structurally (det R=8, N_Phi=1, theta_eff=0). [E] EXTERNAL-RATE band = external physics quoted (m_p/m_e +-7.5% v374; n_s/r N* band; eta_B 1.07x v212), fenced v187. [C] each prediction gets 'central value +- computed first correction'. A harvest of v388, no new number.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv393_corrections_numeric.py", "sourceSha256": "93b91c30006fde1193229e50f41f459a1eb64d9803c4dca30de38f61bfbc2ab0", "linkedClaimIds": [ "CORRECTIONS.NUMERIC.01" ], "sectionIds": [ "section:2b8d2aba4baeb7a0c36b", "section:303925994b6f141b3a0e", "section:3317d161dfba545d677a", "section:51b5da5a67a36e5155ae", "section:697c671889813baf24f5", "section:7a7de20f53ed3e69fb6f", "section:9a49b0a6b8928419303b", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:ea55650cbf1afb16c587", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:3317d161dfba545d677a", "section:697c671889813baf24f5", "section:7a7de20f53ed3e69fb6f", "section:9a49b0a6b8928419303b", "section:ab9e7e520130ecc7da7c", "section:ea55650cbf1afb16c587", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v393_corrections_numeric.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v393_corrections_numeric.py", "pubMirrorHash": "93b91c30006fde1193229e50f41f459a1eb64d9803c4dca30de38f61bfbc2ab0", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v393_corrections_numeric.py" }, { "id": "v396_phi0_icosahedral", "filename": "v396_phi0_icosahedral.py", "path": "verification/v396_phi0_icosahedral.py", "cluster": "frontier", "synopsis": "HYP.PHI0.01: the phi0 leading term from icosahedral combinatorics (sharpening v312/v395). [E] ICO COUNTS ANCHOR-FORCED: V=12, E=30=h(E8), F=20=g_car(g_car-1), |Aut|=120=4h=|2I|. [E] LEADING TERM EXACT: phibase=1/(6 pi)=(4/3)c3=F/(4h pi)=F/(|Aut| pi)=(F/(g_car N_fam))c3. [E] F/h=|Z2|/N_fam; phibase=(F/h)/(4 pi)=c3(g_car-1)/N_fam. [E] GAUSS-BONNET: icosahedron deficit sum 4 pi; c3=1/(|Z2| 4 pi) (v216/v342). [E] HONEST NEGATIVE: puncture 48 c3^4 not rational hypergraph fraction. [C] phibase = (hyperedges)/(g_car N_fam) x c3, not independent injection; puncture [O].", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv396_phi0_icosahedral.py", "sourceSha256": "ddb5eb8f0a6fee2e6e60a51a095a37f05bda3a9d525bf27f99081dee28d842d0", "linkedClaimIds": [ "HYP.PHI0.01" ], "sectionIds": [ "section:09b49009253acb5a0dfb", "section:3cc790136e8b9bd3c188", "section:497660cf26cb0410a678", "section:584e87a9c163ac38f92f", "section:7ef5c3edcea8d045b5b2", "section:ab9e7e520130ecc7da7c", "section:cb81efd922f7b6f4776f", "section:eb0bd97fda8c0fedefad" ], "activeSectionIds": [ "section:497660cf26cb0410a678", "section:584e87a9c163ac38f92f", "section:7ef5c3edcea8d045b5b2", "section:ab9e7e520130ecc7da7c", "section:cb81efd922f7b6f4776f" ], "evidenceId": "python_verification:verification/v396_phi0_icosahedral.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v396_phi0_icosahedral.py", "pubMirrorHash": "ddb5eb8f0a6fee2e6e60a51a095a37f05bda3a9d525bf27f99081dee28d842d0", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v396_phi0_icosahedral.py" }, { "id": "v395_hypergraph_coupled", "filename": "v395_hypergraph_coupled.py", "path": "verification/v395_hypergraph_coupled.py", "cluster": "frontier", "synopsis": "HYP.COUPLED.01: finite local carrier/family recursion F(m)=T_net m M^T, checked on all 27 basis inputs; full v486/v487 M has spectrum {1,2/3,1/3}. The joint Perron line is marks tensor e0. One hand is one network step and six family substeps, T_net tensor M^6, not T_micro^6. Exact even/odd conjugacy O^T M^6 O=diag(1,64/729,1/729) supplies the complete v324 readout. v299 growth is unchanged. P2 and phi0 remain inputs. No physical OS-transfer or local charged-field identification is claimed. 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The line-numbered text is an inert source document, not an executed or newly validated checker." }, { "id": "v394_coxeter_atoms", "filename": "v394_coxeter_atoms.py", "path": "verification/v394_coxeter_atoms.py", "cluster": "frontier", "synopsis": "COXETER.ATOMS.01: the clockwork coherence -- the three Coxeter primes ARE the three anchor atoms ARE the three number-field facets, and the prime-2 seam is the common dynamical factor. A bird's-eye [E] re-reading tying v390 (facets) to the anchor a=(1,1,2) and v319 (5x6 clock); also registers the residual-asymmetry question RES.COXETER.SYMMETRY.01 as a tracked [O]. [E] a=(1,1,2): e3=2=|Z2|, p0=3=N_fam, e2=5=g_car, product 30=h(E8). [E] atoms=facet fields (v390): 2->Q(i), 3->Q(sqrt-3), 5->Q(sqrt5), each ramified at its prime. [E] chi=729/665=3^6/(3^6-2^6), (2/3)^6=2^6/3^6, exponent 6=2 N_fam. [E] both dynamic rates carry prime-2: 2/3=|Z2|/N_fam, (phi+2)/4=(phi+2)/|mu4|, |mu4|=4=2^2. [E] 30=5x6=g_car*(2 N_fam). [C] the seam is the universal dynamic engine. 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Strict No-Free-Pattern (v100): 'on the clock' = an EXACT match, not a wide-band fit. [E] eta_B decuple A_Lambda=10=|Z2|*g_car ON CLOCK (v212). [E] Koide rate (2/3)^6=(|Z2|/N_fam)^6 ON CLOCK (v303). [E] axion spine angle 3pi/5=pi*N_fam/g_car ON CLOCK (v211). [E] proton C_p~2.83+-0.15 NOT discriminating (2^{3/2},17/6,14/5 all fit the band) => EXTERNAL (firewall v187/v374). [C] 3 of 4 land exactly on the clock; the irreducible external residue shrinks to the proton QCD number C_p -- 'external physics' was overstated. [E] anti-numerology: refuses to assign C_p a clock value.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv397_external_clock_probe.py", "sourceSha256": "0dcca10be5fc28ca9f628e99c70520b68f7fcbcac696f3005847d9e123d93ea5", "linkedClaimIds": [ "FR.CLOCK.PROBE.01" ], "sectionIds": [ "section:ab9e7e520130ecc7da7c", "section:cb09371605fac20095ba", "section:fbc55d19f88e095d54eb" ], "activeSectionIds": [ "section:ab9e7e520130ecc7da7c", "section:cb09371605fac20095ba", "section:fbc55d19f88e095d54eb" ], "evidenceId": "python_verification:verification/v397_external_clock_probe.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v397_external_clock_probe.py", "pubMirrorHash": "0dcca10be5fc28ca9f628e99c70520b68f7fcbcac696f3005847d9e123d93ea5", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v397_external_clock_probe.py" }, { "id": "v403_facet_compositum", "filename": "v403_facet_compositum.py", "path": "verification/v403_facet_compositum.py", "cluster": "frontier", "synopsis": "ARITH.HULL.01: the three number-field facets (v390) COMPOSE to K=Q(i,sqrt-3,sqrt5), a degree-8=rank(E8) abelian field -- the arithmetic hull dual to the E8 lattice hull. [E] -1,-3,5 independent in Q*/(Q*)^2 so [K:Q]=2^3=8=rank E8=g_car+N_fam, Galois (Z/2)^3 order 8; 2^omega(h(E8))=2^3=8=rank E8 is E8-special (E7: h=18, omega=2, 2^2=4!=7). [E] exactly 7 quadratic subfields {-1,-3,5,3,-5,-15,15} = 4 imaginary (|mu4|, CM/dynamic) + 3 real (N_fam, RM/static). [E] ramified only at {2,3,5} = the atoms = primes of h(E8)=30. [C] K is the abelian (Z/2)^3 arithmetic hull dual to E8; the 7 subfields a candidate for the 7 E8 audit slices. 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[E] chi_E8^3=j (q-series). [E] SEAM tau=i (Q(i), order 4): cross-ratio 2 => j=1728 => chi_E8(i)=12 (E8 present, v214/v282). [E] FAMILY tau=omega (Q(sqrt-3), order 6): equianharmonic lambda (lambda^2-lambda+1=0) => j=0 => chi_E8(omega)=0 (E4 vanishes, v220/v267). [E] tau=i,tau=omega are the only elliptic points of PSL(2,Z) so the values are forced. [C] the seam/flavor rigidity duality: seam rigid where E8 present (chi=12), flavor the soft residual where E8 degenerates (chi=0); dual-keystone candidate. Core values j=1728/j=0 already mirrored (v214/v220/v267/v282).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv404_e8_char_cm_duality.py", "sourceSha256": "525a457c96ff275433d08a57398caa76e997940a0e586dfc1e14f61c34517d2d", "linkedClaimIds": [ "E8.CMDUAL.01" ], "sectionIds": [ "section:20ef03b5c6c62b042300", "section:2b8d2aba4baeb7a0c36b", "section:303925994b6f141b3a0e", "section:8e3e6d08d3c102a09298", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:20ef03b5c6c62b042300", "section:8e3e6d08d3c102a09298", "section:ab9e7e520130ecc7da7c", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v404_e8_char_cm_duality.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v404_e8_char_cm_duality.py", "pubMirrorHash": "525a457c96ff275433d08a57398caa76e997940a0e586dfc1e14f61c34517d2d", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v404_e8_char_cm_duality.py" }, { "id": "v405_seam_equiv_omega", "filename": "v405_seam_equiv_omega.py", "path": "verification/v405_seam_equiv_omega.py", "cluster": "frontier", "synopsis": "SEAM.EQUIV.02: the dual keystone at tau=omega -- the family/flavor sector as the order-3 Eisenstein/A2 face of E8, dual to the seam = (E8)_1 at tau=i (v404). A named contract, NOT a closure. [E] chi_E8(omega)=0 (E8 degenerates at the family CM point) vs chi_E8(i)=12. [E] A2 = the tau=omega Eisenstein lattice (Cartan det 3=N_fam, h=3=N_fam, mu6=mu3 x mu2). [E] R lives in E6 x A2: 248=78+8+2*27*3, ||R||_F^2=78=dim E6, det R=8=dim A2=rank E8. [E] delta_PMNS=4pi/3 = the tau=omega CM phase (arg zeta6=pi/3). [E] cusp weights {0,1/3,2/3}=order-3 deck=N_fam=det Q, Spec(Q+)=(1,2,3). [C] the family sector is the order-3 Eisenstein/A2 face; the two keystones sit at the only two elliptic points of PSL(2,Z). [O] residual = the canonical Z3 map (v140) + the v_geo-class scale (No-Unit v153).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv405_seam_equiv_omega.py", "sourceSha256": "10ba46ab87e6a1b634e83be76c7966ad8fe3fe6db1d5ce96ad8eee8cb9cd8635", "linkedClaimIds": [ "SEAM.EQUIV.02" ], "sectionIds": [ "section:20ef03b5c6c62b042300", "section:2b8d2aba4baeb7a0c36b", "section:303925994b6f141b3a0e", "section:51b5da5a67a36e5155ae", "section:5d8f619883df80c56b36", "section:697c671889813baf24f5", "section:6ff4670b89c8b83d4b0f", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:ef3ac63aa9e6dcddf33d", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:20ef03b5c6c62b042300", "section:5d8f619883df80c56b36", "section:697c671889813baf24f5", "section:ab9e7e520130ecc7da7c", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v405_seam_equiv_omega.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v405_seam_equiv_omega.py", "pubMirrorHash": "10ba46ab87e6a1b634e83be76c7966ad8fe3fe6db1d5ce96ad8eee8cb9cd8635", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v405_seam_equiv_omega.py" }, { "id": "v406_pmns_phase_origin", "filename": "v406_pmns_phase_origin.py", "path": "verification/v406_pmns_phase_origin.py", "cluster": "neutrinos", "synopsis": "FLAV.PMNS.CLOSE.01: the PMNS dynamics closed modulo the tau=omega keystone (v405) -- the CP-phase ORIGIN is the family CM point and the absolute scale is one v_geo-class unit, so PMNS has zero free flavor dials beyond v_geo. [E] the three angles (sin^2 th12=1/3-phi0/2, th23=1/2, sin^2 th13=phi0 e^{-5/6}; v9/v268) assemble to a unitary U_PMNS (v270). [C] CP-phase origin: delta_PMNS=4pi/3 is the tau=omega CM phase (v405), upgrading v270's [O] assembled input to a keystone consequence. [C] J_PMNS=-0.0297 derived. [E] absolute scale = one seesaw ratio = v_geo-class UV input (v272/v153), not a flavor gap. [C] net: PMNS = angles+delta[keystone]+J+scale[v_geo], zero free flavor dials. [O] residual = the seesaw operator realisation (M_R not a clean Mbar power, v272/v184; one-parameter carrier-normalised candidate v481) + the NO Sigma m_nu floor kill test.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv406_pmns_phase_origin.py", "sourceSha256": "b00e2152e510897b02c121999443bf186c757dcf7b395263d2c6f80712bd9350", "linkedClaimIds": [ "FLAV.PMNS.CLOSE.01" ], "sectionIds": [ "section:20ef03b5c6c62b042300", "section:2b8d2aba4baeb7a0c36b", "section:303925994b6f141b3a0e", "section:51b5da5a67a36e5155ae", "section:697c671889813baf24f5", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:20ef03b5c6c62b042300", "section:697c671889813baf24f5", "section:ab9e7e520130ecc7da7c", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v406_pmns_phase_origin.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v406_pmns_phase_origin.py", "pubMirrorHash": "b00e2152e510897b02c121999443bf186c757dcf7b395263d2c6f80712bd9350", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v406_pmns_phase_origin.py" }, { "id": "v407_dn_pairings_omega", "filename": "v407_dn_pairings_omega.py", "path": "verification/v407_dn_pairings_omega.py", "cluster": "uwall", "synopsis": "FLAV.SELECTOR.CLOSE.01: the R4' residue folds into the tau=omega keystone (v405) -- the three (d,n) selector pairings ARE the tau=omega family-slice atoms. [E] the frame (1,a,sigma) is a Z^3 basis det=11=||Pl(K)||_1, n=(5,-9,6) the unique covector with n.1=2, n.a=8, n.sigma=121=11^2 -> (d,n)=>R columnwise (v136/v139). [E] n.a=8=rank E8=dim A2=det R = the A2 (tau=omega) block dimension reading R in E6 x A2. [E] the pairings {2,8,121}={|Z2|, dim A2=det R, ||Pl(K)||_1^2} = the tau=omega family-slice atoms. [E] the square selects the point (sigma-pairing 11(11+t), square only at t=0). [C] deriving (d,n) folds into SEAM.EQUIV.02 (d anchor-derived v139, pairings = slice atoms). [O] the lone flagged residue why 11=||Pl(K)||_1.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv407_dn_pairings_omega.py", "sourceSha256": "64696c1c123906cb34f1aebe276dd00f6cb91dd20dd2e0becb99296bddf07eb0", "linkedClaimIds": [ "FLAV.SELECTOR.CLOSE.01" ], "sectionIds": [ "section:20ef03b5c6c62b042300", "section:2b8d2aba4baeb7a0c36b", "section:303925994b6f141b3a0e", "section:3c0ef7a887cebe028f40", "section:5d8f619883df80c56b36", "section:6ff4670b89c8b83d4b0f", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:cb81efd922f7b6f4776f", "section:e77e5218c82783443690", "section:ef3ac63aa9e6dcddf33d", "section:fb4cf64c8cbaeb3f6d74", "section:fe85126d1b3e41ef8954" ], "activeSectionIds": [ "section:20ef03b5c6c62b042300", "section:3c0ef7a887cebe028f40", "section:5d8f619883df80c56b36", "section:ab9e7e520130ecc7da7c", "section:cb81efd922f7b6f4776f", "section:e77e5218c82783443690", "section:fb4cf64c8cbaeb3f6d74", "section:fe85126d1b3e41ef8954" ], "evidenceId": "python_verification:verification/v407_dn_pairings_omega.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v407_dn_pairings_omega.py", "pubMirrorHash": "64696c1c123906cb34f1aebe276dd00f6cb91dd20dd2e0becb99296bddf07eb0", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v407_dn_pairings_omega.py" }, { "id": "v408_phi0_puncture_heatkernel", "filename": "v408_phi0_puncture_heatkernel.py", "path": "verification/v408_phi0_puncture_heatkernel.py", "cluster": "frontier", "synopsis": "HYP.PHI0.PUNCTURE.01: name the phi0 puncture term dtop = 48 c3^4 as the order-4 local boundary heat-kernel (Seeley-DeWitt) contact term of the mu4 puncture divisor -- the analytic complement of the icosahedral tree term (v396, HYP.PHI0.01). [E] THE SPLIT IS EXACT: phi0 = phibase + dtop = 1/(6 pi) + 48 c3^4 (v396/ARCH.QUAD.01), a tree term plus a fourth-order boundary correction. [E] PUNCTURE COUNT = Omega_adm = N_fam dim S+ = 48, order = |mu4| = 4: dtop = Omega_adm c3^|mu4|. [E] CLOSED FORM dtop = 48 c3^4 = 3/(256 pi^4); c3 = 1/(|Z2| 4 pi) Gauss-Bonnet (v216/v342) so c3^4 is a fourth-order boundary heat-kernel power (cf. v391). [E] HONEST NEGATIVE: dtop not a rational hypergraph fraction (dtop/phibase < 1%). [O] THE TARGET: prove Omega_adm c3^4 IS the order-4 boundary Seeley-DeWitt contact term of the mu4 puncture summed over the Omega_adm admissible states. [C] two engines, two terms; a FACE of the seam boundary analysis (the c3 datum), not a new gate. No new number.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv408_phi0_puncture_heatkernel.py", "sourceSha256": "db1e58d685fa8b53d6e0ca777b77e8982f87c3514a2ba66e16158ad56945e933", "linkedClaimIds": [ "HYP.PHI0.PUNCTURE.01" ], "sectionIds": [ "section:09b49009253acb5a0dfb", "section:3cc790136e8b9bd3c188", "section:584e87a9c163ac38f92f", "section:ab9e7e520130ecc7da7c", "section:cb81efd922f7b6f4776f", "section:db9b59159ab5489cccfa", "section:e77e5218c82783443690", "section:eb0bd97fda8c0fedefad", "section:fe85126d1b3e41ef8954" ], "activeSectionIds": [ "section:584e87a9c163ac38f92f", "section:ab9e7e520130ecc7da7c", "section:cb81efd922f7b6f4776f", "section:db9b59159ab5489cccfa", "section:e77e5218c82783443690", "section:fe85126d1b3e41ef8954" ], "evidenceId": "python_verification:verification/v408_phi0_puncture_heatkernel.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v408_phi0_puncture_heatkernel.py", "pubMirrorHash": "db1e58d685fa8b53d6e0ca777b77e8982f87c3514a2ba66e16158ad56945e933", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v408_phi0_puncture_heatkernel.py" }, { "id": "v409_coxeter_prime2_lemma", "filename": "v409_coxeter_prime2_lemma.py", "path": "verification/v409_coxeter_prime2_lemma.py", "cluster": "frontier", "synopsis": "RES.COXETER.SYMMETRY.01 closed as a STRUCTURAL LEMMA: prime-2 is NECESSARY but NOT autonomous -- no prime-2-only attractor exists (resolves the v394/COXETER.ATOMS.01 open question's falsifiable corollary). [E] SHEET INVOLUTION: sigma=diag(1,-1,-1), sigma^2=I, spectrum {+1,-1} (parity). [E] SHEET PROJECTOR P=(I+sigma)/2=diag(1,0,0), P^2=P, spectrum {0,1} (projection). [E] NO CONTRACTION RATE: none of {-1,0,1} lies in (0,1), whereas the genuine rates 2/3 and (1/3)^6 do -- prime-2 alone gives parity/projection, never a nonzero rate. [E] FACTOR NOT RATE: 2/3=|Z2|/N_fam needs prime-3, (phi+2)/4=(phi+2)/|mu4| with |mu4|=2^2 needs the golden phi (prime-5). [E] 30=g_car(2 N_fam), carrier static, 2*3 dynamic. [C] prime-2 is the universal dynamical parity factor, necessary in every sheet-paired transport but not an autonomous attractor; dynamics begins after coupling to family-3 or carrier-5 (mu4=2^2 the Galois bridge). No new number.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv409_coxeter_prime2_lemma.py", "sourceSha256": "e0779b170d5e9085ff26ed0dd55a3b549d96c59b5ccc237753b46293d4639d5b", "linkedClaimIds": [ "RES.COXETER.SYMMETRY.01", "FORM.COXETER.PRIME2.01" ], "sectionIds": [ "section:09b49009253acb5a0dfb", "section:2b8d2aba4baeb7a0c36b", "section:303925994b6f141b3a0e", "section:36246a833c23944e824a", "section:3cc790136e8b9bd3c188", "section:584e87a9c163ac38f92f", "section:7ee581db787f8ddbcb4a", "section:8d1e955857da6655fadd", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:c519f45910c30ff3c0ae", "section:cb81efd922f7b6f4776f", "section:eb0bd97fda8c0fedefad", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:36246a833c23944e824a", "section:584e87a9c163ac38f92f", "section:8d1e955857da6655fadd", "section:ab9e7e520130ecc7da7c", "section:cb81efd922f7b6f4776f", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v409_coxeter_prime2_lemma.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v409_coxeter_prime2_lemma.py", "pubMirrorHash": "e0779b170d5e9085ff26ed0dd55a3b549d96c59b5ccc237753b46293d4639d5b", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v409_coxeter_prime2_lemma.py" }, { "id": "v410_sheet_generator_binary", "filename": "v410_sheet_generator_binary.py", "path": "verification/v410_sheet_generator_binary.py", "cluster": "registry", "synopsis": "The sheet generator V = Q diag(0,1,1) (the rank-2 sheet axis of the centered cross, v95/v218) is a binary internal compiler: V^n = ((0,2^(n-1),0),(0,2^n,0),(0,2^(n+1)-2,1)) (induction F(n)V=F(n+1)), so V^n.1 = (2^(n-1),2^n,2^(n+1)-1) = (1,2,3),(2,4,7),(4,8,15),(8,16,31); the bilinears 1.V^n.1=7*2^(n-1)-1, 1.V^n.a=7*2^(n-1), a.V^n.a=11*2^(n-1), a.V^n.1=11*2^(n-1)-2 give (6,7,9,11) at n=1 and 13=Delta_Q, 27=1.R.a, 55, 56=dim 56_E7; the binary spine is FORCED by Spec(V)={0,1,2}, the carrier (rank E8=8, dim S+=16, 248/8=31) and theta (sigma3(2)=9=a.V.1, sigma3(3)=28=1.V^3.a=det(I+R), sigma3(5)=126) readings audit-typed.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv410_sheet_generator_binary.py", "sourceSha256": "1bca4281199a0906ff5212711993cf99a54a6998435611c67a4e215b0804c905", "linkedClaimIds": [ "SHEET.GEN.BINARY.01" ], "sectionIds": [ "section:2678ed3ba0ed508e2d8e", "section:2ff762f6d6932ac2b2c5", "section:4061f274c55499fb2ed1", "section:848c49f799255f4cda92", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:ac418863c3194ed2d0cf", "section:bb2a02a767e560376342", "section:c4cf080b9ae6f25f7a71" ], "activeSectionIds": [ "section:2ff762f6d6932ac2b2c5", "section:4061f274c55499fb2ed1", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:ac418863c3194ed2d0cf", "section:bb2a02a767e560376342" ], "evidenceId": "python_verification:verification/v410_sheet_generator_binary.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v410_sheet_generator_binary.py", "pubMirrorHash": "1bca4281199a0906ff5212711993cf99a54a6998435611c67a4e215b0804c905", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v410_sheet_generator_binary.py" }, { "id": "v411_ud_ratio_vpower", "filename": "v411_ud_ratio_vpower.py", "path": "verification/v411_ud_ratio_vpower.py", "cluster": "registry", "synopsis": "The quark u/d ratio is a pure V-power readout: the established c_u/c_d = g_car ||Pl(K)||_1/(N_fam^2 Delta_Q) = 55/117 (v94) re-expresses EXACTLY via the sheet generator (v410) as c_u/c_d = (1.V^4.1)/((a.V.1)(1.V^2.1)) = 55/(9*13), with 55=1.V^4.1, 9=a.V.1=N_fam^2, 13=1.V^2.1=Delta_Q; the same number as 5*11/(9*13), so the V-power numerator repackages g_car*11=55; an exact RE-ENCODING, the value and u/d identification stay [C] (U_wall readout rigidity).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv411_ud_ratio_vpower.py", "sourceSha256": "640df91647fd95ff6ebe80c7e6f521a7803c4c9e1ab5d96db6534ae151eb50ca", "linkedClaimIds": [ "FLAV.UD.VPOWER.01" ], "sectionIds": [ "section:2678ed3ba0ed508e2d8e", "section:2ff762f6d6932ac2b2c5", "section:4061f274c55499fb2ed1", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c" ], "activeSectionIds": [ "section:2ff762f6d6932ac2b2c5", "section:4061f274c55499fb2ed1", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v411_ud_ratio_vpower.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v411_ud_ratio_vpower.py", "pubMirrorHash": "640df91647fd95ff6ebe80c7e6f521a7803c4c9e1ab5d96db6534ae151eb50ca", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v411_ud_ratio_vpower.py" }, { "id": "v412_sheet_source_corner_J", "filename": "v412_sheet_source_corner_J.py", "path": "verification/v412_sheet_source_corner_J.py", "cluster": "registry", "synopsis": "The sheet source corner J: the determinant surface has two s-independent iso-volume walls (v135) t=-1 (det=4=|mu4|, carries K) and t=-2 (det=2=|Z2|); the operator on the Z2 wall, J=M(1,-2)=C-2V=((4,1,0),(4,1,2),(5,1,1)), was unnamed and completes the sheet axis J,K,C,F=M(1,-2..1). chi_J=lambda^3-6lambda^2+3lambda-2 gives (tr,e2,det)=(6,3,2)=(|R^+(A3)|,N_fam,|Z2|); a.J.a=30=h(E8), det(I+J)=12=dim g_SM=chi_E8(i), det(2I+J)=40=|R(D5)| (Lie readings audit-typed like the G2/F4 shadows of v95/v218).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv412_sheet_source_corner_J.py", "sourceSha256": "6dc64fada7aeae2c3ad4b555f43dd41d9bb3758e5df08daaea3370e8658a434e", "linkedClaimIds": [ "DIAMOND.SHEET.SOURCE.J.01" ], "sectionIds": [ "section:2678ed3ba0ed508e2d8e", "section:2ff762f6d6932ac2b2c5", "section:49689ab702d7c648da00", "section:6696018adf21f42f20da", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:bb2a02a767e560376342" ], "activeSectionIds": [ "section:2ff762f6d6932ac2b2c5", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:bb2a02a767e560376342" ], "evidenceId": "python_verification:verification/v412_sheet_source_corner_J.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v412_sheet_source_corner_J.py", "pubMirrorHash": "6dc64fada7aeae2c3ad4b555f43dd41d9bb3758e5df08daaea3370e8658a434e", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v412_sheet_source_corner_J.py" }, { "id": "v413_sheet_characteristic_calculus", "filename": "v413_sheet_characteristic_calculus.py", "path": "verification/v413_sheet_characteristic_calculus.py", "cluster": "registry", "synopsis": "The sheet axis is a discrete characteristic-difference calculator: on M_t=C+tV (v95/v218) the elementary-symmetric coefficients encode atoms as DIFFERENCE ORDERS -- e1(t)=3t+12, e2(t)=2t^2+15t+25, e3(t)=det M_t=4t^2+14t+14 give Delta e1=3=N_fam, Delta^2 e2=4=|mu4|, Delta^2 e3=8=rank E8 (the e3 curvature cross-cited to v218/v224; the full (e1,e2,e3) ladder is new); the anchor energy a.M_t.a=52+11t (step 11=a.V.a, v410) reads 30->41->52->63=(h(E8),10 b1,dim F4,7 N_fam^2); four-row axis J,K,C,F (tr,e2,det)/a.M.a = (6,3,2)/30,(9,12,4)/41,(12,25,14)/52,(15,42,32)/63.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv413_sheet_characteristic_calculus.py", "sourceSha256": "01d451781ba19dcd0064dc85aefc2eda30fdf441d85985d2a9731902a7dc8555", "linkedClaimIds": [ "DIAMOND.SHEET.CALCULUS.01" ], "sectionIds": [ "section:2678ed3ba0ed508e2d8e", "section:2ff762f6d6932ac2b2c5", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c" ], "activeSectionIds": [ "section:2ff762f6d6932ac2b2c5", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v413_sheet_characteristic_calculus.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v413_sheet_characteristic_calculus.py", "pubMirrorHash": "01d451781ba19dcd0064dc85aefc2eda30fdf441d85985d2a9731902a7dc8555", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v413_sheet_characteristic_calculus.py" }, { "id": "v414_center_resolvent_portal", "filename": "v414_center_resolvent_portal.py", "path": "verification/v414_center_resolvent_portal.py", "cluster": "registry", "synopsis": "The center C is a resolvent portal G2 -> F4 -> E8: the center C=M(1,0) (v95) is the t=0 evaluation of V; tr C=12=dim g_SM=chi_E8(i), det C=14=dim G2, sum C=31=2^g_car-1=248/8; the shifted determinants climb the exceptional ladder det(C)=14=dim G2, det(I+C)=52=dim F4, det(2I+C)=120=|R^+(E8)| -- the shell ladder G2->F4->E8^+ as det(C+kI), k=0,1,2 (the resolvent ladder is the new content; reading audit-typed).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv414_center_resolvent_portal.py", "sourceSha256": "5b2779034bd729184a2e40ab5304c1c473dd9c429300d2a36f584753453a6c70", "linkedClaimIds": [ "DIAMOND.CENTER.RESOLVENT.01" ], "sectionIds": [ "section:2678ed3ba0ed508e2d8e", "section:2ff762f6d6932ac2b2c5", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:bc972235a8e75d6dcfea" ], "activeSectionIds": [ "section:2ff762f6d6932ac2b2c5", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:bc972235a8e75d6dcfea" ], "evidenceId": "python_verification:verification/v414_center_resolvent_portal.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v414_center_resolvent_portal.py", "pubMirrorHash": "5b2779034bd729184a2e40ab5304c1c473dd9c429300d2a36f584753453a6c70", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v414_center_resolvent_portal.py" }, { "id": "v415_gaussian_operator", "filename": "v415_gaussian_operator.py", "path": "verification/v415_gaussian_operator.py", "cluster": "flavor", "synopsis": "The square CM-norm dictionary is operator-realised and the mu4 deck is intrinsic: the Gaussian arithmetic of v222/v230 lifted from numbers to OPERATORS via J=[U,V]/3, the complex structure born from the commutator of the binary V and ternary U compilers (v410/v95). J=((-1,1,0),(-2,1,0),(-3,1,0)) is integer, Spec(J)={i,-i,0}, J^2=-I on the rank-2 image, J^3+J=0 (a mu4 quarter-turn); 3I+2J has spectrum {3+2i,3-2i,3} and 5I+4J has {5+4i,5-4i,5}, so the Gaussian integers 3+2i (norm 13=Delta_Q) and 5+4i (norm 41=10b1) are LITERAL operator eigenvalues; (3I+2J)(3I-2J) has Spec {13,13,9} and (5I+4J)(5I-4J) has Spec {41,41,25} (kernel slot = real part^2: 9=N_fam^2, 25=g_car^2); the intrinsic deck D=-I+J-J^2 is order 4 (Spec {i,-1,-i}, chi=(x+1)(x^2+1)) with chi2 line ker[U,V]=(0,0,1)=a-1; the geometric-deck identification sharpens (not closes) the v140 Z3 residue.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv415_gaussian_operator.py", "sourceSha256": "fd097db8e95c6a56dbc9f5173991c134220b58880b8aec29ae808ee45a6d83a0", "linkedClaimIds": [ "DIAMOND.GAUSS.01" ], "sectionIds": [ "section:2678ed3ba0ed508e2d8e", "section:649c3b4e330a4dfc876d", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:b3159de77fcabb12cc0c", "section:b76309fbfced7aff0c43", "section:bb2a02a767e560376342" ], "activeSectionIds": [ "section:649c3b4e330a4dfc876d", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:b3159de77fcabb12cc0c", "section:bb2a02a767e560376342" ], "evidenceId": "python_verification:verification/v415_gaussian_operator.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v415_gaussian_operator.py", "pubMirrorHash": "fd097db8e95c6a56dbc9f5173991c134220b58880b8aec29ae808ee45a6d83a0", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v415_gaussian_operator.py" }, { "id": "v416_atom_trichotomy", "filename": "v416_atom_trichotomy.py", "path": "verification/v416_atom_trichotomy.py", "cluster": "core", "synopsis": "The atom trichotomy: {2,3,5} are ramified/inert/split in the two exceptional CM rings, and each atom is the unique ramified prime of one quadratic facet of K=Q(i,sqrt-3,sqrt5) (v403). Z[i] (square/seam, tau=i): 2=|Z2| ramifies (2=-i(1+i)^2), 3=N_fam inert (norm 9=N_fam^2), 5=g_car splits ((2+i)(2-i)) -- the carrier rank factors on the seam; Z[omega] (hex/flavor, tau=omega): 3=N_fam ramifies (N(1-omega)=3), 2 inert (norm 4), 5 inert (norm 25=g_car^2); the ramified prime of each ring IS its atom (Z[i] at 2 = sheet/seam, Z[omega] at 3 = family/flavor); the three facets Q(i)/Q(sqrt-3)/Q(sqrt5) (disc -4,-3,5) ramify over one atom each, product 2*3*5=30=h(E8); 2 imaginary (CM/dynamic) + 1 real (RM/static).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv416_atom_trichotomy.py", "sourceSha256": "d46e4f092c6e5953ea10f023a718d54ebf1c11ba19830f8ad10e9bb325fa81b3", "linkedClaimIds": [ "ARITH.TRICHOTOMY.01" ], "sectionIds": [ "section:09b49009253acb5a0dfb", "section:3cc790136e8b9bd3c188", "section:4061f274c55499fb2ed1", "section:584e87a9c163ac38f92f", "section:ab9e7e520130ecc7da7c", "section:bb2a02a767e560376342", "section:eb0bd97fda8c0fedefad" ], "activeSectionIds": [ "section:4061f274c55499fb2ed1", "section:584e87a9c163ac38f92f", "section:ab9e7e520130ecc7da7c", "section:bb2a02a767e560376342" ], "evidenceId": "python_verification:verification/v416_atom_trichotomy.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v416_atom_trichotomy.py", "pubMirrorHash": "d46e4f092c6e5953ea10f023a718d54ebf1c11ba19830f8ad10e9bb325fa81b3", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v416_atom_trichotomy.py" }, { "id": "v417_eisenstein_cp_operator", "filename": "v417_eisenstein_cp_operator.py", "path": "verification/v417_eisenstein_cp_operator.py", "cluster": "flavor", "synopsis": "The Eisenstein/CP operator (hex dual of v415): the family rotation P=(1 2 3) and the CP clock W=-P^2 put the tau=omega flavor side on operators, unified with the seam into ONE order-30 clock. P^3=I, P^2+P+I=ONES (Eisenstein omega^2+omega+1=0 on the plane perp to (1,1,1)); (3I+2P)(3I+2P^2)=7I+6 ONES with Spec {7,7,25} -- 7=N_omega(3+2omega)=scalaron on the omega-plane, 25=g_car^2 on (1,1,1) -- the dual of v415's {13,13,9} (NEG: (5I+4P)(5I+4P^2)->{21,21,81}, N_omega(5,4)=21!=41); the CP clock W=-P^2 (order 6, =rho v233) has W^2=P, W^3=-I, Spec {-1,zeta6,zeta6^-1}, so delta_CKM=arg(zeta6)=pi/3 and delta_PMNS=arg(zeta6^4)=4pi/3 (W^4=P^2); all flavor clocks are powers of zeta30 (zeta30^15=-1, ^10=omega, ^6=zeta5, ^5=zeta6 = orders 2,3,5,6) while the seam mu4=i is the Galois side (Z/30)^x of order phi(30)=8=rank E8; the carrier mu5 has no clean 3x3 operator (golden phi an output-side trace, v313/v349).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv417_eisenstein_cp_operator.py", "sourceSha256": "c5f1fe26b9e6fd30bf2ad45354de6819a184c4a86b491f19ab21cb53b21c2b7e", "linkedClaimIds": [ "DIAMOND.EISEN.01" ], "sectionIds": [ "section:2678ed3ba0ed508e2d8e", "section:4061f274c55499fb2ed1", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:b3159de77fcabb12cc0c" ], "activeSectionIds": [ "section:4061f274c55499fb2ed1", "section:9bab697ba19c86420aea", "section:ab9e7e520130ecc7da7c", "section:b3159de77fcabb12cc0c" ], "evidenceId": "python_verification:verification/v417_eisenstein_cp_operator.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v417_eisenstein_cp_operator.py", "pubMirrorHash": "c5f1fe26b9e6fd30bf2ad45354de6819a184c4a86b491f19ab21cb53b21c2b7e", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v417_eisenstein_cp_operator.py" }, { "id": "v418_cyclotomic_norm_triple", "filename": "v418_cyclotomic_norm_triple.py", "path": "verification/v418_cyclotomic_norm_triple.py", "cluster": "core", "synopsis": "The cyclotomic norm triple: the carrier split (3,2) read in the three atom-rings gives (7,13,55)=(scalaron, Delta_Q, quark numerator), and the missing carrier-5 clock of v417 is found as the 4x4 Phi5-companion C5. C5 has chi=x^4+x^3+x^2+x+1, C5^5=I, tr=-1, and the golden ratio is its real-part data (2cos(72)=1/phi, 2cos(144)=-phi; output-side, v313/v349; dim 4, not 3 -- refines v417's gap); N_Z[zeta5](3+2 zeta5)=det(3I+2 C5)=55=5*11=g_car*||Pl(K)||_1=quark numerator (v410/v411); the triple det(3I+2 Comp(Phi_n))=(7,13,55) for n=3,4,5 over Z[omega],Z[i],Z[zeta5] (atoms 3,2,5, v416) is one (3,2)-generated family; NEG control: the anchor (5,4)->(21,41,461), 21=N_omega(5,4) and 41=10b1 named (v222) but the carrier ring 461 prime/un-named, so the carrier ring separates (3,2)->55 from (5,4)->461; HONEST: (3,2) is FORCED (v14) not unique, the clean splits are {(2,1)->(3,5,11),(3,2)->(7,13,55)}; the sharper reading: only (3,2) spans three physics sectors (gravity/flavor/masses), the unique cross-sector seed, while (2,1) is all-core.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv418_cyclotomic_norm_triple.py", "sourceSha256": "88b95b445bfce64f7d20a6bf9c84ed1c8de56f0367ced908cc163e01d62b0ba2", "linkedClaimIds": [ "ARITH.NORMTRIPLE.01" ], "sectionIds": [ "section:09b49009253acb5a0dfb", "section:36246a833c23944e824a", "section:3cc790136e8b9bd3c188", "section:4061f274c55499fb2ed1", "section:4e9f1abfa575088fe498", "section:584e87a9c163ac38f92f", "section:5b3637090ad83e509233", "section:5e1509353325b787484d", "section:ab9e7e520130ecc7da7c", "section:eb0bd97fda8c0fedefad" ], "activeSectionIds": [ "section:36246a833c23944e824a", "section:4061f274c55499fb2ed1", "section:584e87a9c163ac38f92f", "section:5b3637090ad83e509233", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v418_cyclotomic_norm_triple.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v418_cyclotomic_norm_triple.py", "pubMirrorHash": "88b95b445bfce64f7d20a6bf9c84ed1c8de56f0367ced908cc163e01d62b0ba2", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v418_cyclotomic_norm_triple.py" }, { "id": "v419_seam_galois_carrier", "filename": "v419_seam_galois_carrier.py", "path": "verification/v419_seam_galois_carrier.py", "cluster": "core", "synopsis": "The seam mu4 IS the carrier's Galois group: a positive resolution of the v409/RES.COXETER.SYMMETRY.01 cyclic/Galois asymmetry. 30=2*3*5 is squarefree so Z/30 has no order-4 element -- the seam mu4 (order 4) cannot be a cyclic hand and is forced onto the Galois side; (Z/30)^x = (Z/2)^x x (Z/3)^x x (Z/5)^x = mu4 x Z2 (order phi(30)=8=rank E8), where the mu4 (Z/4) factor IS (Z/5)^x (carrier 5) and the Z2 IS (Z/3)^x (family/CP); so the seam mu4 = Gal(Q(zeta5)) = (Z/5)^x, the Frobenius zeta5->zeta5^2, realised on the carrier clock C5 (v418) by the explicit order-4 operator G with G C5 G^-1 = C5^2, G^4=I, G^2 C5 G^-2 = C5^-1; resolves v409 (the 2^2=4 is the order of (Z/5)^x; 'no contraction rate' because the seam is an automorphism, not a hand); Q(zeta30) carries both E8 invariants (cyclic h=30, Galois rank=8).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv419_seam_galois_carrier.py", "sourceSha256": "cc6152ad7ea68c67725020e386e49eec32810ab25bb483c76bae99964399c2fd", "linkedClaimIds": [ "SEAM.GALOIS.01" ], "sectionIds": [ "section:09b49009253acb5a0dfb", "section:2b8d2aba4baeb7a0c36b", "section:303925994b6f141b3a0e", "section:36246a833c23944e824a", "section:3cc790136e8b9bd3c188", "section:4defd98603f63d26dd3f", "section:584e87a9c163ac38f92f", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:eb0bd97fda8c0fedefad", "section:fb4cf64c8cbaeb3f6d74" ], "activeSectionIds": [ "section:36246a833c23944e824a", "section:4defd98603f63d26dd3f", "section:584e87a9c163ac38f92f", "section:ab9e7e520130ecc7da7c", "section:fb4cf64c8cbaeb3f6d74" ], "evidenceId": "python_verification:verification/v419_seam_galois_carrier.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v419_seam_galois_carrier.py", "pubMirrorHash": "cc6152ad7ea68c67725020e386e49eec32810ab25bb483c76bae99964399c2fd", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v419_seam_galois_carrier.py" }, { "id": "v420_fpole_qed_running", "filename": "v420_fpole_qed_running.py", "path": "verification/v420_fpole_qed_running.py", "cluster": "frontier", "synopsis": "F_pole external: the Koide source->pole transfer is a ONE-LOOP ELECTROMAGNETIC effect, not an algebraic step -- the honest 'do the external physics' follow-up to v93 and the clock No-Go. Koide Q(m)=sum m/(sum sqrt m)^2 is rescaling-invariant (Q(c*m)=Q(m)) so flavor-UNIVERSAL running leaves it fixed -- the source->pole shift is purely flavor-SPLIT; the tree->pole gap 2/3-Q_src=0.002203 is one-loop-EM-sized (= phi0/24 to 0.6%, = alpha/pi to ~5%), and the PDG pole sits AT 2/3 (the IR attractor); a 1-loop QED per-lepton-log pole<->MSbar estimate shifts Koide by EM-loop order toward 2/3 (the v82 IR-attractor direction); the EXACT flow time t~2.84 (v93) is scheme/scale-dependent external QED, NOT derived, only sized. F_pole stays [C], firewalled (v187): the lens forces the RATE (2/3)^6 (v327/v82), this external EM physics supplies the flow. Numerical (mpmath), Python-only.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv420_fpole_qed_running.py", "sourceSha256": "c9cc784c6a27030600d512463df8bb6d76ae1c8b8af16d2d9e94cfb605c730a6", "linkedClaimIds": [ "FR.POLE.QED.01" ], "sectionIds": [ "section:8ac4310a6a4cf6c449f1", "section:ab9e7e520130ecc7da7c", "section:eb0ad9c39f3387e3dcf3" ], "activeSectionIds": [ "section:8ac4310a6a4cf6c449f1", "section:ab9e7e520130ecc7da7c", "section:eb0ad9c39f3387e3dcf3" ], "evidenceId": "python_verification:verification/v420_fpole_qed_running.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v420_fpole_qed_running.py", "pubMirrorHash": "c9cc784c6a27030600d512463df8bb6d76ae1c8b8af16d2d9e94cfb605c730a6", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v420_fpole_qed_running.py" }, { "id": "v422_galois_net_bridge", "filename": "v422_galois_net_bridge.py", "path": "verification/v422_galois_net_bridge.py", "cluster": "core", "synopsis": "The Galois<->Net bridge: the seam mu4 = Gal(Q(zeta5)) is the SAME cyclic Z/4 as the (E8)_1 simple-current glue -- not a mere order-4 coincidence -- connecting the Galois gearbox of v419 to G_net/SEAM.EQUIV.01. disc(A3)=disc(D5)=Z/4 (one SNF invariant factor 4 = cyclic, det 4); D_n disc is Z/4 for n ODD, Z2xZ2 for n EVEN, so the carrier D5 (rank 5=g_car, odd) is cyclic while the control D8 (rank 8, even) is Klein; Gal(Q(zeta5))=(Z/5)^x=<2> is cyclic order 4 (only the carrier prime 5 among the atoms gives order 4); in disc(D5(+)A3)=Z4xZ4 (16=dim S+) the simple current (1,1) is order 4 (cyclic) with Lagrangian quotient 16/4^2=1 => (E8)_1 (1 primary, holomorphic). NEG control: the Klein Z2xZ2 / order-2 halfway <(2,2)> gives 16/2^2=4=|disc(D8)|=SO(16) (det 4), NOT E8 (det 1) -- cyclic Z/4 -> E8, Klein -> D8, so the carrier-Galois matches E8 not D8. The bridge: one cyclic Z/4 threads the seam deck mu4 (v419), Gal(Q(zeta5)) (v419) and the (E8)_1 glue (v1/v89/v154); cyclicity forced by 5, Klein excluded. This is the four-fold mu4 identity (deck/divisor=Galois=discriminant=simple-current); per v428 a COMPRESSION (one object read four ways, a unification that makes the carrier less axiomatic), NOT four independent witnesses that multiply.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv422_galois_net_bridge.py", "sourceSha256": "601271180c0bc8c46464714c5f0fb5c6d5c09b1f9756d40a94797727ae49cedd", "linkedClaimIds": [ "SEAM.GALOIS.NET.01" ], "sectionIds": [ "section:04b7cfb5801c917940c7", "section:09b49009253acb5a0dfb", "section:3cc790136e8b9bd3c188", "section:4defd98603f63d26dd3f", "section:584e87a9c163ac38f92f", "section:a9b1f3ad9bb703cf14c6", "section:ab9e7e520130ecc7da7c", "section:eb0bd97fda8c0fedefad" ], "activeSectionIds": [ "section:04b7cfb5801c917940c7", "section:4defd98603f63d26dd3f", "section:584e87a9c163ac38f92f", "section:a9b1f3ad9bb703cf14c6", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v422_galois_net_bridge.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v422_galois_net_bridge.py", "pubMirrorHash": "601271180c0bc8c46464714c5f0fb5c6d5c09b1f9756d40a94797727ae49cedd", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v422_galois_net_bridge.py" }, { "id": "v423_no_ambient_dependency", "filename": "v423_no_ambient_dependency.py", "path": "verification/v423_no_ambient_dependency.py", "cluster": "frontier", "synopsis": "The No-Ambient-Dependency certificate: no frozen TFPT readout is COMPUTED from the ambient QG measure QG.AMB.01 -- sharpening the v369/v384 prose redundancy into a machine-checked DAG+script fact, told honestly. Gap-decoupling margin Delta_eff = 6 ln(3/2) - 31/(4 pi^2) ~ 1.648 > 0 (31=2^g_car-1), susceptibility chi=729/665 finite (neg control gap->0 => chi diverges). QG.AMB.01 is a certification SINK: every claim that lists it as a dependency is a gravity-gate/QG row, none a frozen prediction; and it is not a value source -- it has no producing script while every frozen prediction is computed by a compiler script (alpha<-v3, theta12<-v9, theta13<-v268, cosmology<-v7), none an ambient-measure script. The one transitive link is architectural: only theta13 references QG.AMB.01, via the 4D-QFT contract spine (PS.DIRAC->CONTRACT.QFT4D->QG.G2->GATE.METRIC), a coherence edge not a numerical input; alpha/theta12/cosmology have no route at all. So QG.AMB.01 is gap-decoupled certification (v369 as a DAG/script fact); honestly, this does not prove SEAM.EQUIV.01 -- the readouts depend on the seam being (E8)_1; QG.AMB.01 specifically is dead.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv423_no_ambient_dependency.py", "sourceSha256": "182b7aa7405e73924b13d1381160ea36536c4c81d025992f02c0b231e6ffa55b", "linkedClaimIds": [ "QGAMB.NODEP.01" ], "sectionIds": [ "section:2ee299d2f97d03685885", "section:ab9e7e520130ecc7da7c", "section:f5274c8105ff62e99dcd" ], "activeSectionIds": [ "section:2ee299d2f97d03685885", "section:ab9e7e520130ecc7da7c", "section:f5274c8105ff62e99dcd" ], "evidenceId": "python_verification:verification/v423_no_ambient_dependency.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v423_no_ambient_dependency.py", "pubMirrorHash": "182b7aa7405e73924b13d1381160ea36536c4c81d025992f02c0b231e6ffa55b", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v423_no_ambient_dependency.py" }, { "id": "v424_seam_lto_rp_reduction", "filename": "v424_seam_lto_rp_reduction.py", "path": "verification/v424_seam_lto_rp_reduction.py", "cluster": "frontier", "synopsis": "The (LTO-RP) reduction of the keystone: an honest MMST-style reduction of SEAM.EQUIV.01's one open lemma -- the raw collar's intrinsic Bisognano-Wichmann property (the v308/v309 residual) -- to the cited commuting-projector theorem of Naaijkens-Penneys-Wallick (arXiv:2605.10693), with the central mapping CORRECTED. The mu4 clock is a modular SYMMETRY ([rho,K]=0, v309/v199), not the flow -- 'sigma^psi=rho' is type-wrong (one-parameter group vs finite order-4 element). NPW26's (LTO-RP) means u_Theta=J (reflection = modular conjugation) = the intrinsic BW condition theta K theta=-K, DISTINCT from omega o rho=omega: a positive character-block-diagonal K satisfies [rho,K]=0 but never theta K theta=-K, so clock-invariance does not imply (LTO-RP). Make-or-break: NPW26 prove (LTO-RP) for topologically-ordered models (Toric Code |det K|=4 via a trace; Levin-Wen anyonic), while the seam is invertible (|det Cartan(E8)|=1, no anyons) and a beta=1 KMS state (not a trace) -- in neither proved bucket (neg control D8 |det|=4). So SEAM.EQUIV.01's BW residual reduces to NPW26 Theorem A modulo two open sub-steps (realise the seam as a Z/2-reflection commuting-projector LTO; extend (LTO-RP) to the invertible KMS case) -- a reduction, not a closure; SEAM.EQUIV.01 stays open.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv424_seam_lto_rp_reduction.py", "sourceSha256": "3f128ce9aed9a9cfb49ad36a867811fbaf7d002e4c06765c87ebf65b9f4dd973", "linkedClaimIds": [ "SEAM.EQUIV.LTORP.01" ], "sectionIds": [ "section:4cda0736bf43dbd624d7", "section:586aafa793fa108ed39d", "section:6a93c4dd5fe420e1990e", "section:7ca01292e7152e165e80", "section:8e4972dbe899b5debb90", "section:9d4f17be173ce81f109e", "section:a9b1f3ad9bb703cf14c6", "section:ab9e7e520130ecc7da7c", "section:c6b6da016e7f30bbb7c1", "section:d90bd5e1e6d8fa41397d", "section:debae20192b75c7a987d", "section:f6d50ad015506eb0de3c" ], "activeSectionIds": [ "section:4cda0736bf43dbd624d7", "section:586aafa793fa108ed39d", "section:7ca01292e7152e165e80", "section:8e4972dbe899b5debb90", "section:9d4f17be173ce81f109e", "section:a9b1f3ad9bb703cf14c6", "section:ab9e7e520130ecc7da7c", "section:c6b6da016e7f30bbb7c1", "section:debae20192b75c7a987d", "section:f6d50ad015506eb0de3c" ], "evidenceId": "python_verification:verification/v424_seam_lto_rp_reduction.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v424_seam_lto_rp_reduction.py", "pubMirrorHash": "3f128ce9aed9a9cfb49ad36a867811fbaf7d002e4c06765c87ebf65b9f4dd973", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v424_seam_lto_rp_reduction.py" }, { "id": "v425_dyn_transfer_universal", "filename": "v425_dyn_transfer_universal.py", "path": "verification/v425_dyn_transfer_universal.py", "cluster": "frontier", "synopsis": "DYN.TRANSFER.UNIVERSAL.01 -- the single-flow reduction of F_transfer: the four frontier transfers (F_pole, F_Boltzmann, F_relic, F_QCD) do not each need a separate external solver; their dynamics is the ONE native flow of the theory (the seam modular/recovery semigroup, v238/v240, gap 6 ln(3/2)) restricted to each sector -- native flow + external anchors, firewall-clean. The recovery spectrum {1,(2/3)^6,(1/3)^6} gives H_OS=-log T with gap 6 ln(3/2) and e^{-Delta}=(2/3)^6 exactly; the v99 Koide generator linearised at q=2 has rate -Delta so the time-1 contraction is the recovery eigenvalue (2/3)^6 (q=5 unstable); the Boltzmann washout is that same contraction with the native CP phase 4pi/3 (v320); the QCD rate is b3=-7, b0(n_f=6)=7. Only the anchors (v_geo, the lattice C_p, the seesaw M_R) stay external; F_relic's cosmological initial condition theta_i is the one genuine wall. Extends v383 (static universal gap) to a dynamic universal flow; a reduction, not internalisation (no new premise).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv425_dyn_transfer_universal.py", "sourceSha256": "ccddb6693a37253f9d155dbca0bffca30cdb3103462bc5368004f19219c3576b", "linkedClaimIds": [ "DYN.TRANSFER.UNIVERSAL.01" ], "sectionIds": [ "section:0aa531691d44e875db34", "section:37d6ecba160419b2f272", "section:3d2a5b53f3345969fcbc", "section:568b5e9acdb7b04367d3", "section:83d94e33024ba3df4db8", "section:848c49f799255f4cda92", "section:ab9e7e520130ecc7da7c", "section:b5985d0cb2d5eb8aa959", "section:c4cf080b9ae6f25f7a71", "section:f0ac30137703825661c6", "section:f6d50ad015506eb0de3c", "section:fb925495ff0f316b1a06", "section:fdf63a1d99769ab37ccb" ], "activeSectionIds": [ "section:37d6ecba160419b2f272", "section:3d2a5b53f3345969fcbc", "section:83d94e33024ba3df4db8", "section:ab9e7e520130ecc7da7c", "section:b5985d0cb2d5eb8aa959", "section:f6d50ad015506eb0de3c", "section:fb925495ff0f316b1a06", "section:fdf63a1d99769ab37ccb" ], "evidenceId": "python_verification:verification/v425_dyn_transfer_universal.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v425_dyn_transfer_universal.py", "pubMirrorHash": "ccddb6693a37253f9d155dbca0bffca30cdb3103462bc5368004f19219c3576b", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v425_dyn_transfer_universal.py" }, { "id": "v426_seam_lto_rp_kms", "filename": "v426_seam_lto_rp_kms.py", "path": "verification/v426_seam_lto_rp_kms.py", "cluster": "frontier", "synopsis": "SEAM.EQUIV.LTORP.KMS.01 -- the invertible beta=1-KMS variant of (LTO-RP), the corner NPW26 leave open (they prove it for topologically-ordered models; the TFPT seam is invertible + beta=1 KMS, not a trace). A constructive Tomita-Takesaki witness advancing v424 sub-step (ii); does NOT close SEAM.EQUIV.01. One-particle dictionary: modular operator Delta=e^{-K}, (LTO-RP)/BW <=> u_Theta=J <=> Theta K Theta=-K, the mu4 clock a modular symmetry [rho,K]=0. Build K reflection-odd/mu4-even/gapped (gap 2k=6 ln(3/2)); C=1/(1+e^K) the beta=1 KMS covariance satisfies C/(1-C)=e^{-K} (genuine KMS, not trace); Theta K Theta=-K and [rho,K]=0 both hold, so (LTO-RP) is satisfied by direct Tomita-Takesaki; |det Cartan(E8)|=1 (invertible, no anyons) vs anyonic |det|=4, and the state is not a trace (Delta!=I) -- neither NPW26 bucket. Neg controls: a side-even reflection gives +K (BW fails), an off-mu4-block K breaks [rho,K]. SEAM.EQUIV.01 stays open (the continuum sub-step (i) remains).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv426_seam_lto_rp_kms.py", "sourceSha256": "b4c9cbcc7f0730a82c23b4741bfa980653b9e13d774af6c2ef7c654cf5f887da", "linkedClaimIds": [ "SEAM.EQUIV.LTORP.KMS.01" ], "sectionIds": [ "section:013b22f7d203ce0c7da1", "section:0739148b5a5974d0d662", "section:4cda0736bf43dbd624d7", "section:586aafa793fa108ed39d", "section:6a93c4dd5fe420e1990e", "section:6bcd4464dbd4c8f8f003", "section:7ca01292e7152e165e80", "section:8872501633bb702220cd", "section:8e4972dbe899b5debb90", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:c6b6da016e7f30bbb7c1", "section:d90bd5e1e6d8fa41397d", "section:f6d50ad015506eb0de3c" ], "activeSectionIds": [ "section:013b22f7d203ce0c7da1", "section:4cda0736bf43dbd624d7", "section:586aafa793fa108ed39d", "section:6bcd4464dbd4c8f8f003", "section:7ca01292e7152e165e80", "section:8e4972dbe899b5debb90", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:c6b6da016e7f30bbb7c1", "section:f6d50ad015506eb0de3c" ], "evidenceId": "python_verification:verification/v426_seam_lto_rp_kms.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v426_seam_lto_rp_kms.py", "pubMirrorHash": "b4c9cbcc7f0730a82c23b4741bfa980653b9e13d774af6c2ef7c654cf5f887da", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v426_seam_lto_rp_kms.py" }, { "id": "v427_overdet_witness_map", "filename": "v427_overdet_witness_map.py", "path": "verification/v427_overdet_witness_map.py", "cluster": "registry", "synopsis": "", "publicationNotes": [ "Non-scientific synopsis omitted." ], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv427_overdet_witness_map.py", "sourceSha256": "cff164ec9b00f99a8d7493d40c0d41f34a255b10277fd4e371c5ed1deb61c35d", "linkedClaimIds": [ "OVERDET.WITNESS.MAP.01" ], "sectionIds": [ "section:0534241ef38a39dcc3cc", "section:3ff315fdd4e19bf322ac", "section:ab9e7e520130ecc7da7c", "section:b37031f13445096fcccf", "section:d59ca752d5e1a51b75b5", "section:f6d50ad015506eb0de3c" ], "activeSectionIds": [ "section:0534241ef38a39dcc3cc", "section:3ff315fdd4e19bf322ac", "section:ab9e7e520130ecc7da7c", "section:b37031f13445096fcccf", "section:d59ca752d5e1a51b75b5", "section:f6d50ad015506eb0de3c" ], "evidenceId": "python_verification:verification/v427_overdet_witness_map.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v427_overdet_witness_map.py", "pubMirrorHash": "cff164ec9b00f99a8d7493d40c0d41f34a255b10277fd4e371c5ed1deb61c35d", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v427_overdet_witness_map.py" }, { "id": "v428_overdet_reclass", "filename": "v428_overdet_reclass.py", "path": "verification/v428_overdet_reclass.py", "cluster": "registry", "synopsis": "OVERDET.WITNESS.RECLASS.01 -- the honest correction of v427: applying v427's own multiply-vs-compress test to v427 itself. The (2,3,5) Brieskorn singularity (v236) is the ONE generator -- Milnor mu=(2-1)(3-1)(5-1)=8=rank E8, 30=2*3*5=h(E8), phi(30)=8 -- so each of v427's seven witnesses maps to a facet of that same object (primes 2,3,5 of 30, the clock 30, or E8): all seven collapse to one generator (distinct objects=1), which by v427's own definition is COMPRESSION, not seven independent multiplications. What honestly multiplies is the INPUT forced four independent ways -- the '8' in c3=1/(8 pi) from rank(E8), the carrier Coxeter h(D5)=2(5-1), the totient phi(30) and the Milnor number -- plus the FOREIGN witness alpha^-1~137 (prime, not in the (2,3,5)-skeleton; v305). Refines and partly walks back v427; consistent with v236/v305/v313.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv428_overdet_reclass.py", "sourceSha256": "a0fafb585ee17ecc58a9ec4c973d0d596e7291907e525f15e479b1c7883536be", "linkedClaimIds": [ "OVERDET.WITNESS.RECLASS.01" ], "sectionIds": [ "section:0534241ef38a39dcc3cc", "section:09b49009253acb5a0dfb", "section:3cc790136e8b9bd3c188", "section:3ff315fdd4e19bf322ac", "section:584e87a9c163ac38f92f", "section:a9b1f3ad9bb703cf14c6", "section:ab9e7e520130ecc7da7c", "section:b37031f13445096fcccf", "section:d59ca752d5e1a51b75b5", "section:eb0bd97fda8c0fedefad" ], "activeSectionIds": [ "section:0534241ef38a39dcc3cc", "section:3ff315fdd4e19bf322ac", "section:584e87a9c163ac38f92f", "section:a9b1f3ad9bb703cf14c6", "section:ab9e7e520130ecc7da7c", "section:b37031f13445096fcccf", "section:d59ca752d5e1a51b75b5" ], "evidenceId": "python_verification:verification/v428_overdet_reclass.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v428_overdet_reclass.py", "pubMirrorHash": "a0fafb585ee17ecc58a9ec4c973d0d596e7291907e525f15e479b1c7883536be", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v428_overdet_reclass.py" }, { "id": "v430_other_side_reverse_audit", "filename": "v430_other_side_reverse_audit.py", "path": "verification/v430_other_side_reverse_audit.py", "cluster": "registry", "synopsis": "E8.OTHERSIDE.AUDIT.01: the 'other side of the seam' (double-cover deck / conjugate sheet S⁻) audited against E8's UNMAPPED Casimir degrees -- the sheet/deck complement of v354/v355, answering 'is the leftover where the second sheet lives?' with a disciplined NEGATIVE. [E] DECK=DEGREE-2: the one-sided cover contributes |Z2|=2 (the 1/2 in c3=1/(2·4π)=1/(8π), v58/v216); 2=min(E8 degrees)=the metric, one of the matched primary readouts {2,8,30} (v354), NOT one of the unmapped {12,14,18,20,24}. [E] TWO SHEETS=128-SPINOR: dim S⁺=dim S⁻=16, the spinor block 128=rank·dim S⁺=8·16=2^(rank−1)=Σdeg, the spinor half of 248=120+128; S⁻ is the conjugate (16̄,4̄), 128=2·64, not a spare singlet. [E] FORCED-DISJOINT: the sheet/deck integer set {2,16,32,128} has EMPTY intersection with {12,14,18,20,24}, its only degree-alphabet contact the matched 2. [O] DISCIPLINED DECLINE: each unmapped degree needs an UNFORCED coefficient from sheet atoms and admits ≥2 readings (the v355 discriminator) -- no forced sheet→unmapped-degree identity. [E] 'S⁻=DM' DOWNGRADED + WIMP NO-GO: v227 replaced the over-strong 'S⁻ is dark matter'; 128=(16,4)+(16̄,4̄) is the SAME matter spinor (no spare singlet), DM is the determinant-line axion (a phase). [O] the only live 'other side' question (the 128 phase/glue dark sector, v227) concerns MATCHED structure, not the unmapped degrees. A clean structural NEGATIVE; Wolfram-mirrored, Python (sympy).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv430_other_side_reverse_audit.py", "sourceSha256": "a42001b760df50ea30bd085179c6bb583bd002aa88d368ae27f444abc8b90eca", "linkedClaimIds": [ "E8.OTHERSIDE.AUDIT.01" ], "sectionIds": [ "section:7a7de20f53ed3e69fb6f", "section:8a517836f882378cde88", "section:8a623c8ec8a4cfe2a678", "section:989e899750d5a86edf1e", "section:a719d5d4b287729fc27d", "section:ab9e7e520130ecc7da7c", "section:b37031f13445096fcccf", "section:f9ed8e942e9df8db94c7" ], "activeSectionIds": [ "section:7a7de20f53ed3e69fb6f", "section:8a517836f882378cde88", "section:989e899750d5a86edf1e", "section:ab9e7e520130ecc7da7c", "section:b37031f13445096fcccf", "section:f9ed8e942e9df8db94c7" ], "evidenceId": "python_verification:verification/v430_other_side_reverse_audit.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v430_other_side_reverse_audit.py", "pubMirrorHash": "a42001b760df50ea30bd085179c6bb583bd002aa88d368ae27f444abc8b90eca", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v430_other_side_reverse_audit.py" }, { "id": "v429_axion_pentagon_phi", "filename": "v429_axion_pentagon_phi.py", "path": "verification/v429_axion_pentagon_phi.py", "cluster": "frontier", "synopsis": "DM.AXION.PENTAGON.01 -- the 'unmapped' icosahedral/golden E8 structure surfaces in the ONE external cosmological input theta_i, answering 'why does idle E8 structure exist?' for the one case where it has a job. Because N_fam=g_car-2, the spine quotient theta_i=pi N_fam/g_car=(g_car-2)pi/g_car is EXACTLY the interior angle of the regular g_car-gon; for g_car=5 the PENTAGON, theta_i=3 pi/5=108 deg -- the carrier polygon, not a bare rational multiple of pi. Its cosine is golden: cos(3 pi/5)=(1-sqrt5)/4=-1/(2 phi), partner 2 cos(2 pi/5)=1/phi=phi-1, phi=2 cos(pi/5)=(1+sqrt5)/2. The golden character is unique to g_car=5: among small n-gons only n=5 has an irrational interior-angle cosine (n=3,4,6 give 1/2,0,-1/2). So the golden ratio v354 called 'unmapped' (and v313 named the g_car=5 signature) IS the angular data of theta_i=3 pi/5 (the spine branch v211/DM.AXION.SPINE.01). A re-reading: it REFINES v354 from 'phi in NO physical readout' to 'phi touches ONLY the [C] spine misalignment angle', and gives a geometric motive for the spine over the hilltop ~170 deg; it does NOT upgrade DM.AXION.SPINE.01 (stays [C]) and closes no gate (the abundance is cosmology, decided by the finite-T solver, v185/v211).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv429_axion_pentagon_phi.py", "sourceSha256": "80873c1a8f85ce2486fd2e8683bee9371b9c1c84d611465bf04e0ae709402350", "linkedClaimIds": [ "DM.AXION.PENTAGON.01" ], "sectionIds": [ "section:09b49009253acb5a0dfb", "section:3af896f0e07d57463462", "section:3cc790136e8b9bd3c188", "section:584e87a9c163ac38f92f", "section:7a7de20f53ed3e69fb6f", "section:989e899750d5a86edf1e", "section:a9b1f3ad9bb703cf14c6", "section:ab9e7e520130ecc7da7c", "section:eb0bd97fda8c0fedefad" ], "activeSectionIds": [ "section:3af896f0e07d57463462", "section:584e87a9c163ac38f92f", "section:7a7de20f53ed3e69fb6f", "section:989e899750d5a86edf1e", "section:a9b1f3ad9bb703cf14c6", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v429_axion_pentagon_phi.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v429_axion_pentagon_phi.py", "pubMirrorHash": "80873c1a8f85ce2486fd2e8683bee9371b9c1c84d611465bf04e0ae709402350", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v429_axion_pentagon_phi.py" }, { "id": "v431_e8_degree_ladder", "filename": "v431_e8_degree_ladder.py", "path": "verification/v431_e8_degree_ladder.py", "cluster": "registry", "synopsis": "E8.DEGREE.LADDER.01: the reverse-audit 'unmapped' E8 Casimir degrees are NOT diffuse overhead but the forced two-family decomposition deg(E8) = 6·spine{2,3,4,5} (+) ({2} U flavor-det-ladder{8,14,20}) -- the structural complement of v354/v355/v430. [E] TWO-FAMILY SPLIT FORCED BY 30=2·3·5: the E8 exponents are the φ(30)=8 totatives of h=30=2·N_fam·g_car (coprime to 6 => ±1 mod 6), so the degrees occupy ONLY the residue classes {0,2} mod 6. [I] 6k family {12,18,24,30}/6 = {2,3,4,5} = the v91 spine {e3,e1,e2,p0}(a=(1,1,2)). [I] 6k+2 family {2,8,14,20}: {8,14,20}=(det R,det C,det L)=the winding line det M(s,0)=6s+8 of the flavor diamond (v135), C=R+Q diag(1,0,0). [E] '18'=6·N_fam is NOT a holdout (spine family, not on the det-ladder). [E] SPECIAL TO E8 among the simply-laced exceptionals (E6/E7/D5 fail the clean {0,2}-mod-6 split). [P] HONEST v355 LINE: the arithmetic decomposition is exact [I], but the FUNCTORIAL claim '6k+2 Casimir stratum = flavor sheet operators' needs a rep-theoretic map ([P]); 12,24 admit two canonical readings each, so this is a STRUCTURE theorem, not a forced functorial flavor map -- reclassifies v354 overhead to zero orphan degrees, closes no gate. Wolfram-mirrored, Python (sympy).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv431_e8_degree_ladder.py", "sourceSha256": "a6035afc01e00d083280dacc78cdb0b6fb9fb5360c188b6b523984190a5296c2", "linkedClaimIds": [ "E8.DEGREE.LADDER.01" ], "sectionIds": [ "section:44fb2c4f56d2211a1e7f", "section:5accfde4a70bd57ce618", "section:7a7de20f53ed3e69fb6f", "section:ab9e7e520130ecc7da7c", "section:b37031f13445096fcccf", "section:d59ca752d5e1a51b75b5" ], "activeSectionIds": [ "section:44fb2c4f56d2211a1e7f", "section:5accfde4a70bd57ce618", "section:7a7de20f53ed3e69fb6f", "section:ab9e7e520130ecc7da7c", "section:b37031f13445096fcccf", "section:d59ca752d5e1a51b75b5" ], "evidenceId": "python_verification:verification/v431_e8_degree_ladder.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v431_e8_degree_ladder.py", "pubMirrorHash": "a6035afc01e00d083280dacc78cdb0b6fb9fb5360c188b6b523984190a5296c2", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v431_e8_degree_ladder.py" }, { "id": "v432_overdet_floor", "filename": "v432_overdet_floor.py", "path": "verification/v432_overdet_floor.py", "cluster": "registry", "synopsis": "OVERDET.FLOOR.01: the UNCONDITIONAL improbability floor + the L1<->L2 bridge -- the defensible number that survives even if a skeptic REJECTS the declared formula grammar, complementing the conditional null model (v100) and the multiply-vs-compress framework (v427/v428). [E] DISJOINT PIECES (v428): compression removed (v427's seven readouts are one (2,3,5)/E8 object, NOT multiplied); what multiplies is the input '8' forced FOUR ways {rank E8, h(D5)=2(g_car-1), φ(30), Milnor(2,3,5)} plus the FOREIGN witness α^-1~137 (prime, outside (2,3,5)). [C] CONSERVATIVE FLOOR: multiplying ONLY across disjoint pieces (input over-determination × the α grammar census 1/94500 (v100) × the φ0-seed cluster counted ONCE × one downstream witness) the floor stays ≤1e-6 across a grid of generous assignments, nominal ~1e-10 -- 'extraordinary' WITHOUT the declared grammar. [E] THE BRIDGE: the floor (~1e-10) sits ~20 orders ABOVE the conditional 10^{-30.7} (v100); that gap = the value of proving the FORMS forced, so L1 (ALPHA.QUILLEN.EXACT.01, v382) and L2 (this floor) are the SAME lever. [C] HONEST SCOPE: bounds ONLY 'is it numerology?', NOT the physics bridge (firewall v187); a conservative FLOOR, not a posterior. Numerical/methodological [C], Python-only (mpmath) -- deliberately NOT Wolfram-mirrored (a bound, not an identity).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv432_overdet_floor.py", "sourceSha256": "8c253b772556ff5b7f3982c4f064998e92484e4716b11945c269c4011b434063", "linkedClaimIds": [ "OVERDET.FLOOR.01" ], "sectionIds": [ "section:0534241ef38a39dcc3cc", "section:ab9e7e520130ecc7da7c", "section:b37031f13445096fcccf", "section:d59ca752d5e1a51b75b5", "section:e7cdfe28203ecac9114d" ], "activeSectionIds": [ "section:0534241ef38a39dcc3cc", "section:ab9e7e520130ecc7da7c", "section:b37031f13445096fcccf", "section:d59ca752d5e1a51b75b5", "section:e7cdfe28203ecac9114d" ], "evidenceId": "python_verification:verification/v432_overdet_floor.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v432_overdet_floor.py", "pubMirrorHash": "8c253b772556ff5b7f3982c4f064998e92484e4716b11945c269c4011b434063", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v432_overdet_floor.py" }, { "id": "v436_overdet_floor2", "filename": "v436_overdet_floor2.py", "path": "verification/v436_overdet_floor2.py", "cluster": "registry", "synopsis": "OVERDET.FLOOR.02: HARDENS OVERDET.FLOOR.01 (v432) -- the 'is it numerology?' floor does NOT rest on v432's subjective chance assignments. [E] ASSUMPTION-MINIMAL FLOOR: the α cubic-class census (v100 layer D) is PURE COUNTING -- of N=94500 complexity-matched F_U(1) variants only 1 hits the 4e-8 CODATA window (the TFPT instance, α^-1=137.0359992), so p_α ≤ 1/94500 = 1.06e-5 ~ 4.40σ with NO subjective probability, prior or multi-observable grammar. [E] MONOTONE CONCESSION LADDER: -log10(p) full scorecard+α ~30.7 → scorecard-only ~25.8 → α-census-only ~4.98 (=4.40σ); the 'not chance (>4σ)' verdict holds at the MOST adversarial rung. [E] INDEPENDENCE: strip ALL of v432's subjective factors (0.1³×0.012×0.15=1.8e-6) and the floor is still 4.40σ -- they only sharpen it. [C] HONEST 5σ GAP: 5σ (p=5.7e-7) is crossed by the census times exactly ONE more independent factor ≤0.054 (the input-'8' four-fold over-determination or one foreign witness), stated openly. [C] FIREWALL: bounds numerology only, not the physics bridge (v187). Python-only (imports the v100 census live), deliberately NOT Wolfram-mirrored (a counting bound, not an identity).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv436_overdet_floor2.py", "sourceSha256": "0e62b917d6e5e3c9748b52a1527bd437d36bab186abf15ef0b388dafa7ee7b38", "linkedClaimIds": [ "OVERDET.FLOOR.02" ], "sectionIds": [ "section:0534241ef38a39dcc3cc", "section:ab9e7e520130ecc7da7c", "section:d59ca752d5e1a51b75b5", "section:e7cdfe28203ecac9114d" ], "activeSectionIds": [ "section:0534241ef38a39dcc3cc", "section:ab9e7e520130ecc7da7c", "section:d59ca752d5e1a51b75b5", "section:e7cdfe28203ecac9114d" ], "evidenceId": "python_verification:verification/v436_overdet_floor2.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v436_overdet_floor2.py", "pubMirrorHash": "0e62b917d6e5e3c9748b52a1527bd437d36bab186abf15ef0b388dafa7ee7b38", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v436_overdet_floor2.py" }, { "id": "v437_e8_degree_joint", "filename": "v437_e8_degree_joint.py", "path": "verification/v437_e8_degree_joint.py", "cluster": "registry", "synopsis": "E8.DEGREE.JOINT.01: a CONSOLIDATION of v6/v66/v355/v431 deriving more from the E8 Casimir degrees WITHOUT crossing the v354/v355 anti-numerology line -- no new per-degree coincidence, only a joint lock. [E] E8 IS FIXED BY ITS DEGREE MULTISET: from deg(E8)={2,8,12,14,18,20,24,30} alone -- rank=#deg=8 (=2nd deg), h=max=30, #pos roots=Σexp=120, #roots=240, dim=248, |W|=∏deg=696729600, Σdeg=128=2^7=dim S^+. [E] THE JOINT QUADRATIC: the two structural integers (g_car,N_fam) are the UNIQUE root pair of x²-(rank E8)x+(h/2)=x²-8x+15=(x-3)(x-5) -- sum=rank E8=8 (rank-fill, v6), product=h/2=15=g_car·N_fam (2 g_car N_fam=h, v431); {3,5} the unique factor pair of 15 summing to 8, so BOTH are forced together by two degree-invariants. [E] the 3 mapped degrees {2,8,30}=min/rank/max (the canonical invariants); g_car=5=max prime of 30. [E] DISCIPLINE: no new per-degree mining; the 5 non-primary degrees keep their v431 homes. Exact integer/lattice [E], mirrored in wolfram/tfpt_readouts_extension.wl.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv437_e8_degree_joint.py", "sourceSha256": "a502dc852fb03fcdc8951870058af1339721c1eda8139e3f06f95ead8be2bbef", "linkedClaimIds": [ "E8.DEGREE.JOINT.01" ], "sectionIds": [ "section:44fb2c4f56d2211a1e7f", "section:7a7de20f53ed3e69fb6f", "section:ab9e7e520130ecc7da7c" ], "activeSectionIds": [ "section:44fb2c4f56d2211a1e7f", "section:7a7de20f53ed3e69fb6f", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v437_e8_degree_joint.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v437_e8_degree_joint.py", "pubMirrorHash": "a502dc852fb03fcdc8951870058af1339721c1eda8139e3f06f95ead8be2bbef", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v437_e8_degree_joint.py" }, { "id": "v438_seam_hsmi_borchers", "filename": "v438_seam_hsmi_borchers.py", "path": "verification/v438_seam_hsmi_borchers.py", "cluster": "frontier", "synopsis": "SEAM.EQUIV.BW.HSMI.01: the half-sided modular inclusion (Borchers/Wiesbrock) as an INTRINSIC Bisognano-Wichmann route for face (ii) of SEAM.EQUIV.01 -- geometric modular flow WITHOUT presupposing covariance. [E] STANDARD-PAIR ALGEBRA (ladder, exact): K=diag(n), P=raising shift give [K,P]=P and the Borchers scaling Δ^{it}PΔ^{-it}=e^{-t}P. [E] BW REFLECTION: J(n→-n) gives JKJ=-K (u_Θ=J) and JPJ=P_- (opposite translation). [E] POSITIVE ENERGY: in the unitary lowest-weight sl(2,R) rep P_line=L0-(L+ +L-)/2 is POSITIVE (min eig>0); the boost direction is the indefinite neg control. [C] SYNTHESIS: P≥0 + [K,P]=P + J is a Longo STANDARD PAIR / +half-sided modular inclusion, so by Borchers the flow is geometric INTRINSICALLY (complementary to Adamo-Giorgetti-Tanimoto); face (ii) becomes a STRUCTURE consequence. [C]/[O] assembling the finite algebra + positive-energy rep into ONE continuum standard pair is the continuum existence; SEAM.EQUIV.01 stays [O]. Python-only (numpy/scipy).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv438_seam_hsmi_borchers.py", "sourceSha256": "8d784c0258d8054ee65be20a80497d235621462d35a6e7b4a83750f9a450987f", "linkedClaimIds": [ "SEAM.EQUIV.BW.HSMI.01" ], "sectionIds": [ "section:136a1e576865c1424f29", "section:6a93c4dd5fe420e1990e", "section:8e4972dbe899b5debb90", "section:8f5691e12b337bb463ce", "section:9f2ef8163653328e6c3e", "section:ab9e7e520130ecc7da7c", "section:c6b6da016e7f30bbb7c1", "section:d90bd5e1e6d8fa41397d", "section:fcc9c4aa50365441ef12" ], "activeSectionIds": [ "section:8e4972dbe899b5debb90", "section:8f5691e12b337bb463ce", "section:ab9e7e520130ecc7da7c", "section:c6b6da016e7f30bbb7c1", "section:fcc9c4aa50365441ef12" ], "evidenceId": "python_verification:verification/v438_seam_hsmi_borchers.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v438_seam_hsmi_borchers.py", "pubMirrorHash": "8d784c0258d8054ee65be20a80497d235621462d35a6e7b4a83750f9a450987f", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v438_seam_hsmi_borchers.py" }, { "id": "v439_seam_lieb_robinson", "filename": "v439_seam_lieb_robinson.py", "path": "verification/v439_seam_lieb_robinson.py", "cluster": "frontier", "synopsis": "SEAM.EQUIV.CONTINUUM.LR.01: the Lieb-Robinson/Nachtergaele-Sims continuum-existence MOTOR for the gapped seam collar -- grounds the BULK half of the cited MMST existence in the explicit v367 p+ip model. [E] UNIFORM GAP: Δ(N)=const>0 across N=20..160 (lattice image of the OS transfer gap 6 ln(3/2)>0, v302/v329). [E] EXPONENTIAL CLUSTERING: |⟨c_i†c_j⟩|~e^{-r/ξ}, ξ finite and STABLE across N (gapped ⇒ Hastings-Koma decay). [E] LIEB-ROBINSON LIGHT CONE: |(e^{-iHt})_ij| confined to |i-j|≲v_LR t with finite v_LR (~2t). [C] NACHTERGAELE-SIMS LIFT: uniform gap + finite LR velocity ⇒ exponential clustering with N-independent ξ AND existence+uniqueness of the thermodynamic-limit ground state with a finite light cone -- derived for OUR collar. [C]/[O] the bulk thermodynamic limit EXISTS; SEAM.EQUIV.01 stays [O], the open step narrowed to the CHIRAL massless EDGE scaling limit. Python-only (numpy/scipy).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv439_seam_lieb_robinson.py", "sourceSha256": "322d5f457532d168080afd7828c4405cf3c36a6ffc6c5d0e82568ecc8fec30c3", "linkedClaimIds": [ "SEAM.EQUIV.CONTINUUM.LR.01" ], "sectionIds": [ "section:6a93c4dd5fe420e1990e", "section:8e4972dbe899b5debb90", "section:ab9e7e520130ecc7da7c", "section:c6b6da016e7f30bbb7c1", "section:cccf91ab17849ec5feae", "section:d90bd5e1e6d8fa41397d" ], "activeSectionIds": [ "section:8e4972dbe899b5debb90", "section:ab9e7e520130ecc7da7c", "section:c6b6da016e7f30bbb7c1", "section:cccf91ab17849ec5feae" ], "evidenceId": "python_verification:verification/v439_seam_lieb_robinson.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v439_seam_lieb_robinson.py", "pubMirrorHash": "322d5f457532d168080afd7828c4405cf3c36a6ffc6c5d0e82568ecc8fec30c3", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v439_seam_lieb_robinson.py" }, { "id": "v440_seam_lto_rp_beta", "filename": "v440_seam_lto_rp_beta.py", "path": "verification/v440_seam_lto_rp_beta.py", "cluster": "frontier", "synopsis": "SEAM.EQUIV.LTORP.BETA.01: the β-interpolation connecting the NPW26-PROVEN trace case (β=0) to the seam's β=1 KMS case along an obstruction-free homotopy -- upgrading the single-point v426 witness for v424 sub-step (ii) to a PATH argument. [E] β-INDEPENDENT (LTO-RP) DATA: ΘKΘ=-K and [ρ,K]=0 are conditions on K alone. [E] THE KMS PATH: C_β=1/(1+e^{βK}) has β=0→C=½I (NPW26 TRACE), β=1→seam KMS, β→∞→ground state; at every β ΘC_βΘ=1-C, [ρ,C_β]=0, 0≤C_β≤1. [E] NO OBSTRUCTION: β→C_β norm-continuous, stays in the (LTO-RP)-valid set -- a continuous homotopy, no wall. [E] NEG CONTROLS: reflection-EVEN K' breaks ΘC_βΘ=1-C for β>0; off-mu4 K breaks [ρ,C_β]. [C]/[O] a PATH argument for v424 (ii), stronger than v426; SEAM.EQUIV.01 stays [O]. 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[E] MMST HYPOTHESES: D=16 Majoranas (=2^{g_car-1}), c=8 (=g_car+N_fam), rank E8=8, range rank≤c≤D (8≤8≤16), gapped, quasi-free CAR -- all internal computed facts. [E] NPW26: (LTO-RP)=u_Θ=J, gap, Z2 reflection, mu4 clock, [ρ,K]=0 internal; the seam invertible |det Cartan E8|=1 + β=1 KMS is OUTSIDE NPW26's bucket (|det|=4) -- a TEMPLATE not a direct import. [E] ADAMO (arXiv:2508.07109): covariance is a CONSEQUENCE (defuses the v215 circularity, downgrades cov. ASSUMPTION→[E]). [E] of 12 hypotheses, 11 internal [E] and exactly 1 external -- the continuum EXISTENCE of the chiral massless scaling limit. [C]/[O] external dependence pinned to ONE analytic fact; SEAM.EQUIV.01 stays [O]. 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[E] EXACT UNIFORM 4-SECTOR COMMUTATION: ρ=diag(i^n) has EXACTLY 4 distinct eigenvalues for all N, and a genuinely character-block-diagonal K (random Hermitian within each n mod 4 class, not merely diagonal) has [ρ,K]=0 EXACTLY for N=4..256 (extends v398's N≤64). [E] UNIFORM GAP: Δ(N)=const>0 across N=20..160 (Nachtergaele-Sims, shared with v439). [E] N-INDEPENDENT RIGIDITY BOUND: a FIXED local clock-breaking perturbation gives ||[ρ,V]||=2 EXACTLY for all N. [E] NEG CONTROL: a clock-PRESERVING perturbation gives ||[ρ,V']||=0; an order-2 clock has only 2 sectors -- the order (4 marks) is the discriminator. [C]/[O] band-limited rigidity is uniform in N; SEAM.RIGIDITY.01/SEAM.EQUIV.01 stays [O]: the full-L² forcing is the cited rigidity/MMST step. 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[E]/[X] PRIMARY/GSD: |det Cartan(E8)|=1 (ONE primary, holomorphic) vs |det Cartan(D8)|=4 (FOUR primaries); torus GSD=#primaries=1 vs 4 -- a seam with GSD>1 falsifies (E8)_1. [E]/[X] CURRENT/THETA: level-1 currents dim E8=248 vs dim SO(16)=120; E8 lattice theta has 240 norm-2 roots (=112 integer + 128 spinor, computed) vs D8's 112. [E] c=8 IS NOT A DISCRIMINATOR (the v277 ambiguity); only the order-4 mu4 condensation + det K=1 (genus-1, v90) selects E8. [E] NON-VACUITY: the discriminators all fire on the rival. [X]/[C] mode D as concrete kill tests; SEAM.EQUIV.01 stays [O]. 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On the SAME explicit v367/v368 p+ip collar it shows the lattice edge carries the kinematic AND conformal data of a chiral c=1/2 Majorana CFT, converging under refinement. [E] CHIRAL LINEAR EDGE DISPERSION: the in-gap branch is linear near its zero-crossing (top v=0.983, R^2=0.9999) and the two boundaries carry OPPOSITE velocities -- one chiral Majorana per edge. [E] ALGEBRAIC EDGE TWO-POINT: the equal-time edge correlator decays as r^{-η} with η=1.00 (the chiral free-fermion CFT exponent) -- a CRITICAL edge. [E] EXPONENTIAL BULK (neg control): the bulk-row correlator decays exponentially (ξ~1.1) -- only the edge is critical. [E] TRIVIAL-PHASE NEG CONTROL: M=3 (no edge) has an exponential edge-row -- the power law is the topological edge, not the geometry. [E] SCALING-COLLAPSE: η is N-stable (1.001±0.007) and the edge profile is Cauchy-convergent under refinement (successive spread shrinks 0.028→0.013, Nx=36..60). [C] EDGE CENTRAL CHARGE: η=1 ⇔ one chiral Majorana (c=1/2)/edge, so the 16-copy carrier has a chiral c_-=8 edge CFT (=(E8)_1, c_-=g_car+N_fam). [C]/[O] grounds the EDGE half of the cited MMST scaling limit (v336) the way v439 grounds the bulk; SEAM.EQUIV.01 stays [O]. 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[E] FORCING (commute <=> block-diagonal, EXACT): for rho=diag(i^n), [rho,K]=0 iff K_ij=0 whenever i!=j mod 4 -- entrywise, swept N=4..128 (the converse of v442). [E] EXACT COMMUTANT DIMENSION: dim{K:[rho,K]=0}=sum_s n_s^2 (ad_rho nullspace), a PROPER subspace of the N^2 algebra (N=16: 64<256). [E] OFF-BLOCK <=> NON-COMMUTING: every off-block E_ij has ||[rho,E_ij]||>=sqrt(2)>0 -- zero slack. [E] THE ORDER IS THE DISCRIMINATOR: order-4 gives 4 sectors, order-2 a STRICTLY LARGER commutant -- the four marks force strictly more structure than two; only index-4 is (E8)_1 (det 1; v281/v154/v351). [E] NONDEGENERACY: exactly 4 distinct eigenvalues for all N>=4. [C] SYNTHESIS: commuting with the order-4 clock is EQUIVALENT to mu4-block-diagonality, so RP-definability (v54/v398) + clock-invariance FORCE block-diagonal Lambda_Sigma. [C]/[O] the residual is now precisely 'transfer in commutant' (clock-invariance, v323/v335); SEAM.EQUIV.01 stays [O]. 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[E] OS RECONSTRUCTION INHERITS THE SYMMETRY: for a mu4-invariant RP covariance ([rho,C(t)]=0), the OS canonical transfer Lambda=C(1)C(0)^-1=e^{-h} (fixed by RP+reflection, v54) has [rho,Lambda]=0 -- swept N=4..32 over random block-diagonal h. [E] SHARPNESS/NEG CONTROL: a mu4-BREAKING covariance gives [rho,Lambda]!=0 -- iff-sharp. [E] CONTRACTION/OS-VALIDITY: Lambda has spectrum in (0,1]. [E] MODULAR (Tomita-Takesaki): the free modular Hamiltonian K=log((1-C)C^-1) (v258) of the invariant state has [rho,K]=0, broken control [rho,K]!=0. [C] SYNTHESIS: [rho,Lambda_Sigma]=0 is a CONSEQUENCE of mu4-invariance of the seam RP data (the four marks, v216/v323) via OS reconstruction (v54) + the modular fact (v258), not an extra assumption. [C]/[O] the residual reduces from an operator commutation to 'the RP data is mu4-symmetric' (QGEO.SYM.01); SEAM.EQUIV.01 stays [O]. 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[E] INTEGER CHERN NUMBER: the M=1 collar lower band has Chern C=+1 (Fukui-Hatsugai-Suzuki lattice link-variable method, an EXACT integer, no fit). [E] TRIVIAL-PHASE NEG CONTROL: M=3 (v368) has C=0; M=-1 has C=-1 (opposite chirality, matching v444). [E] BULK-EDGE CORRESPONDENCE: the open strip has EXACTLY |C|=1 in-gap edge branch per boundary (0 trivial). [E] LI-HALDANE: the half-cut bulk ground state's entanglement spectrum has in-gap modes at 1/2 in the topological phase, none trivial. [C] EDGE CENTRAL CHARGE: c_-=N_Maj*(1/2)*|C|=16*(1/2)*1=8=g_car+N_fam, from the Chern integer -- the SAME c_-=8 as v444 from an independent observable. [C]/[O] corroborates v444's (E8)_1 reading; SEAM.EQUIV.01 stays [O]. 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[E] QUASI-FREE/WICK: the ground-state correlation matrix is an exact projector G^2=G (~1e-13), so the state is quasi-free and all n-point are Wick sums -- the MMST quasi-free CAR hypothesis (ledger entry 5) literally holds (structural: the BdG state is free). [E] FOUR-POINT CAUCHY CONVERGENCE: the edge four-point cross-ratio Q=[G01 G23]/[G02 G13] at commensurate positions (1,2,4,7)*(Nx/12) is Cauchy-convergent (spread shrinks, Nx=36..60). [E] CONFORMAL FOUR-POINT: Q converges to the free-fermion conformal cross-ratio sin(5pi/12)/sin(pi/12)=2+sqrt(3)~3.732 (eta=1). [E] BULK NEG CONTROL: the bulk four-point is orders of magnitude off (exponential). [C] the one external MMST fact (continuum existence) is now empirically supported at BOTH 2-point (v444) and 4-point order; SEAM.EQUIV.01 stays [O]. 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[E] CROSS-RATIO A CONVERGES: the edge four-point Q(1,2,4,7)/12 -> sin(5pi/12)/sin(pi/12)=2+sqrt(3), deviation shrinks monotonically (Nx=36,48,60). [E] CROSS-RATIO B (independent positions): Q(1,3,5,9)/12 -> its OWN value 2 -- a second observable with a different limit, so convergence is not a tuned point. [E] UNIFORM 1/N RATE: |Q(N)-Q_inf|*N <= 4 for BOTH cross-ratios and every Nx in {36,48,60} (one N-independent constant across two independent observables). [E] BULK NEG CONTROL: the bulk cross-ratio is off-scale. [C]/[O] the MMST uniform-convergence hypothesis is empirically satisfied (multi-observable uniform rate); SEAM.EQUIV.01 stays [O] -- the abstract existence theorem (v336) is strengthened in evidence, not proved. 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[E] CALABRESE-CARDY LAW: the block entanglement entropy of the critical XX (Dirac) chain fits S=(c/3)ln[(L/pi)sin(pi l/L)]+const with c_Dirac=1.000 -- the universal scaling-limit signature. [E] c PER MAJORANA = 1/2: c_Dirac=1=2*c_Majorana (Dirac=two Majoranas), so c_Majorana=1/2. [E] GAPPED NEG CONTROL: a dimerised chain has saturating (c=0) entanglement. [C] c_-=N_Maj*c_Majorana=16*(1/2)=8=g_car+N_fam, the SAME c_-=8 as v444/v447 from a third observable. [C]/[O] three observables agree; SEAM.EQUIV.01 stays [O]. 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On the critical Majorana ring (the v367/v368 edge universality class). [E] SPIN DIMENSION h_sigma=1/16: the periodic(R)-antiperiodic(NS) ground-energy split gives (E0_R-E0_NS)*L/(2pi v)=0.06250 (v=2), stable across L=200,400,800. [E] ENERGY DIMENSION h_epsilon=1/2: the lowest NS pair excitation gives 2*eps_min*L/(2pi v)=0.50000. [E] CONFORMAL SCALING: both dimensions are L-independent (gaps scale exactly as 1/L). [C] {c,h_sigma,h_epsilon}={1/2,1/16,1/2} is the chiral Ising (free Majorana) CFT; with N_Maj=16 and bulk-edge (v447), c_-=16*(1/2)=8=g_car+N_fam. [C]/[O] the edge CFT is named by central charge (v450) AND operator content (this); SEAM.EQUIV.01 stays [O]. 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[E] S-INVARIANCE: chi(-1/tau)=chi(tau) for chi=E4/eta^8 (weight 0), to ~1e-30 -- ONE primary, S-matrix=[1]. [E] T-PHASE: chi(tau+1)/chi(tau)=e^{-2pi i/3}=e^{-2pi i c/24} (c=8), to ~1e-30. [E] LEADING POWER => c=8: chi*q^{1/3}->1 so the leading power is q^{-c/24}=q^{-1/3} => c=8=g_car+N_fam. [E] HOLOMORPHIC CONSTRAINT: c=8=0 mod 8 (even unimodular rank-8 lattice E8). [C]/[O] the (E8)_1 modular data is the torus signature of the seam net; with the edge readings (v444/v447/v450/v451) (E8)_1 is pinned on torus AND edge; SEAM.EQUIV.01 stays [O]. 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[E] THE MARKS ARE mu4: the four Gauss-Bonnet marks are exactly {1,i,-1,-i}=roots of z^4-1 (v168/v216/v323). [E] THE CLOCK PERMUTES THE MARKS: z->iz is a 4-cycle of order 4 (fixes the configuration setwise). [E] MOEBIUS STABILISER: z->iz preserves the cross-ratio 2 (in the D4 stabiliser, v168). [E] THE FORM BASIS IS mu4-GRADED: omega_k=z^{k-1}dz/(z^4-1)->i^k omega_k (k=1,2,3->{i,-1,-i}, weights (1,2,3)=A3 exponents). [C]/[O] QGEO.SYM.01 is a CONSEQUENCE of marks=mu4 + QGEO.REALIZE.01 (the EXISTING premise), NO new premise; the rigidity chain (this->v446->v445) closes modulo realisation, SEAM.EQUIV.01 stays [O]. 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[E] CASIMIR c: E_0(L)=e_inf*L - pi*v*c/(6L) (Affleck-Cardy) gives c_Dirac=1.000 -> 1/2 per Majorana (parameter-free, L=64..1024). [E] KAC-MOODY LEVEL: the lattice U(1) current has <0|J_n J_-n|0>=n exactly (n=1..8) -- the affine level-1 central extension closes; a gapped control gives a vanishing non-linear term. [E] SUGAWARA EXACT: c=dim G/(1+h^v)=8 for BOTH SO(16)_1 (120/15) and (E8)_1 (248/31). [C] 16 Majoranas => c_-=8=g_car+N_fam. [C]/[O] SEAM.EQUIV.01 stays [O]. 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[E] UNIFORM BW: ||Theta K Theta + K||=0 exactly at every size (N=8..128) -- u_Theta=J holds uniformly. [E] UNIFORM GAP: the gap of K is N-independent (6 ln(3/2)) -- Delta=e^{-K} uniformly bounded from 1, a genuine KMS (not trace) limit. [E] UNIFORM CLOCK: [rho,K]=0 exactly at every N. [E] N-INDEPENDENT NEG CONTROL: a side-even reflection gives ||Theta K Theta+K||=2||K|| growing with N, an off-mu4 K breaks [rho,K] at every N. [C]/[O] the inductive limit inherits u_Theta=J; SEAM.EQUIV.01 stays [O]. 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[E] c3's '8' IS THE ONE-SIDED COUNT: 8pi=|Z2|*intK=2*(2pi*chi(S^2))=2*4pi, integer 8=|Z2|*(intK/pi)=2*4. [E] REFLECTION REVERSES C: the p+ip model has Chern C=+1, its ky->-ky partner C=-1. [E] TWO-SIDED => NON-CHIRAL: a gapped boundary with an orientation-reversing symmetry has C=-C=0 (c_-=0). [C] ONE-SIDED => CHIRAL: the one-sided seam (the same |Z2| of c3) has no such reflection, so C!=0 is forced. [C]/[O] c_-=8=rank E8 is the SAME 8 as c3's 8pi; S3 follows from P1; SEAM.EQUIV.01 existence stays [O]. 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[E] (E8)_1 CHARACTER TOWER: chi=E4/eta^8=q^{-1/3}(1+248q+4124q^2+34752q^3+...) -- exact (E8)_1 tower degeneracies. [E] CURRENT-COUNT DISCRIMINATOR: weight-1 multiplicity=248=dim E8=120(SO16)+128(spinor) -- not the free 120. [E] SECTOR-COUNT DISCRIMINATOR: |det Cartan E8|=1 (invertible) vs |det Cartan D8|=4. [X] KILL CRITERION: 120 (not 248), OR 4 sectors (not 1), OR a wrong tower coeff would FALSIFY (E8)_1; data give 248/1/{1,248,4124}, PASSED. [C]/[O] SEAM.EQUIV.01 existence stays [O]. 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[C] H1 ALGEBRA CLASS: CAR 16-Majorana collar -- MATCH. [C] H2 MASSLESS POS-ENERGY LIMIT: the edge IS that limit (v439/v444) -- MATCH. [E] H3 PER-COPY c=1/2: 16 chiral Majoranas, each the proven Theorem A case. [C] H4 DECOUPLED ADDITIVITY: 16*(1/2)=8 -> free SO(16)_1 c=8. [C] H5 WZW RANGE 8<=8<=16 + 120 bilinear currents. [O] H6 RESIDUAL = the 128-spinor extension (248=120+128), outside MMST's bilinear method, handed to v459. [C]/[O] the c=8 EXISTENCE is citable; SEAM.EQUIV.01 stays [O], residual narrowed to the holomorphic extension. 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[E] E8 EVEN UNIMODULAR: det Cartan=1, all 240 roots norm 2 -- A_{E8} is a holomorphic net (det K=1). [E] LATTICE CURRENTS 248=8+240: weight-1 = 8 Cartan + 240 roots. [E] THE 240 ROOTS SPLIT 112+128=SPINOR: 8+112=120=so(16), the 128 half-integer roots ARE the spinor (248=120+128=8+240). [C] AGT: A_Q of an even lattice IS a 2d conformal net, so the SO(16)_1->(E8)_1 extension is constructed, not assumed. [C]/[O] two complementary routes cover (E8)_1; residual = the one realization input (collar=A_{E8}), tied to P1 by v456; SEAM.EQUIV.01 stays [O]. 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[E] FLAT-BAND PARENT: the flattened Bloch Q=h/|h| of v367's p+ip collar has Q^2=I (flat +-1 bands) and P=(I-Q)/2 is an exact projector EQUAL to the occupied ground-state projector -- a frustration-free commuting-projector parent with the same gapped ground state. [E] GAP-PROTECTED QUASI-LOCALITY: the gapped projector kernel |P(n,0)| decays rapidly (xi~1.14 at M=1, exp R^2=0.995, |P(20,0)|<1e-6), xi grows as the gap closes (2.7 at gap 0.02); the GAPLESS point decays as a clean power law |R|^{-2.1} (R^2=0.999, tail ~2e-4) -- locality needs the gap. [E] Z/2 REFLECTION + mu4 INHERITED: the flattened modular Hamiltonian K_flat=sign(K) inherits Theta K_flat Theta=-K_flat (BW/u_Theta=J) and [rho,K_flat]=0 (mu4) EXACTLY (sign is odd; rho commutes with any f(K)). [E] NEG CONTROLS: a side-even reflection gives 2||K_flat||!=0 (BW fails), an off-mu4 K mixing opposite-sign marks breaks [rho,sign(K)]!=0. [C]/[O] the chiral c_-=8!=0 (FHS Chern |C|=1) obstructs STRICT finite-range commuting-projector locality (Kapustin-Fidkowski; C!=0 forbids exp-localised Wannier), so the realisation is the quasi-local LTO net of NPW26; advances v424 sub-step (i), SEAM.EQUIV.01 stays [O]. Python-only (numpy).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv460_seam_s3_lto.py", "sourceSha256": "e0a693cf6841bd52808a568529ea91520a3478dc275fea46bdc94edd47642eb7", "linkedClaimIds": [ "SEAM.S3.LTO.01" ], "sectionIds": [ "section:586aafa793fa108ed39d", "section:6a93c4dd5fe420e1990e", "section:8e4972dbe899b5debb90", "section:9d4f17be173ce81f109e", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d" ], "activeSectionIds": [ "section:586aafa793fa108ed39d", "section:8e4972dbe899b5debb90", "section:9d4f17be173ce81f109e", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v460_seam_s3_lto.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v460_seam_s3_lto.py", "pubMirrorHash": "e0a693cf6841bd52808a568529ea91520a3478dc275fea46bdc94edd47642eb7", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v460_seam_s3_lto.py" }, { "id": "v461_seam_strict_locality", "filename": "v461_seam_strict_locality.py", "path": "verification/v461_seam_strict_locality.py", "cluster": "frontier", "synopsis": "SEAM.S3.LOCALITY.01: the Kapustin-Fidkowski/Thouless strict-locality OBSTRUCTION made explicit -- sharpening v460's verdict from a cited statement to an exhibited topological obstruction. [E] CHERN INTEGER: the FHS Chern of v367's p+ip collar = +1 (chiral M=1), 0 (trivial M=3), -1 (opposite mass). [E] WILSON-LOOP / WANNIER-CENTRE WINDING = CHERN: the hybrid Wannier centre theta(ky) winds by |C|=1 (chiral) and 0 (trivial) over the BZ -- exp-localised Wannier exist IFF winding=0 (Brouder et al.), so the chiral collar has NO exp-localised Wannier basis. [E] OBSTRUCTION INTEGERS TIED: winding=|C|=1!=0 and c_-=16/2=8=g_car+N_fam=rank E8!=0. [E] NEG CONTROL: BOTH phases gapped, yet only the trivial (winding 0) admits exp-localised Wannier and a strict finite-range commuting projector -- it is the CHIRALITY, not the gap. [C]/[O] a strictly finite-range commuting projector would force winding 0, C=0; since C=1!=0 none exists, so v424 sub-step (i)'s realisation is PROVABLY the quasi-local NPW26 LTO net; SEAM.EQUIV.01 stays [O]. 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[E] (E8)_1 TOWER FROM SO(16)_1 SECTORS: the exact Jacobi/E8 identity theta2^8+theta3^8+theta4^8=2E4 gives chi_{(E8)_1}=E4/eta^8 = chi_o^{SO16}+chi_s^{SO16} -- the holomorphic (E8)_1 character IS the SO(16)_1 vacuum+spinor sector sum. [E] 128 SPINOR WEIGHT-1 STATES FILL 120 -> 248: chi_o gives 120, chi_s gives 128, summing to the exact (E8)_1 tower {1,248,4124,34752}. [E] FINITE 16-MAJORANA FOCK: C(16,2)=120 NS bilinear currents and 2^8=256 Ramond ground states = 128 spinor + 128 cospinor. [E] FINITE-L -> CONTINUUM CONVERGENCE: the critical free-fermion ring Casimir gives c_Dirac -> 1 (c_-=8) and the lowest scaled NS gap x_1 -> 1 with |x_1-1| ~ 1/L^2 (L=64..1024). [C]/[O] the rigorous holomorphic extension is supplied by AGT/AMT (v459); SEAM.EQUIV.01 existence (v336) stays [O]. Mixed exact (theta identity + tower + 120/128/256, Wolfram-mirrored) + numerical.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv462_seam_spinor_continuum.py", "sourceSha256": "ded872c95540a51085355cef80a2eb387166ccef8e7e642f81c8ab4cf8e07c59", "linkedClaimIds": [ "SEAM.EQUIV.SPINOR.01" ], "sectionIds": [ "section:6a93c4dd5fe420e1990e", "section:8e4972dbe899b5debb90", "section:9d4f17be173ce81f109e", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d" ], "activeSectionIds": [ "section:8e4972dbe899b5debb90", "section:9d4f17be173ce81f109e", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v462_seam_spinor_continuum.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v462_seam_spinor_continuum.py", "pubMirrorHash": "ded872c95540a51085355cef80a2eb387166ccef8e7e642f81c8ab4cf8e07c59", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v462_seam_spinor_continuum.py" }, { "id": "v463_seam_c8_holomorphic_uniqueness", "filename": "v463_seam_c8_holomorphic_uniqueness.py", "path": "verification/v463_seam_c8_holomorphic_uniqueness.py", "cluster": "frontier", "synopsis": "SEAM.EQUIV.UNIQ.01: the c=8 holomorphic-uniqueness pin -- the positive lever that makes the IDENTIFICATION half of SEAM.EQUIV.01 classification-forced (B of the A+B round). [E] c=8 NOT UNIQUE AT LEVEL 1: c=dim/(1+h^v)=8 has THREE simple solutions -- A8 (80), D8=so(16) (120), E8 (248); c=8 is necessary but NOT sufficient. [E] HOLOMORPHY FORCES dim V_1=248: the only weight-0 form with leading q^{-1/3} and integer coeffs is j^{1/3}=E4/eta^8, q^1 coeff 248. [E] dim 248 + level-1 c=8 => E8 uniquely (248/(1+30)=8); A8/D8 excluded. [E] tower {1,248,4124,34752,213126}=E4/eta^8; E4/eta^8=j^{1/3}. [C] Dong-Mason/Schellekens: holomorphic c=8 VOA unique = V_{E8}; so the identification half of SEAM.EQUIV.01 is [C], leaving the realisation R1 (v464). SEAM.EQUIV.01 stays [O]. Exact (sympy q-series + Lie scan; mpmath) Wolfram-mirrored.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv463_seam_c8_holomorphic_uniqueness.py", "sourceSha256": "970dae3399b411d143b0e02ed052e0b9fe91ededf092f7c23cd4c79265d0c58a", "linkedClaimIds": [ "SEAM.EQUIV.UNIQ.01" ], "sectionIds": [ "section:013b22f7d203ce0c7da1", "section:6a93c4dd5fe420e1990e", "section:8e4972dbe899b5debb90", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:ce5afee193d0ce1ea07e", "section:d90bd5e1e6d8fa41397d" ], "activeSectionIds": [ "section:013b22f7d203ce0c7da1", "section:8e4972dbe899b5debb90", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:ce5afee193d0ce1ea07e" ], "evidenceId": "python_verification:verification/v463_seam_c8_holomorphic_uniqueness.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v463_seam_c8_holomorphic_uniqueness.py", "pubMirrorHash": "970dae3399b411d143b0e02ed052e0b9fe91ededf092f7c23cd4c79265d0c58a", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v463_seam_c8_holomorphic_uniqueness.py" }, { "id": "v464_seam_oneparticle_rigidity", "filename": "v464_seam_oneparticle_rigidity.py", "path": "verification/v464_seam_oneparticle_rigidity.py", "cluster": "frontier", "synopsis": "SEAM.EQUIV.ONEPARTICLE.01: the one-particle RIGIDITY + scaling limit attacking R1, the REALISATION input of SEAM.EQUIV.01 (A of the A+B round). The seam is quasi-free (v113/v160/v161), so by Araki self-dual CAR the whole net is the second quantisation of its one-particle symbol P. [C] ARAKI: state <-> symbol P bijectively. [E] RIGIDITY: the gapped ground state is the UNIQUE quasi-free state with P=projection onto K<0 (P^2=P), K fixed by gap+chirality+reflection (v426). [E] ONE-PARTICLE SCALING LIMIT EXISTS: kernel Cauchy on a fixed window (~1/N). [E] LIMIT IS c=1 DIRAC: entanglement S=(c/3)ln L gives c->1, 16 copies -> c_-=8 (ties v450). [C] Shale-Stinespring: implementable Bogoliubov map; R1 upgraded from a bald axiom to an audited [C]; with v463 the SEAM.EQUIV.01 residual is entirely certification, zero open internal mechanism. SEAM.EQUIV.01 stays [O]. 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TFPT says a CMB EB/TB birefringence angle beta and a quark Cabibbo angle lambda_C=|Vus| (unrelated in the SM) are two readouts of the ONE axiom seed phi0. [E] plumbing: axiom phi0 reproduces the frozen lambda_C, sin^2 theta12, beta to 1e-9. [N] CROSS-SECTOR: back-solving phi0 independently from beta (CMB) and lambda_C (quark) gives the SAME seed within 0.01 sigma_combined. [N] one-parameter fit: error-weighted mean of the 3 back-solved phi0 reproduces the axiom to 0.06%; joint chi^2 at the axiom (0 free params, 3 dof)=0.007, chi^2/dof<1, combined pull 0.08 sigma. [N] theta13 EXCLUSION declared: adding sin^2 theta13 raises chi^2 by ~4 (the ~2 sigma pressure, v328/v338). [N] NEG/POWER: data<->formula shuffle explodes the cluster chi^2 by >5e4x. Consistency statistic (subset of v306); phi0 FIXED by axioms, upgrades no prediction. Python-only.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv465_seed_crosssector_joint.py", "sourceSha256": "7405ad56647f4cc7ab427921830b316cec18ef1fa431c1c25d99c3479a4a4fe9", "linkedClaimIds": [ "SEED.CROSSSECTOR.01" ], "sectionIds": [ "section:0541834291cb75f95ce2", "section:239f008e8aa92b407eb9", "section:7a7de20f53ed3e69fb6f", "section:9736dbf5091605f1747b", "section:990b0c61d0a9e705bf40", "section:9b90248eafa8cb1d0229", "section:ab9e7e520130ecc7da7c", "section:ea55650cbf1afb16c587" ], "activeSectionIds": [ "section:239f008e8aa92b407eb9", "section:7a7de20f53ed3e69fb6f", "section:9736dbf5091605f1747b", "section:ab9e7e520130ecc7da7c", "section:ea55650cbf1afb16c587" ], "evidenceId": "python_verification:verification/v465_seed_crosssector_joint.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v465_seed_crosssector_joint.py", "pubMirrorHash": "7405ad56647f4cc7ab427921830b316cec18ef1fa431c1c25d99c3479a4a4fe9", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v465_seed_crosssector_joint.py" }, { "id": "v466_seed_leptonmass_channel", "filename": "v466_seed_leptonmass_channel.py", "path": "verification/v466_seed_leptonmass_channel.py", "cluster": "registry", "synopsis": "SEED.LEPTONMASS.01: a sixth, new-sector seed channel -- the charged-lepton mass ratio m_e/m_mu=(12/7)phi0^2 points to the SAME axiom seed phi0, extending the empirical seed over-determination (v306/v465) from three measurement sectors to five. [E] plumbing: axiom phi0 reproduces the frozen m_e/m_mu=(12/7)phi0^2=0.00484673 to 1e-9. [N] NEW SECTOR: back-solving phi0 from the measured POLE ratio m_e/m_mu=0.004836 (PDG) gives phi0=0.053113, only -0.11% from the axiom -- a charged-lepton MASS reading, a 4th measurement sector beyond {neutrino mix, CMB, quark mix}. [C] TRANSPORT CAVEAT: the formula is the SOURCE ratio, the datum the POLE ratio; the source->pole shift is the seam-gapped class (bound (2/3)^6=8.78%, v393) but largely cancels for m_e/m_mu, so the 0.11% residual sits far inside the band -- added as a CONSISTENT new sector, not a sharper pin. [N] EXTENDS: the 6-channel cluster (v306's 5 + this) has chi^2/dof<1 and the error-weighted mean stays at the axiom to <0.1%; with the corroborating heavy-quark m_t/m_b (-0.23%) it is a 7-channel, FIVE-sector agreement. [N] NEG/POWER: a data<->formula shuffle explodes the cluster chi^2 by >100x; m_c/m_s=(34/47)/phi0 is scheme-ambiguous (FLAG 11-14), a WEAK channel not counted. [C] HONEST: still the ONE seed (v305 multiplicity 1) -- an EMPIRICAL strengthening, NOT theoretical independence; phi0 FIXED by axioms, upgrades no prediction, closes no gate. 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[E] LR LOCALITY INTEGER: h_s(SO(16)_1) = 16/16 = 1 in Z => statistics phase +1 -- the Longo-Rehren criterion HOLDS, the Z2 simple-current crossed product is a LOCAL index-2 extension (LR RMP 7 (1995); Boeckenhauer RMP 8 (1996); BE CMP 197 (1998)); KLM mu = 4/2^2 = 1 => holomorphic => (E8)_1 (v463 pin, E4/eta^8 q^1 = 248). The AGT/AMT 2024/2025-preprint leg (v459) DEMOTED to independent second witness -- the extension now rests on 1995-2001 peer-reviewed journals. [E] index-4 parallel: mu4 glue h(J^k) = {1,1,1} all integer (= v125 isotropy at net level), mu = 16/16 = 1. [E] R1' invariants computed: FHS Chern 1/0, nu = 16, c_- = 8; nu mod 16 = 0 = the Kitaev-E8 class (16-fold way). [E] chain T1->T4 composes (Kitaev/Kapustin-Spodyneiko -> MMST+Boeckenhauer -> LR/BE+KLM -> Dong-Mason+v463). [C] R1 -> R1': collar_realizes replaceable by collar_invariants (quasi-free [C] + gap [E] + class D + c_-=8 [E from P1]); quasi-freeness stays the ONE [C]. [O] SEAM.EQUIV.01 stays [O]. 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[E] target re-verified: alpha^-1 = 137.0359992168 unique root; Quillen split < 1e-35 (v341/v382). [E] the invariant computed: FHS Chern C(M=1)=1, C(M=3)=0 (the v367/v461 integers, read as the U(1) response). [C] k0 = |C| = 1 under the EM1 reading: the a^3 coefficient EQUALS the computed bulk invariant -- 'why exactly 1' answered by computation + cited inflow (TKNN 1982/ASS 1983 quantisation; Callan-Harvey 1985 inflow; APS/AGDPM/Witten RMP 88 eta=CS part of delta log det; Quillen/Bismut-Freed integrality) -- replacing v435's minimality assumption. [E] k_Y = tr(Y^2)/tr(T3^2) = (5/6)/(1/2) = 5/3 (Ginsparg 1987); (3/5)(41/6) = 41/10 = b1; 41/6 = 20/3 + 1/6. [C] F-normalisation retyped: fixed by k_Y once the seam net is (E8)_1 level 1 -- no dial, ZERO independent content (a face of SEAM.EQUIV.01). [E] UNIFICATION: one invertible phase, two responses -- c_- = 8 (feeds SEAM.EQUIV.01/S3) and C = 1 (feeds EM1); closing R1' (v469) feeds both. [O] the bridge lemma stays cited; ALPHA.QUILLEN.EXACT.01 stays [O]; alpha^-1 stays [E]. 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Replica => EH form on a real operator: dG/d ln m = 2C(gamma) on deficit cones (0.01-0.05%) and replica sheets n=2 (0.8%), n=3 (1.5%); EH coefficient cutoff-independent (0.5% drift) while the zeta-scale mu_lat drifts = the v152 anchor exhibited (no canonical ln(m/mu)=3/4 emerges); BFK/Schur split exact (~1e-16) with the Calderon factor conically clean (pure cut-edge law, tip term 0, power check) and the halves carrying 2C_cone (Kac doubling exact); the v302 transfer masses 6ln(3/2), 6ln3 sit on the calibrated EH line (<=0.05%) and the Perron/attractor mode (m=0) is IR-divergent -- the recovery gap makes the induced-gravity coefficient finite. Honest scope: finite level; SEAM.THEOREM.01 stays open, residual = continuum leg (MMST class, = the SEAM.EQUIV.01 residual) + the anchor. 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[E] Bloch level re-verified: BZ Chern C(M=1)=1, C(M=3)=0, C(M=-1)=-1 (the v470/v367 integers). [E] the Quillen object computed: the same collar h(k) in real space with twisted boundary conditions (the twist torus = moduli of flat U(1) connections); the FHS curvature of the DETERMINANT LINE of the occupied frame over that torus = 1 exactly (1e-9) at M = 1, for L = 4 AND L = 6 (size-independent). [E] controls: trivial M=3 -> 0, orientation flip M=-1 -> -1. [E] two tori, one level: twist-moduli integer == Bloch-BZ integer for all three M (Niu-Thouless-Wu PRB 31 (1985), exhibited on the S3 collar model). [E] section globally defined: Fermi gap 2.0 open over the whole twist torus (the Dai-Freed section has no zero). [C] the reading: det-line holonomy over the U(1) moduli = inflow level k0 = |C| = 1 -- the v470 bridge lemma 'delta log det_zeta(seam) = the inflow response' holds verbatim at the finite/model level. [O] not closed: the abstract-seam zeta-determinant identification (continuum leg, = the SEAM.EQUIV.01 face); ALPHA.QUILLEN.EXACT.01 stays [O]; alpha^-1 stays [E]. 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Rev. D 111, 066001 (2025); arXiv:2408.14391) quantified as an EXTERNAL CANDIDATE for the local volume action behind TFPT's parameter-free Einstein equation (v358/v359, typed 'equation of state, not a from-action quantisation' [O]). [E] carrier Hodge count: her Omega^{0,1,2} fiber on the five-slot carrier C^5 (not 4d spacetime, fiber 1+4+6=11) counts 1+5+10 = 16 = 2^(g_car-1) = dim S+_{D5}, Hodge-folded onto L^even C^5 (vector-space identity only). [E] coefficient match (the one quantitative pin): her weak-coupling L = 3 beta R - alpha L_m matched to 1/(16 pi G) = c3/(2G) fixes beta'_B = c3/6 = 1/(48 pi) exactly; the 6 = 3 blocks x 2 = p2 = |R+(A3)| (echo, not proof). [E] entropy potential: Lambda_G = (1/2 beta)Tr(G - I - ln G) >= 0, quadratic at the fixed point => eps_* = e^{-1/alpha} Q reproduces the v60 branch (3/4 pi^2) e^{-2/alpha} with exact target Tr Q^2 = 32 c3^4 = 1/(128 pi^4) = (2/3) delta_top ([C] until Q constructed). [E] Frullani: her log action = all-scale heat kernel, right genre vs S_rel,chi. [E] R^2 kill test: raw (c3/6)^2 vs Starobinsky 1/(12 c3^7) -- exact gap 3 (8 pi)^9 ~ 1.2e13 (13 orders); direct identification FALSE without a mechanism -- pre-registered. [C] compression conjecture P (G~ g~^-1) P = Delta^1/2 + operator Hodge items open; Lorentzian positivity not automatic (OS route sturdier). [O] nothing closes, zero knobs added. 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[E] CAR => Clifford: ten Gamma's on the carrier Fock space Lambda^* C^5 (dim 2^g_car = 32) satisfy {Gamma_a,Gamma_b} = 2 delta_ab exactly -- the so(10) = D5 Clifford algebra acts on the carrier exterior algebra. [E] S+ = Lambda^even as D5-module: the 45 bilinears commute with (-1)^N, span exactly 45 = dim so(10), zero leak from the 16-dim even subspace -- the half-spinor IS the even exterior algebra WITH its spinor structure (operator level of v2/v44/v197). [E] Hodge-Dirac symbol: c(xi)^2 = -|xi|^2 Id for symbolic xi -- Bianconi's D = d + delta is Clifford multiplication at symbol level. [E] the fold is 5 -> 5bar: traceless u(5) weights of Lambda^4 = negatives of Lambda^1, so the Hodge fold conjugates the vector block -- her fiber 1+5+10 becomes the GUT half-spinor 16 = 1 + 5bar + 10 (the SM carrier decomposition). [E] honest obstruction: Omega^{<=2} is NOT Clifford-invariant (Lambda^2 -> Lambda^3 leak); only Lambda^even is -- the bridge must go through the fold, never degree truncation. [E] Q-target enumeration (the v473 conjecture DECIDED): d k^2 = 32 with integer k has exactly the supports (2,4), (8,2), (32,1) = {|Z2|, rank E8, 2^g_car}; minimal uniform q = c3^2 = 1/(64 pi^2) per Fock mode; the two-form block 10 and the fiber 16 need irrational multipliers => the naive pair-block reading is KILLED; bonus Tr Q^2/delta_top = 32/48 = 2/3. [C] physical Q choice; [O] AP2 compression + R^2 mechanism open, no marker moves. 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[E] max-symmetric eigenvalues (her Appendix-B flattening verified): R~ g~^-1 has eigenvalues exactly {R; R/4 x4; R/6 x6} on a general diagonal 4d metric, incl. the 6x6 two-form flattening. [E] exact vacuum f(R): L_B(R) = -[ln(1-bR) + 4 ln(1-bR/4) + 6 ln(1-bR/6)] = 3 beta R + (17/24) beta^2 R^2 + O(R^3) -- the 3 re-derives her Eq. (45) (the v473 pin), 17/24 the exact tensorial R^2 factor. [E] raw scalaron TRANS-PLANCKIAN: with beta' = c3/6 both routes give m_raw^2 = 4608 pi^2/17 Mbar^2, m_raw ~ 51.7 Mbar ~ 1.3e20 GeV -- heavy, not light (TFPT: c3^{7/2} Mbar = 3.06e13 GeV); required enhancement EXACTLY (72/17)(8 pi)^9 ~ 1.69e13 in mass^2 -- v473's interpretation 2 (light G-trace mode) KILLED in naive form. [E] domain: first log pole at R = 384 pi^2 Mbar^2 (trans-Planckian) -- the obstruction is the mass, not the domain. [E] Lorentzian witness: timelike gradient gives eigenvalue 1 - alpha v^2 <= 0 for v^2 >= 1/alpha (ln undefined); spacelike/Euclidean positive -- the v473 caveat exhibited, the OS route sturdier. [C] verdict: interpretation 1 survives (Einstein + Lambda level), 3 (KMS-spectral renormalisation) is the only surviving R^2 route. [O] unchanged: AP2 compression + the R^2 gate; no marker moves. 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[N] pure gapped bulk: staggered-mass chain, ground-state covariance a projection (pure bulk, thermal boundary -- the seam situation). [N] compression is thermal (v155 in the bridge context): spec(PCP) strictly inside (0,1), Peschel K finite, S > 0. [N] ORDER OBSTRUCTION (the reading decided): on the pure bulk f(x) = x/(1-x) is singular on spec(C) = {0,1} -- the literal operator-side reading P f(C) P is ILL-POSED while f(PCP) is finite: the identity can only be read STATE-SIDE (build Delta_Sigma from the compressed relative metric), matching Bianconi's own local construction -- AP2 retyped, not weakened. [E] block algebra (symbolic): [C^n]_AA - (C_AA)^n carries the cross block twice -- first order vanishes identically, the mismatch is exactly quadratic in cross-cut correlations (= the entanglement content). [N] gap control at the bounded level: bulk identity f(C_T) = e^{-h/T} exact; mismatch obeys d <= x^2 and falls with the gap; decoupled cut exact -- the two readings converge in the gap-dominated regime, where TFPT operates. [C] retyped conjecture; [O] AP2 open (continuum seam statement), no marker moves. Numerical, Python-only by nature.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv476_entropic_compression_toy.py", "sourceSha256": "ec0bcd63b049ecc0119aafe2bd19a37db1ad9d2b2c661da4f829e5e246559d25", "linkedClaimIds": [ "GRAV.ENTROPIC.COMPRESS.01" ], "sectionIds": [ "section:67117a94f5952e2ebab9", "section:671808877239add5f598", "section:6a93c4dd5fe420e1990e", "section:93b8868beb643874af75", "section:9a6aaf6fc60f9b74b301", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d", "section:eb00caf29086b02d5bf5" ], "activeSectionIds": [ "section:67117a94f5952e2ebab9", "section:671808877239add5f598", "section:9a6aaf6fc60f9b74b301", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v476_entropic_compression_toy.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v476_entropic_compression_toy.py", "pubMirrorHash": "ec0bcd63b049ecc0119aafe2bd19a37db1ad9d2b2c661da4f829e5e246559d25", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v476_entropic_compression_toy.py" }, { "id": "v477_entropic_scaleflow", "filename": "v477_entropic_scaleflow.py", "path": "verification/v477_entropic_scaleflow.py", "cluster": "frontier", "synopsis": "GRAV.ENTROPIC.SCALEFLOW.01: the scale-flow representation of the entropic action -- v475's surviving interpretation 3 typed precisely: the (72/17)(8 pi)^9 gap collapses to ONE moment condition on the scale weight, satisfied by the SAME KMS moment TFPT already fixes (v36 f0 <-> M^2 = c3^7 Mbar^2); zero new dials, nothing closes. [E] scale-flow identity: -ln A = flat scale-integral of relative heat-kernel actions (Frullani symbolic + 1e-20 quadrature of the chi-form) -- TFPT's S_rel,chi evaluates ONE KMS scale with a weight: the bridge is a choice of scale measure. [E] moment dictionary: weight w(t) dt/t gives 3 beta R mu1 + (17/24) beta^2 R^2 mu2; flat weight = unit moments = the v475 raw coefficients. [E] the one moment condition: demanding m^2 = c3^7 Mbar^2 forces exactly mu2/mu1^2 = (72/17)(8 pi)^9 -- the kill-test number IS a moment ratio, and the closure (4608 pi^2/17)/((72/17)(8 pi)^9) = c3^7 holds identically: the 13 orders are a scale-measure datum, not a bridge mismatch. [E] v36 consistency: same mass from f0 = 6(4 pi)^2/c3^7 -- one KMS moment, two parametrisations. [C] consistency not derivation (the weight is TFPT input); negative side-record: the exact lattice-BW commutator attempt for AP2 did not hold in simple forms (logged, kept out). [O] unchanged.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv477_entropic_scaleflow.py", "sourceSha256": "cef5988c2693f66333cdf81d1d5e7a44f22aad8f6c68ee7ddd3b5bb7df80cf88", "linkedClaimIds": [ "GRAV.ENTROPIC.SCALEFLOW.01" ], "sectionIds": [ "section:671808877239add5f598", "section:8f73277edff787de34d0", "section:93b8868beb643874af75", "section:9a6aaf6fc60f9b74b301", "section:ab9e7e520130ecc7da7c", "section:eb00caf29086b02d5bf5" ], "activeSectionIds": [ "section:671808877239add5f598", "section:8f73277edff787de34d0", "section:9a6aaf6fc60f9b74b301", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v477_entropic_scaleflow.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v477_entropic_scaleflow.py", "pubMirrorHash": "cef5988c2693f66333cdf81d1d5e7a44f22aad8f6c68ee7ddd3b5bb7df80cf88", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v477_entropic_scaleflow.py" }, { "id": "v478_entropic_continuum_legs", "filename": "v478_entropic_continuum_legs.py", "path": "verification/v478_entropic_continuum_legs.py", "cluster": "frontier", "synopsis": "GRAV.ENTROPIC.LEGS.01: first computable steps on the two remaining legs of the entropic-action bridge. LEG A (AP2 continuum): [N] the compressed critical interval has S(L) = (c/3) ln L + k with c_est = 1.00089/1.00038/1.00021 (monotone -> Dirac c = 1; gapped control ~6e-8, area law); the Peschel modular Hamiltonian's NN couplings organise on the CHM weight beta(x) = x(L-x)/L (corr 0.87 -> 0.99, plateau drift shrinking); even-range bands vanish identically and the odd tail is 1.8% with parabolic envelope -- the state-side Delta_Sigma (v476's forced reading) flows to the CHM/BW geometric form that TFPT's Einstein derivation consumes (v323/v358): the bridge's modular side and TFPT's gravity side meet in the continuum limit. LEG B (measure): [E] single-scale corollary -- mu2/mu1^2 = e^{t0} exactly, so the v477 condition forces t0 = ln(72/17) + 9 ln(8 pi) = 30.461 (exact closed form); the near-miss to h(E8) = 30 is explicitly DECLINED (v354/v355 discipline); deriving the measure stays open. [C] meeting point; [O] both legs, no marker moves. High-precision numerical (mpmath 50 digits), Python-only by nature.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv478_entropic_continuum_legs.py", "sourceSha256": "ddf0bd549c65c69d8eaef9653b58a4332a080ffb3a52e5aacf06768c69d13b2b", "linkedClaimIds": [ "GRAV.ENTROPIC.LEGS.01" ], "sectionIds": [ "section:136a1e576865c1424f29", "section:51b5da5a67a36e5155ae", "section:671808877239add5f598", "section:697c671889813baf24f5", "section:6a93c4dd5fe420e1990e", "section:8f5691e12b337bb463ce", "section:93b8868beb643874af75", "section:9a6aaf6fc60f9b74b301", "section:9f2ef8163653328e6c3e", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:d90bd5e1e6d8fa41397d", "section:db9b59159ab5489cccfa", "section:e99d6098550f62e277de", "section:eb00caf29086b02d5bf5" ], "activeSectionIds": [ "section:671808877239add5f598", "section:697c671889813baf24f5", "section:8f5691e12b337bb463ce", "section:9a6aaf6fc60f9b74b301", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:db9b59159ab5489cccfa", "section:e99d6098550f62e277de" ], "evidenceId": "python_verification:verification/v478_entropic_continuum_legs.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v478_entropic_continuum_legs.py", "pubMirrorHash": "ddf0bd549c65c69d8eaef9653b58a4332a080ffb3a52e5aacf06768c69d13b2b", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v478_entropic_continuum_legs.py" }, { "id": "v479_kronheimer_quiver_bridge", "filename": "v479_kronheimer_quiver_bridge.py", "path": "verification/v479_kronheimer_quiver_bridge.py", "cluster": "core", "synopsis": "SEAM.KRONHEIMER.01: the R3 'combinatorial-to-geometric bridge' of the det K=1 keystone (SEAM.DETK.01/v344) is Kronheimer's theorem (JDG 29 (1989) 665+685) with all finite input data already compiler outputs. [E] Kac marks = null vector of the affine-E8 Cartan AND Perron vector (A delta = 2 delta) = the v312 rewrite-attractor vector; [E] hyper-Kaehler quotient dimension count dim_R X = 4 (the C^2/Gamma geometry), with sum_edges d_i d_j = sum d_i^2 = 120 forced by the null identity; [E] gauge datum = |2I| = 120 = |mu4| h(E8), h(E8) = 30 = 2*3*5; [E] resolution = 8 spheres with unimodular -E8 form (det 1 = Poincare link = the det K=1 face) and 24 = 3*rank deformation parameters. [C] Kronheimer cited, not re-proved (import class of NPW26/MMST/AGT). [O] the residual premise transforms to 'the raw seam supplies the ALE/orbifold datum' -- the same single arrow as SEAM.EQUIV.01; nothing closes.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv479_kronheimer_quiver_bridge.py", "sourceSha256": "c3d627fa57516c5127778380f92d49dc87a21cb45391f5482c23995ce9ad331e", "linkedClaimIds": [ "SEAM.KRONHEIMER.01" ], "sectionIds": [ "section:2585b5d786c3bdb7ddb7", "section:2b8d2aba4baeb7a0c36b", "section:303925994b6f141b3a0e", "section:307c4c95a7c84b5efc0b", "section:6a93c4dd5fe420e1990e", "section:6e8f8f12ea28ee07020a", "section:701d23928f8e38ea7d4b", "section:70380cf4813f5dcd47e6", "section:a153934887244824336d", "section:a7805cce6b04546f1147", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:d90bd5e1e6d8fa41397d", "section:e99d6098550f62e277de", "section:fb4cf64c8cbaeb3f6d74", "section:fe85126d1b3e41ef8954" ], "activeSectionIds": [ "section:2585b5d786c3bdb7ddb7", "section:6e8f8f12ea28ee07020a", "section:70380cf4813f5dcd47e6", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:e99d6098550f62e277de", "section:fb4cf64c8cbaeb3f6d74", "section:fe85126d1b3e41ef8954" ], "evidenceId": "python_verification:verification/v479_kronheimer_quiver_bridge.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v479_kronheimer_quiver_bridge.py", "pubMirrorHash": "c3d627fa57516c5127778380f92d49dc87a21cb45391f5482c23995ce9ad331e", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v479_kronheimer_quiver_bridge.py" }, { "id": "v480_multilocal_four_interval", "filename": "v480_multilocal_four_interval.py", "path": "verification/v480_multilocal_four_interval.py", "cluster": "frontier", "synopsis": "QGEO.MULTILOCAL.01: the four mu4 marks make the seam circle a FOUR-INTERVAL free-fermion geometry -- the class whose multi-interval modular theory is exactly known (Casini-Huerta mixing term; Longo-Xu; Rehren-Tedesco multilocal fermions; KLM: holomorphic <=> trivial multi-interval inclusion, mu=1 -- the same bit as det K=1). On the exactly solvable antiperiodic ring: [E-num] binary clock rho^4 = -1 exactly (the fermionic mu4 clock is the order-8 double-cover lift, the same Z2-lift pattern as 2I over I); [E-num] the primitive-8th-root character projectors decouple the 4-interval covariance at 1e-15 (the multilocal diagonal-cover isomorphism); [E-num] each sector = single-interval quarter-ring kernel with twist lambda_k, spectra match at 1e-14; [E-num] rho C rho^-1 = C at 1e-14 => omega o rho = omega MANIFEST at the state level; [E-num] negative control: one displaced interval re-couples sectors at 1e-2; [N] cross-interval K peaks on the conjugate diagonal (Casini-Huerta mixing shadow). [C] continuum theory cited; [O] the raw-seam premise stays open -- mechanism exhibited, not closed.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv480_multilocal_four_interval.py", "sourceSha256": "29cf4907d3f6eb670ed6e82f8a449374205f8149be74d792a7404bbf8caf501e", "linkedClaimIds": [ "QGEO.MULTILOCAL.01" ], "sectionIds": [ "section:0794eefc4054e642456a", "section:1d121fa86acdab3e383f", "section:2525c189f32461c9368a", "section:2585b5d786c3bdb7ddb7", "section:6a93c4dd5fe420e1990e", "section:6cd1a267e72b20619327", "section:6d6494c465792be08ad9", "section:888628823bf71f709698", "section:93b8868beb643874af75", "section:9a6aaf6fc60f9b74b301", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:b93e6ae7b00f32ee1201", "section:d90bd5e1e6d8fa41397d", "section:e99d6098550f62e277de", "section:eb00caf29086b02d5bf5", "section:f5274c8105ff62e99dcd", "section:fe85126d1b3e41ef8954" ], "activeSectionIds": [ "section:2585b5d786c3bdb7ddb7", "section:888628823bf71f709698", "section:9a6aaf6fc60f9b74b301", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:e99d6098550f62e277de", "section:f5274c8105ff62e99dcd", "section:fe85126d1b3e41ef8954" ], "evidenceId": "python_verification:verification/v480_multilocal_four_interval.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v480_multilocal_four_interval.py", "pubMirrorHash": "29cf4907d3f6eb670ed6e82f8a449374205f8149be74d792a7404bbf8caf501e", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v480_multilocal_four_interval.py" }, { "id": "v481_seesaw_carrier_ladder", "filename": "v481_seesaw_carrier_ladder.py", "path": "verification/v481_seesaw_carrier_ladder.py", "cluster": "neutrinos", "synopsis": "FLAV.NUSCALE.02: the absolute neutrino-mass scale under the CARRIER Yukawa normalisation y_nu = y_t -- FLAV.NUSCALE.01's two-parameter (y_nu, M_R) trade-off collapses to ONE parameter, and the required M_R lands INSIDE the compiler's own PS window; the nearby integer c3-rung is explicitly DECLINED at 1-loop (anti-numerology). [P] carrier normalisation (named premise): one SO(10) 16 per family + minimal Yukawa sector (10_H / PS (1,2,2)) => y_nu = y_t at the matching scale. [N] inversion: m_3 = 0.0503 eV demands M_R = 9.3e13 GeV, inside [4.2e13, 2.4e15] (v249), at log_c3(Mbar/M_R) = 3.15 (y_nu = 1 gives the structureless 2.58). [X] integer-rung honesty gate: M_R = c3^3 Mbar predicts m_3 = 0.030 eV (40% low at 1-loop; ADKLR run-down 0.794) -- NEAR, not ON: pin DECLINED; decision computation named (2-loop + PS thresholds). [N] falsifiable band [0.002, 0.115] eV brackets the observation; DESI cuts the window from below; NO floor Sigma = 0.059 eV. [C]/[O] candidate class (genre v467/v468); frozen record untouched; nothing closes.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv481_seesaw_carrier_ladder.py", "sourceSha256": "bfd4843fe1df88c3a4f18d9edffe572f28a524fd7c91ef10d404e6dd309bb270", "linkedClaimIds": [ "FLAV.NUSCALE.02" ], "sectionIds": [ "section:213a1f15f7373957fc2f", "section:51b5da5a67a36e5155ae", "section:64a9e573649942dd32e9", "section:697c671889813baf24f5", "section:ab9e7e520130ecc7da7c", "section:c00f76407fefd9782fd7", "section:db9b59159ab5489cccfa", "section:e77e5218c82783443690", "section:e99798f44eef9d7cdf0c", "section:e99d6098550f62e277de", "section:fe85126d1b3e41ef8954" ], "activeSectionIds": [ "section:213a1f15f7373957fc2f", "section:64a9e573649942dd32e9", "section:697c671889813baf24f5", "section:ab9e7e520130ecc7da7c", "section:c00f76407fefd9782fd7", "section:db9b59159ab5489cccfa", "section:e77e5218c82783443690", "section:e99798f44eef9d7cdf0c", "section:e99d6098550f62e277de", "section:fe85126d1b3e41ef8954" ], "evidenceId": "python_verification:verification/v481_seesaw_carrier_ladder.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v481_seesaw_carrier_ladder.py", "pubMirrorHash": "bfd4843fe1df88c3a4f18d9edffe572f28a524fd7c91ef10d404e6dd309bb270", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v481_seesaw_carrier_ladder.py" }, { "id": "v482_seesaw_rung_decision", "filename": "v482_seesaw_rung_decision.py", "path": "verification/v482_seesaw_rung_decision.py", "cluster": "neutrinos", "synopsis": "FLAV.NUSCALE.03: the decision computation named by v481, EXECUTED in bracketed form -- the integer rung M_R = c3^3 Mbar is EXCLUDED as an unstructured exact pin (conditional on the carrier premise y_nu = y_t). [E-num] gap: m_3(rung) = 0.0301 eV vs 0.0503 observed, rescue factor x1.670; [E-num] bracketed exclusion: m_t +-3 GeV (>3 sigma), alpha_s >3 sigma, kappa run-down +-10%, PS-leg beta envelope x[0.5,1.5] -- max single shift x1.10, all-favourable combined x1.165, far below x1.670: the 1-loop miss is NOT an RG artifact. [C] named escape recorded and DECLINED: only a third-generation Majorana structure factor r ~ 1.67 revives the rung; post-hoc r = 1.6696 sits 0.18% from g_car/N_fam = 5/3 -- no forcing mechanism, declined per the anti-numerology rule (the t0 ~ 30 pattern). [O] the v481 one-parameter window candidate stands unchanged; frozen record untouched; nothing closes.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv482_seesaw_rung_decision.py", "sourceSha256": "bc09d14f1352641742c9f5d0bb81370e91ca8a9dfc7ca9e243640975d8035195", "linkedClaimIds": [ "FLAV.NUSCALE.03" ], "sectionIds": [ "section:51b5da5a67a36e5155ae", "section:697c671889813baf24f5", "section:ab9e7e520130ecc7da7c", "section:c00f76407fefd9782fd7", "section:db9b59159ab5489cccfa", "section:e99798f44eef9d7cdf0c" ], "activeSectionIds": [ "section:697c671889813baf24f5", "section:ab9e7e520130ecc7da7c", "section:c00f76407fefd9782fd7", "section:db9b59159ab5489cccfa", "section:e99798f44eef9d7cdf0c" ], "evidenceId": "python_verification:verification/v482_seesaw_rung_decision.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v482_seesaw_rung_decision.py", "pubMirrorHash": "bc09d14f1352641742c9f5d0bb81370e91ca8a9dfc7ca9e243640975d8035195", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v482_seesaw_rung_decision.py" }, { "id": "v483_pillowcase_exact_traces", "filename": "v483_pillowcase_exact_traces.py", "path": "verification/v483_pillowcase_exact_traces.py", "cluster": "core", "synopsis": "HYP.PHI0.GEOM.01: the GEOMETRIC side of the phi0 puncture target (HYP.PHI0.PUNCTURE.01/v408) is EXACT -- every twisted/orbifold heat trace of the flat tau = i pillowcase is a t-INDEPENDENT RATIONAL, so the pi^-4 in dtop = 48 c3^4 cannot come from flat orbifold geometry at any order. [E-num] Tr(gamma e^{t Delta}) = 1 exactly for gamma = sigma, rho, rho^3 at every tested t (position-space Gaussian image sums < 1e-9; mode-space proof: only n = 0 is gamma-diagonal); [E] Atiyah-Bott match: 4 x 1/4 (det = 4 = |mu4|) and 2 x 1/2 (det = 2 = |Z2|); [E] pillowcase contact term exactly 1/2 = 4 x 1/8 per mark, clock-equivariant trace exactly 1, all t. [E]/[O] the reduction: dtop's analytic content must sit in the per-insertion coupling normalisation (4 = |mu4| insertions of weight c3 -> c3^4, multiplicity Omega_adm = 48; the bare 1/(2pi) 4-cycle differs by the exact rational 3/16) -- the one remaining [O] is the rule 'per-mark weight = c3' (same class as EM.WARD.02). Target narrows from 'derive the term' to 'derive the weight'; stays open.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv483_pillowcase_exact_traces.py", "sourceSha256": "3c74db8bb4ae0a77acdb5f76f7c68afcbee65d45a83e24011cb5f305538c3847", "linkedClaimIds": [ "HYP.PHI0.GEOM.01" ], "sectionIds": [ "section:09b49009253acb5a0dfb", "section:1fa633590a33e985ed41", "section:25a3a7ca87e0691a61b8", "section:3cc790136e8b9bd3c188", "section:3d3092d4174b4ba2e0ec", "section:584e87a9c163ac38f92f", "section:6a757c5701557192653a", "section:ab9e7e520130ecc7da7c", "section:db9b59159ab5489cccfa", "section:eb0bd97fda8c0fedefad" ], "activeSectionIds": [ "section:25a3a7ca87e0691a61b8", "section:584e87a9c163ac38f92f", "section:6a757c5701557192653a", "section:ab9e7e520130ecc7da7c", "section:db9b59159ab5489cccfa" ], "evidenceId": "python_verification:verification/v483_pillowcase_exact_traces.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v483_pillowcase_exact_traces.py", "pubMirrorHash": "3c74db8bb4ae0a77acdb5f76f7c68afcbee65d45a83e24011cb5f305538c3847", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v483_pillowcase_exact_traces.py" }, { "id": "v484_seam_contact_unit", "filename": "v484_seam_contact_unit.py", "path": "verification/v484_seam_contact_unit.py", "cluster": "core", "synopsis": "SEAM.CONTACT.UNIT.01: the shared 'c3 per boundary insertion' rule of the two open analytic targets (ALPHA.QUILLEN.EXACT.01 c3-ladder {0,3,6}; HYP.PHI0.PUNCTURE.01 per-mark weight c3) is ONE identity and NOT a new unknown: it is the KMS seam unit 2pi = 1/(4c3) with 1/4 = 1/|mu4| (v239) -- one bare boundary propagator orbit-averaged over the four marks. [E] unit chain 1/(2pi) = 4c3 = |mu4| c3 = |Z2| chi(S^2) c3; [E] mechanism derived on the seam circle: G(d) = -(1/pi) ln|2 sin(d/2)| takes INTEGER multiples of c3 ln2 at the mu4 separations (G_marks = -4 c3 ln2 circ(0,1,2,1), spec {4,-2,0,-2}); the orbit-averaged insertion carries exactly -(c3 ln2) C, so the log-det contact expansion is exactly graded in c3 per insertion (Tr C^k = 4^k + 2(-2)^k integer); [E] the grammar is suite-wide: Lambda prefactor 3/(4pi^2) = 48 c3^2 (v60) = the same Omega_adm = 48 as the phi0 puncture at two insertions; g-2 divides by the same 2pi = 1/(4c3). [C]/[O] the two [O] targets MERGE into one named analytic step (diagonal zeta-renormalisation + multiplicity matching); finite cycle sector proven; nothing closes, no coefficient claimed.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv484_seam_contact_unit.py", "sourceSha256": "a7fa16d50ee4fd70c4093f7e5b12837d160784b97d05014d774e0f2bf6db94e4", "linkedClaimIds": [ "SEAM.CONTACT.UNIT.01" ], "sectionIds": [ "section:09b49009253acb5a0dfb", "section:1fa633590a33e985ed41", "section:25a3a7ca87e0691a61b8", "section:3cc790136e8b9bd3c188", "section:3d3092d4174b4ba2e0ec", "section:584e87a9c163ac38f92f", "section:67ccc4df3b51f6dae230", "section:6a757c5701557192653a", "section:6e8f8f12ea28ee07020a", "section:7144b70a605254dfecbc", "section:a3b94e09ceb6d6dbdae4", "section:ab9e7e520130ecc7da7c", "section:aeb16d254373e2e88a13", "section:c852f8ae0a03109ca8ad", "section:c9d9fdab1f8620914792", "section:ca7a45590bd2289527ff", "section:d1b557c6c16fcdfd5e58", "section:daecafc150c9651ad391", "section:eb0bd97fda8c0fedefad" ], "activeSectionIds": [ "section:25a3a7ca87e0691a61b8", "section:584e87a9c163ac38f92f", "section:6a757c5701557192653a", "section:6e8f8f12ea28ee07020a", "section:7144b70a605254dfecbc", "section:ab9e7e520130ecc7da7c", "section:aeb16d254373e2e88a13", "section:c852f8ae0a03109ca8ad", "section:d1b557c6c16fcdfd5e58" ], "evidenceId": "python_verification:verification/v484_seam_contact_unit.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v484_seam_contact_unit.py", "pubMirrorHash": "a7fa16d50ee4fd70c4093f7e5b12837d160784b97d05014d774e0f2bf6db94e4", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v484_seam_contact_unit.py" }, { "id": "v485_contact_diagonal_closed", "filename": "v485_contact_diagonal_closed.py", "path": "verification/v485_contact_diagonal_closed.py", "cluster": "core", "synopsis": "SEAM.CONTACT.UNIT.02: the diagonal channel of the merged analytic target (v484) settled at the computable level -- the merged residual collapses onto the keystone. [E] diagonal zero at the KMS scale: G_reg(0; l) = (1/pi) ln(l/2pi) exactly, vanishing iff l = 2pi = 1/(4c3) (the v239 KMS circumference) -- the seam scale is the unique zero-self-energy scheme point; [E] the log is the pure scale channel, matching F_U(1)'s single log term (transport 8b1 c3^6 ln(1/phi_seam)) vs the log-free phi0 split; [E] closed-form resummation (BFK route, v151 class): det(I - uC) = (1-4u)(1+2u)^2 with u = eps c3 ln2 -- all orders, linear term absent because the diagonal vanishes (Tr C = 0), series = v484's Tr(C^k); [E] weight dichotomy: the SAME 48 = 3x16 states counted flat give the phi0 multiplicity 48 = Omega_adm, and Y^2/loop/GUT-weighted give the alpha budget 41 = 10b1 = 40 + 1 (Tr_16 Y^2 = 10/3 exact, Ginsparg (3/5)(41/6) = 41/10). [C]/[O] with v484 every finite piece of the merged target is proven; the single remaining [O] is the abstract-seam zeta-det identification = a face of SEAM.EQUIV.01 (the v382 typing, now substantiated). Nothing closes.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv485_contact_diagonal_closed.py", "sourceSha256": "a16d73c188354f7e46d2b658e620449304236f54a6237b0d4cc91b61433a7e91", "linkedClaimIds": [ "SEAM.CONTACT.UNIT.02" ], "sectionIds": [ "section:09b49009253acb5a0dfb", "section:1fa633590a33e985ed41", "section:3cc790136e8b9bd3c188", "section:3d3092d4174b4ba2e0ec", "section:584e87a9c163ac38f92f", "section:67ccc4df3b51f6dae230", "section:6a757c5701557192653a", "section:6e8f8f12ea28ee07020a", "section:7144b70a605254dfecbc", "section:7779d02d30f1856735de", "section:a3b94e09ceb6d6dbdae4", "section:ab9e7e520130ecc7da7c", "section:c852f8ae0a03109ca8ad", "section:ca7a45590bd2289527ff", "section:d1b557c6c16fcdfd5e58", "section:e99798f44eef9d7cdf0c", "section:eb0bd97fda8c0fedefad" ], "activeSectionIds": [ "section:584e87a9c163ac38f92f", "section:6a757c5701557192653a", "section:6e8f8f12ea28ee07020a", "section:7144b70a605254dfecbc", "section:ab9e7e520130ecc7da7c", "section:c852f8ae0a03109ca8ad", "section:d1b557c6c16fcdfd5e58", "section:e99798f44eef9d7cdf0c" ], "evidenceId": "python_verification:verification/v485_contact_diagonal_closed.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v485_contact_diagonal_closed.py", "pubMirrorHash": "a16d73c188354f7e46d2b658e620449304236f54a6237b0d4cc91b61433a7e91", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v485_contact_diagonal_closed.py" }, { "id": "v486_transfer_full_rule", "filename": "v486_transfer_full_rule.py", "path": "verification/v486_transfer_full_rule.py", "cluster": "core", "synopsis": "HYP.REWRITE.02: the FULL physical transfer spectrum {1, (2/3)^6, (1/3)^6} now has ONE local recursive generator -- the lazy Z2-pair walk. [E] uniqueness: the symmetric 3-channel rule M(s,h) (one absorbing family channel + Z2 pair) has survival spectrum {s+h, s-h}; demanding the physical pair {2/3, 1/3} forces uniquely (stay, hop, leak) = (1/2, 1/6, 1/3) = (1/|Z2|, 1/(|Z2| N_fam), 1/N_fam); [E] over the order-6 = 2 N_fam = |R+(A3)| hand it generates eig(B^6) = {64/729, 1/729} exactly -- the previously generator-less (1/3)^6 mode gets its origin (subdominant gap 6 ln 3, alongside the recovery gap 6 ln(3/2)); [E] v327's uniform rule (spectrum {2/3, 0}) can never produce the third mode under any power -- superseded as full-spectrum generator (its 2/3 arity story unchanged); [O] the arity {2,3} stays the anchor input and the lazy-vs-uniform split is selected by the physical spectrum (named candidate: stay = 1/|Z2| as the sheet-symmetric choice). Exact, nothing closes.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv486_transfer_full_rule.py", "sourceSha256": "a8315978fb4ecbb4d178754483b03915c1016995667ac1ab7a0ea6e8dacb5825", "linkedClaimIds": [ "HYP.REWRITE.02" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:09b49009253acb5a0dfb", "section:10e10da547a5ac9014b8", "section:3cc790136e8b9bd3c188", "section:3d01f167d55724948536", "section:497660cf26cb0410a678", "section:4d7b24e6cd695cd3409f", "section:584e87a9c163ac38f92f", "section:6c4044608163b007c4c2", "section:6e8f8f12ea28ee07020a", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:a9e4936094020237f825", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:ccaa58843679b0b5ee13", "section:e9ee831b73445d2d858c", "section:eb0bd97fda8c0fedefad" ], "activeSectionIds": [ "section:10e10da547a5ac9014b8", "section:3d01f167d55724948536", "section:497660cf26cb0410a678", "section:4d7b24e6cd695cd3409f", "section:584e87a9c163ac38f92f", "section:6c4044608163b007c4c2", "section:6e8f8f12ea28ee07020a", "section:ab9e7e520130ecc7da7c", "section:ccaa58843679b0b5ee13" ], "evidenceId": "python_verification:verification/v486_transfer_full_rule.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v486_transfer_full_rule.py", "pubMirrorHash": "a8315978fb4ecbb4d178754483b03915c1016995667ac1ab7a0ea6e8dacb5825", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v486_transfer_full_rule.py" }, { "id": "v487_transfer_clock_rungs", "filename": "v487_transfer_clock_rungs.py", "path": "verification/v487_transfer_clock_rungs.py", "cluster": "core", "synopsis": "HYP.REWRITE.03: the lazy split (1/2, 1/6) is FORCED by the resummed clock -- the v486 [O] 'split selection' closes onto v124 structure. [E] rung reading: the lazy rule's one-step spectrum is EXACTLY the complete v124 clock ladder below the wall, eig(M) = {1 - n/3 : n = 0,1,2} = {1, 2/3, 1/3}; v327's uniform rule puts its second pair mode ON the wall (0 = 1 - 3/3). [E] deck parity = rung index: the sigma-even mode carries rung 1 (survival 2/3), the sigma-odd mode rung 2 (survival 1/3) -- each clock step flips the deck parity (the structural home of the v486 parity assignment tested by frb-parity-comb). [E] forcing: faithful ladder (definitional for a full-spectrum generator) + Z2 equivariance + rates >= 0 force uniquely both the split (1/2, 1/6) and the assignment even -> rung 1, odd -> rung 2 (the swap needs hop = -1/6 < 0). [E] bend corollary: omega_1/omega_2 = rate(2)/rate(1) = log_{3/2} 3 -- the parity-comb tone ratio IS the v107/v124 bend. [O] channel count 3 forced by the wall; the ladder stays an [I] identity on frozen spectra (R1/[P] open); arity {2,3} stays the anchor input.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv487_transfer_clock_rungs.py", "sourceSha256": "0c234246906ab637aabd816271b9f733082a1f94021db67b8fa2d4f6c63e560c", "linkedClaimIds": [ "HYP.REWRITE.03" ], "sectionIds": [ "section:09b49009253acb5a0dfb", "section:1787029b68f0eb53a6b8", "section:3cc790136e8b9bd3c188", "section:3d01f167d55724948536", "section:497660cf26cb0410a678", "section:584e87a9c163ac38f92f", "section:6e8f8f12ea28ee07020a", "section:ab9e7e520130ecc7da7c", "section:ccaa58843679b0b5ee13", "section:cfd578b68dd4260cb765", "section:eb0bd97fda8c0fedefad" ], "activeSectionIds": [ "section:3d01f167d55724948536", "section:497660cf26cb0410a678", "section:584e87a9c163ac38f92f", "section:6e8f8f12ea28ee07020a", "section:ab9e7e520130ecc7da7c", "section:ccaa58843679b0b5ee13" ], "evidenceId": "python_verification:verification/v487_transfer_clock_rungs.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v487_transfer_clock_rungs.py", "pubMirrorHash": "0c234246906ab637aabd816271b9f733082a1f94021db67b8fa2d4f6c63e560c", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v487_transfer_clock_rungs.py" }, { "id": "v488_majorana_clebsch_door", "filename": "v488_majorana_clebsch_door.py", "path": "verification/v488_majorana_clebsch_door.py", "cluster": "flavor", "synopsis": "FLAV.NUSCALE.04: the 3/5 Clebsch door of the seesaw rung, enumerated and CLOSED -- v482's named escape (a third-generation Majorana factor r ~ 1.6696, 0.18% from g_car/N_fam = 5/3) is decided NEGATIVE at the group-theory level. [E] no renormalisable channel: sym^2(16) = 136 = 10 + 126 and the 126bar is not in the E8 hull (v247) -- M_R only via the d=5 operator (16 16bar_H)^2/Lambda; [E] channel list 16 x 16bar = 1 + 45 + 210 with only singlet + 45 admissible; [E] charge table: (B-L, T_3R, Y)(nu^c) = (+1, -1/2, 0), Tr_16 Y^2 = 10/3; [E] the {2,3}-smooth theorem: every nu^c channel weight is {2,3}-smooth, so no channel combination reaches 5/3 -- and the unique natural 5 of the embedding (k_Y = 5/3, v470) is decoupled because Y(nu^c) = 0 exactly; [E] Clebsches are generation-blind (family-space scalars) -- diag(1,1,3/5) cannot arise from group theory; [O] compiler-flavor 3/5 inventory typed and declined (wrong slots only). The rung + 5/3 rescue is dead; the v481 window candidate stands.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv488_majorana_clebsch_door.py", "sourceSha256": "d02c476855902a91cafe410a597060b8f8e76125d87a574043ec9f603660ddbd", "linkedClaimIds": [ "FLAV.NUSCALE.04" ], "sectionIds": [ "section:51b5da5a67a36e5155ae", "section:62da8d57db3260c78314", "section:64a9e573649942dd32e9", "section:697c671889813baf24f5", "section:6e8f8f12ea28ee07020a", "section:ab9e7e520130ecc7da7c", "section:e99798f44eef9d7cdf0c" ], "activeSectionIds": [ "section:64a9e573649942dd32e9", "section:697c671889813baf24f5", "section:6e8f8f12ea28ee07020a", "section:ab9e7e520130ecc7da7c", "section:e99798f44eef9d7cdf0c" ], "evidenceId": "python_verification:verification/v488_majorana_clebsch_door.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v488_majorana_clebsch_door.py", "pubMirrorHash": "d02c476855902a91cafe410a597060b8f8e76125d87a574043ec9f603660ddbd", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v488_majorana_clebsch_door.py" }, { "id": "v489_seam_modular_commutator", "filename": "v489_seam_modular_commutator.py", "path": "verification/v489_seam_modular_commutator.py", "cluster": "core", "synopsis": "SEAM.CCC.01: the chiral central charge c_- = 8 measured DIRECTLY from the bulk ground state of the v367 seam lattice model, via the Kim-Shehab-Kim modular commutator J(A,B,C) = i Tr(rho_ABC [K_AB, K_BC]) = (pi/3) c_- on a 120-degree pie tripartition -- the first ground-state witness for premise (i) of SEAM.EQUIV.01 (c_- = 8) INDEPENDENT of both the Chern route (v367) and the KLM counting route (v378); everything reduces to the Peschel Majorana covariance (W = -2 artanh Gamma). [E] purity: eig(i Gamma) = +-1 to 6e-15 (exact BdG ground state). [E] per-layer c_- = 0.499998 (L=32, R=12; 0.499793 at L=16 -> 0.500000 at L=48, dev -1.8e-7). [E] controls: trivial M=3 -> 0.000000, orientation flip M=-1 -> -0.499986. [E] layer additivity exact (1.4e-14). [E] 16-layer carrier: direct c_- = 7.9967 (L=16; L=24 gives 7.999781), additivity route 8.0000 = g_car + N_fam. [E] clip invariance 5e-8. [O] honest fence: pins c_- = 8 on the lattice ground state; does NOT close SEAM.EQUIV.01 (continuum limit MMST v336 stays [O], mu4 condensation stays the cited KLM step v378). Numerical (numpy), Python-only by nature.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv489_seam_modular_commutator.py", "sourceSha256": "bb5038d567c8d14b7eb67546974311c6edf547a961581864e1af9f77f5211684", "linkedClaimIds": [ "SEAM.CCC.01" ], "sectionIds": [ "section:67f92d5b57079948ad55", "section:6a93c4dd5fe420e1990e", "section:7b5da22330a89ad066dc", "section:8e4972dbe899b5debb90", "section:ab9e7e520130ecc7da7c", "section:cb1bdab881371b610e8f", "section:d3f2b7d7ec6acb95794a", "section:d90bd5e1e6d8fa41397d", "section:eea2436d67f35ca41c00", "section:fa69e504a169a4dd0514" ], "activeSectionIds": [ "section:67f92d5b57079948ad55", "section:7b5da22330a89ad066dc", "section:8e4972dbe899b5debb90", "section:ab9e7e520130ecc7da7c", "section:eea2436d67f35ca41c00", "section:fa69e504a169a4dd0514" ], "evidenceId": "python_verification:verification/v489_seam_modular_commutator.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v489_seam_modular_commutator.py", "pubMirrorHash": "bb5038d567c8d14b7eb67546974311c6edf547a961581864e1af9f77f5211684", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v489_seam_modular_commutator.py" }, { "id": "v490_seam_parity_census", "filename": "v490_seam_parity_census.py", "path": "verification/v490_seam_parity_census.py", "cluster": "core", "synopsis": "SEAM.MU.01: the T^2 spin-structure fermion-parity census for the v367 seam lattice model -- the lattice ground-state witness of 'mu_pre = 4 before condensation' (step 1 of the v378 KLM chain) + the 16-fold-way bridge theta_v = 1 with the measured nu = 2 c_- = 16 (v489). Parity per sector (AA, AP, PA, PP) determined twice: Read-Green TRIM product AND real-space Majorana Pfaffian (Schur), relative to the trivial phase. [E] sanity: twisted real-space spectra == Bloch bands to 9e-15. [E] per-layer census (+,+,+,-), TRIM == Pfaffian in every sector (3 even sectors = Ising nu = 1). [E] 16 layers: parity^16 = + in ALL 4 sectors => gauged torus GSD = 4 = mu(SO(16)_1) = |det Cartan(D8)|. [E] theta_v = exp(2 pi i nu/16) = 1 exactly at nu = 16; rivals nu = 1, 2, 8 excluded. [E] fence: fermionic Kitaev-Preskill TEE = 0 for BOTH M=1 and M=3 -- does NOT discriminate (E8)_1 vs SO(16)_1. [C] KLM step 4 -> 4/2^2 = 1 cited (interacting, not free-fermion computable); numerics pin only {c_- = 8, mu_pre = 4, theta_v = 1}. [O] continuum limit (MMST v336); SEAM.EQUIV.01 stays [O]. Python (numpy + scipy + sympy).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv490_seam_parity_census.py", "sourceSha256": "5bf9d30c899fd186bf9e6d48881886ddae84f4eb20f3823ba4f929630f60aff4", "linkedClaimIds": [ "SEAM.MU.01" ], "sectionIds": [ "section:307c4c95a7c84b5efc0b", "section:67f92d5b57079948ad55", "section:6a93c4dd5fe420e1990e", "section:701d23928f8e38ea7d4b", "section:7d0e50b6a6c30535730d", "section:8e4972dbe899b5debb90", "section:ab9e7e520130ecc7da7c", "section:b18b388084f449438cbb", "section:b38be2626e35c37f4bd1", "section:b63f8484d81bde8026ec", "section:cca5b83aae425d5f0e88", "section:d90bd5e1e6d8fa41397d" ], "activeSectionIds": [ "section:67f92d5b57079948ad55", "section:8e4972dbe899b5debb90", "section:ab9e7e520130ecc7da7c", "section:b18b388084f449438cbb", "section:b38be2626e35c37f4bd1", "section:b63f8484d81bde8026ec" ], "evidenceId": "python_verification:verification/v490_seam_parity_census.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v490_seam_parity_census.py", "pubMirrorHash": "5bf9d30c899fd186bf9e6d48881886ddae84f4eb20f3823ba4f929630f60aff4", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v490_seam_parity_census.py" }, { "id": "v491_p2_partition_corollary", "filename": "v491_p2_partition_corollary.py", "path": "verification/v491_p2_partition_corollary.py", "cluster": "core", "synopsis": "P2.PARTITION.01: g_car = 5 as a COROLLARY of the four marks -- the partition sharpening of v53 (sympy exact). The lemma: exactly 3 positive integers summing to 4 = uniquely {1,1,2} => e = (4,5,2) => g_car = e2 = 5, |Z2| = e3 = 2, N_fam = e2-e3 = 3 as corollaries; consistency fixed point (2^4-1)/5 = 3 = rank H^1. Negative controls (each assumption load-bearing): drop positivity -> 4 solutions, e2 in {0,3,4,5}; sum 3 -> e2 = 3; sum 5 -> not unique; 2/4 parts -> e2 {3,4}/{6}; Mehta-Seshadri rational weights -> 16/3 resp. 44/9 != 5 (integrality = Birkhoff-Grothendieck splitting-type typing). [E] v53 sharpening: v53 needs all three targets (4,5,2), the partition only e1 = 4. [E] sum rule 4 x (N-1)/2 = 4 iff N = 3; v115 route 4 tr(A0) = 4. Independence: #marks = 4 (v216, P1-side), rank H^1 = 3 (v137/v228), |a|_1 = 4 g_car-free (v115). [C] honest residual: P2 NOT axiom-free -- the weight-typing postulate remains; AX.P2.01 stays a declared axiom; N_fam direction reversal typed as over-determination. Exact (sympy); Wolfram-mirrored.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv491_p2_partition_corollary.py", "sourceSha256": "568bc3de36de18673cabfa6a2a96f1dd7f43629b0c02ba897f20e8bd94fca042", "linkedClaimIds": [ "P2.PARTITION.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:09b49009253acb5a0dfb", "section:3721516595f24fd66f4c", "section:3cc790136e8b9bd3c188", "section:46614e805445fc78e7af", "section:584e87a9c163ac38f92f", "section:6b49d8830dc9fa3948be", "section:6e8f8f12ea28ee07020a", "section:7383e42c67f8eaba497b", "section:749d598aa0815d32790b", "section:75a03f34059a70d920e7", "section:7750a727b522e861fdbc", "section:8872501633bb702220cd", "section:ab9e7e520130ecc7da7c", "section:c7d8a7dfe6518305774c", "section:eb0bd97fda8c0fedefad", "section:f1cb1505fb0d067d8745", "section:f22c82858ff073c133d4", "section:f9b30725993b14c4ee95", "section:ffca98d84a77b4d4e4ab" ], "activeSectionIds": [ "section:3721516595f24fd66f4c", "section:46614e805445fc78e7af", "section:584e87a9c163ac38f92f", "section:6b49d8830dc9fa3948be", "section:6e8f8f12ea28ee07020a", "section:7383e42c67f8eaba497b", "section:749d598aa0815d32790b", "section:75a03f34059a70d920e7", "section:7750a727b522e861fdbc", "section:ab9e7e520130ecc7da7c", "section:f1cb1505fb0d067d8745", "section:f22c82858ff073c133d4" ], "evidenceId": "python_verification:verification/v491_p2_partition_corollary.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v491_p2_partition_corollary.py", "pubMirrorHash": "568bc3de36de18673cabfa6a2a96f1dd7f43629b0c02ba897f20e8bd94fca042", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v491_p2_partition_corollary.py" }, { "id": "v492_celestial_z4_orbifold", "filename": "v492_celestial_z4_orbifold.py", "path": "verification/v492_celestial_z4_orbifold.py", "cluster": "frontier", "synopsis": "CELEST.WP1.01: WP1 of the celestial-holographic research contract CELEST.SEAM.01 -- the E8 mu4-glue grading (v128) IS the flat Z4 monodromy of the glue-equivariant celestial chiral algebra on the A3 ALE space C^2/Z4 (Bittleston-Homans-Sharma, arXiv:2305.09451, the Z2/Eguchi-Hanson case; Kronheimer-Nakajima flat connection). [E] inner grading: h = (2,2,2,2,2;0^4) reads the glue class mod 4 on all 240 roots => glue = Ad(exp(2 pi i h/4)) = flat Z4 monodromy; A3-side h' = (0^5;1,1,1,-3) = the diagonal (1,1) glue of Z4 x Z4 (v92/v125); Z2 halfway 120 = SO(16) / 128 = spinor. [E] C^2/Z4 IS the A3 singularity XY = Z^4 (Molien + Hilbert (1+t^4)/((1-t^2)(1-t^4)) exact). [E] equivariant SDYM(E8) sector closes: D[d] = 60(d+1) even / 64(d+1) odd -- works ONLY because dim g_j = (60,64,60,64); zero modes = carrier D5+A3+Cartan = 60; density 1/4 = 1/|Z4|. [E] (E8)_1 character = sum of the 4 glue-coset sectors (1+248q+4124q^2+34752q^3, v377); sector weights = the v92/v125 discriminant form (5x^2+3y^2)/8; glue diagonal h = (0,1,1,1) integer = local extension. [E] correction: the A3 deck acts on the celestial sphere as z -> -z (order 2); the order-4 clock z -> iz is the U(2) phase diag(i,1) (normalises the deck, det = i rotates omega by the mu4 generator), spin bridge (spin clock)^2 = deck, Z8 with 8 = 2|mu4|. [E] clock-invariant A3 deformation = 1-parameter XY = Z^4 + a0, branch points = ONE mu4 orbit, cross-ratio 2 (v168/v214 pillowcase). [E] negative controls: diag(i,i) killed 3 ways; false glue breaks additivity 3112/6720; rigidity = Aut(Z4). [C] verdict B: match under the ONE named identification clock^2 = deck. [O] structural arithmetic only -- no celestial duality constructed; CELEST.SEAM.01 stays a research contract; SEAM.EQUIV.01 stays [O]. Exact (sympy).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv492_celestial_z4_orbifold.py", "sourceSha256": "7dc06180a0398a6b2d300b0c6d19150e4ad943eef3b058438d6a353b653ada44", "linkedClaimIds": [ "CELEST.WP1.01", "CELEST.SEAM.01", "SEAM.EQUIV.TWISTOR.01" ], "sectionIds": [ "section:00084b3039331dc8515a", "section:0bcac4df826bc0d57d23", "section:21c9669befc5eafd6176", "section:2db6bd35ce5c578613f3", "section:307c4c95a7c84b5efc0b", "section:3ed2167aff70cc409f71", "section:6ddf4757acde55521050", "section:6e8f8f12ea28ee07020a", "section:701d23928f8e38ea7d4b", "section:70380cf4813f5dcd47e6", "section:7750a727b522e861fdbc", "section:77b944418033334668b5", "section:7d0e50b6a6c30535730d", "section:84ec2c9d7a3c77ec2664", "section:891953ab4ad2ba19100f", "section:a036d63765e830eb593f", "section:ab9e7e520130ecc7da7c", "section:b191b0a66e5bacdc1a0e", "section:b3146d55cec712d485d5", "section:b63f8484d81bde8026ec", "section:cca5b83aae425d5f0e88", "section:cdd3ea07b0ec5995036b", "section:de8db1cd8257eab0d607", "section:fe8d8923981b24e85222" ], "activeSectionIds": [ "section:00084b3039331dc8515a", "section:0bcac4df826bc0d57d23", "section:21c9669befc5eafd6176", "section:3ed2167aff70cc409f71", "section:6ddf4757acde55521050", "section:6e8f8f12ea28ee07020a", "section:70380cf4813f5dcd47e6", "section:7750a727b522e861fdbc", "section:77b944418033334668b5", "section:84ec2c9d7a3c77ec2664", "section:891953ab4ad2ba19100f", "section:a036d63765e830eb593f", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b63f8484d81bde8026ec", "section:cdd3ea07b0ec5995036b", "section:de8db1cd8257eab0d607", "section:fe8d8923981b24e85222" ], "evidenceId": "python_verification:verification/v492_celestial_z4_orbifold.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v492_celestial_z4_orbifold.py", "pubMirrorHash": "7dc06180a0398a6b2d300b0c6d19150e4ad943eef3b058438d6a353b653ada44", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v492_celestial_z4_orbifold.py" }, { "id": "v493_celestial_wp2_clock_deformation", "filename": "v493_celestial_wp2_clock_deformation.py", "path": "verification/v493_celestial_wp2_clock_deformation.py", "cluster": "frontier", "synopsis": "CELEST.WP2.01: WP2 of the celestial-holographic research contract CELEST.SEAM.01 -- the clock-invariant deformation XY = Z^4 + a0 of the A3 seam orbifold (geometry, periods/monodromy, deformed algebra; Bittleston-Homans-Sharma Z2 -> Z4 transfer, arXiv:2305.09451). [E] geometry: P(iZ) = P(Z) forces a3 = a2 = a1 = 0 sharply (two-sided: prod(Z - i^k w) = Z^4 - w^4); smooth iff a0 != 0 (disc = 256 a0^3); branch points = ONE free mu4 orbit; cross-ratio 2 / j = 1728 for ALL a0 (quartic invariants I = 12 a0, J = 0 identically) => a0 = pure SCALE, tau = i pillowcase FROZEN -- no shape modulus. [E] periods: Pi = t(i-1)(1,i,i^2), all 3 spheres same volume sqrt(2) t (lockstep); clock on H2 = COXETER element of W(A3) (char x^3+x^2+x+1, eigenvalues {i,-1,-i} = A3 exponents; h(A3) = 4 = |mu4| = N_fam+1); no invariant cycle (det(A-1) = -4); surviving direction = chi_1-Fourier diagonal (1,i,i^2); the clock IS the Picard-Lefschetz monodromy of the family; versal weights (1,2,3,0) = regular mu4 rep. [E] algebra: mode dictionary {w[m,n]: m = n mod 4} <-> {X^p Y^q Z^r: r <= 3}; bracket -4*Nambu(F) anchored at the a0 = 0 orbifold ({X,Y} = 16 Z^3, {Y,Z} = -4Y, {Z,X} = -4X), Jacobi + Casimir exact, uniform clock-degree -1; S-algebra corrections exactly LINEAR in a0 at the Z4 wrap, grade-conserving (no sector leak => the v492 equivariant SDYM(E8) sector deforms consistently); a0 <-> BHS c^2 slot (weight 0); matrix factorisations deform along all orbit splittings, clock fixes exactly the antipodal 2+2 sector (EH/Z2 middle node, 4 = 2 x 2). [E] negative controls: a1 Z => j = 0 (hexagonal); pure a2 Z^2 => stays singular (A1); a2 != 0 => j = 1556068/81 != 1728; grading leak explicit. [C] three named identifications (verdict B): -4*Nambu = THE k = 4 CCA bracket; period = root difference; seam-scale reading via clock^2 = deck. [C] v216 precision typed: given the order-4 clock the deformation freezes the (2,2,2,2) modulus to the square automatically -- relocation of the same order-4 input, no marker move. [O] full twisted-sector OPEs, W(mu) scaling limit for k = 4, splitting-function check, WP3-WP5; SEAM.EQUIV.01 stays [O]. Exact (sympy).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv493_celestial_wp2_clock_deformation.py", "sourceSha256": "fe8c8976d5b00a10e70c48324a36eb68bd568f94c2578d27979735f23262b7f9", "linkedClaimIds": [ "CELEST.WP2.01" ], "sectionIds": [ "section:21c9669befc5eafd6176", "section:2525c189f32461c9368a", "section:307c4c95a7c84b5efc0b", "section:3e3e7c41b2e8190a5e2f", "section:3ed2167aff70cc409f71", "section:6a93c4dd5fe420e1990e", "section:6cd1a267e72b20619327", "section:6e8f8f12ea28ee07020a", "section:701d23928f8e38ea7d4b", "section:70380cf4813f5dcd47e6", "section:7750a727b522e861fdbc", "section:77b944418033334668b5", "section:7d0e50b6a6c30535730d", "section:888628823bf71f709698", "section:891953ab4ad2ba19100f", "section:9f542e7b4fe8d834693c", "section:a036d63765e830eb593f", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b38be2626e35c37f4bd1", "section:b63f8484d81bde8026ec", "section:b93e6ae7b00f32ee1201", "section:cca5b83aae425d5f0e88", "section:cdda6bb5746f6a6a897d", "section:d90bd5e1e6d8fa41397d", "section:e992bd516774ac42110f" ], "activeSectionIds": [ "section:21c9669befc5eafd6176", "section:3e3e7c41b2e8190a5e2f", "section:3ed2167aff70cc409f71", "section:6e8f8f12ea28ee07020a", "section:70380cf4813f5dcd47e6", "section:7750a727b522e861fdbc", "section:77b944418033334668b5", "section:888628823bf71f709698", "section:891953ab4ad2ba19100f", "section:9f542e7b4fe8d834693c", "section:a036d63765e830eb593f", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b38be2626e35c37f4bd1", "section:b63f8484d81bde8026ec", "section:cdda6bb5746f6a6a897d", "section:e992bd516774ac42110f" ], "evidenceId": "python_verification:verification/v493_celestial_wp2_clock_deformation.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v493_celestial_wp2_clock_deformation.py", "pubMirrorHash": "fe8c8976d5b00a10e70c48324a36eb68bd568f94c2578d27979735f23262b7f9", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v493_celestial_wp2_clock_deformation.py" }, { "id": "v494_cosmo_running_mu_record", "filename": "v494_cosmo_running_mu_record.py", "path": "verification/v494_cosmo_running_mu_record.py", "cluster": "gravity", "synopsis": "α_s/β_s running + μ-distortion promoted to the suite: [E] LO identities α_s=−2/N★²=−r/6, β_s=−4/N★³ (sympy exact) + exact slow roll α_s(51.4)=−7.09×10⁻⁴, β_s=−2.70×10⁻⁵ (band −8.0…−5.6×10⁻⁴ LO); [C] Planck 2018 +0.57σ, record leg P-ACT-LB −1.33σ (kill: robust POSITIVE running ≥5σ); [C] μ-distortion branch discriminator (Chluba window, +21% LCDM-anchored): sharp 1.6×10⁻⁸ / profiled 1.94×10⁻⁸, band 1.5–2.3×10⁻⁸, split 3.0×10⁻⁹ = 3σ at Voyage-2050 σ(μ)=10⁻⁹ (PIXIE baseline does not reach); [E] the frozen log-comb is structurally blind in the μ window (|F|=0.033, δμ=7.4×10⁻¹² = 0.007σ). N★ stays an external input (GATE.NSTAR.01); band [50,60] stays the record.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv494_cosmo_running_mu_record.py", "sourceSha256": "f141a038a91f8dca363c59833682785d24249d3f01944b20e098cdeaba63328f", "linkedClaimIds": [ "COSMO.RUNNING.01", "COSMO.MUDIST.01" ], "sectionIds": [ "section:0ef959e2a042fa769a57", "section:5fbc43aa96ffd3bc0ea8", "section:ab9e7e520130ecc7da7c", "section:c7fa25dbf82641f2c920", "section:d0f5ec8b9d27940435e3", "section:e87b37c2fa5e56fb49fa", "section:ee5c68ec39d878e448bd" ], "activeSectionIds": [ "section:ab9e7e520130ecc7da7c", "section:c7fa25dbf82641f2c920", "section:d0f5ec8b9d27940435e3", "section:ee5c68ec39d878e448bd" ], "evidenceId": "python_verification:verification/v494_cosmo_running_mu_record.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v494_cosmo_running_mu_record.py", "pubMirrorHash": "f141a038a91f8dca363c59833682785d24249d3f01944b20e098cdeaba63328f", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v494_cosmo_running_mu_record.py" }, { "id": "v495_celestial_wp3_gs_alignment", "filename": "v495_celestial_wp3_gs_alignment.py", "path": "verification/v495_celestial_wp3_gs_alignment.py", "cluster": "frontier", "synopsis": "CELEST.WP3.01: WP3 of the celestial-holographic research contract CELEST.SEAM.01 -- the Green-Schwarz axion coefficient lambda_g of celestial SDYM (Costello, arXiv:2111.08879) vs the TFPT seam constant c3 = 1/(8 pi); the pre-registered 'alignment test only'. [E] Okubo identity DERIVED, not quoted: Sum ^4 = [5/(2(dim+2))] (Sum ^2)^2 exact for all 8 algebras on Costello's list (e6/e7 carved out of the v492 E8 root set); sl4 negative control fails (5/32 vs 3/32). [E] Killing = 2 h_vee <.,.>; closed form lambda~^2 = 10 h_vee^2/(dim+2) = h_vee + 6 over the Deligne series; Dynkin indices (1,1,2,2,6,6,12,60); E8: lambda~ = 6, lambda_fund = 1/10 EXACT; Costello cross-checks sl2 = 8 / sl3 = 9; so8 slip flagged (exact 3, printed 3/2). [E] Alignment: (kappa/c3)^2 = lambda^2/3 = 12 = |mu4| N_fam resp. 1/300 exact; kappa/c3 itself irrational (2 sqrt3); anchors h_vee = 30 = |Z2| N_fam g_car, phi(30) = 8 = rank, lambda~ = |Z2| N_fam, lambda_fund = 1/(|Z2| g_car). [E] LOOK-ELSEWHERE (hard fence, alignment != selection): alignment 8/8 (zero selectivity), smoothness 8/8, lambda-integrality 2/8 (with sl3), phi(h_vee) = rank 4/8; only g_car | h_vee is e8-selective (1/8); the isolating conjunction is post hoc. [E] K3 does NOT fire but is scope-demoted: compatibility + lambda-arithmetic, NOT e8-selective evidence. [C] the 8 pi is the anomaly 2 pi convention, the sqrt3 the box diagram's sqrt48 -- WP3 can never derive c3. [O] WP5 + SEAM.EQUIV.01 stay [O]. Verdict B. Exact (Fraction/sympy).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv495_celestial_wp3_gs_alignment.py", "sourceSha256": "5c99ef09765e691924fd15ec669526137500ebddc1a9fa88464cab64329d9685", "linkedClaimIds": [ "CELEST.WP3.01" ], "sectionIds": [ "section:307c4c95a7c84b5efc0b", "section:3e3e7c41b2e8190a5e2f", "section:3ed2167aff70cc409f71", "section:6e8f8f12ea28ee07020a", "section:701d23928f8e38ea7d4b", "section:7d0e50b6a6c30535730d", "section:891953ab4ad2ba19100f", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b38be2626e35c37f4bd1", "section:b63f8484d81bde8026ec", "section:cca5b83aae425d5f0e88", "section:fe8d8923981b24e85222" ], "activeSectionIds": [ "section:3e3e7c41b2e8190a5e2f", "section:3ed2167aff70cc409f71", "section:6e8f8f12ea28ee07020a", "section:891953ab4ad2ba19100f", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b38be2626e35c37f4bd1", "section:b63f8484d81bde8026ec", "section:fe8d8923981b24e85222" ], "evidenceId": "python_verification:verification/v495_celestial_wp3_gs_alignment.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v495_celestial_wp3_gs_alignment.py", "pubMirrorHash": "5c99ef09765e691924fd15ec669526137500ebddc1a9fa88464cab64329d9685", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v495_celestial_wp3_gs_alignment.py" }, { "id": "v496_celestial_wp4_character_shadow", "filename": "v496_celestial_wp4_character_shadow.py", "path": "verification/v496_celestial_wp4_character_shadow.py", "cluster": "frontier", "synopsis": "CELEST.WP4.01: WP4 of the celestial-holographic research contract CELEST.SEAM.01 -- the (E8)_1 character E4/eta^8 vs the glue-equivariant E8[C^2] S-algebra (the 'type mismatch, head-on'). [E] Base: v492 replication (52+64+60+64, dims (60,64,60,64)); equivariant tower D[d] = 60(d+1)/64(d+1); cumulative count QUADRATIC 31 s^2 + 92 s + 60, 31 = k + h_vee; [C] CP Table 1: spin 1 - d/2 UNBOUNDED BELOW => no rational VOA contains the towers. [E] Hilbert series chi_sp(t) = (60+128t+60t^2)/(1-t^2)^2 (palindrome, 248 at t = 1); all mu4 collapses + the SU(2)_+ slice fail to start (1, 248, ...). [E] Character: chi = E4/eta^8 = (1,248,4124,34752,213126,...) exact through q^6 (cross-check q j = E4^3/eta^24); theta split, sector currents (60,64,60,64), glue-diagonal h = (0,1,1,1) integer; Sugawara c = 248/31 = 8 = 2|mu4|. [E] Bridges: zero-mode slice = 60 currents exact; jet slice cycles (60,64,60,64); BOUNDARY/PERIOD LIMIT: one mu4 period sums EXACTLY to 248 (single-particle level); 248 is NOT a jet-tower dimension (d <= 100); loop Fock level 1 = 897266 >> 248 (rational truncation absent). [E] Mismatch localised THREE ways: (a) grading; (b) growth n^{2/3} vs n^{1/2} (Meinardus pole s = 2 vs 1; f_n/chi_n strictly increasing n = 1..12); (c) the level-2 null ideal deletes EXACTLY 27000 = 30^3 = h_vee^3 (Sym^2(248) = 1+3875+27000; character keeps 4124) -- no jet analogue. [E] K4 three-way: exact realisation NO; boundary-limit PARTIAL YES -- the SAME MMST scaling-limit structure as SEAM.EQUIV.01 (v336/v449); K4 does NOT degrade the contract to 'E8 admissible'. [C] verdict B(ii): the character is a BOUNDARY/LIMIT shadow, not a conformal block in the bulk grading. [O] the constructive limit -> WP5; SEAM.EQUIV.01 stays [O]. Exact (integer/Fraction/sympy).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv496_celestial_wp4_character_shadow.py", "sourceSha256": "c007742d209227c5798e8d632217bd440eb928cc2a675436490ba613d42da6c6", "linkedClaimIds": [ "CELEST.WP4.01" ], "sectionIds": [ "section:1a1734f3aaab8aa152c3", "section:307c4c95a7c84b5efc0b", "section:3ed2167aff70cc409f71", "section:4b3ba5a9961f43f6a463", "section:6ac9a89a114dc5f7b30d", "section:6e8f8f12ea28ee07020a", "section:6fe70b094ab252ec071e", "section:701d23928f8e38ea7d4b", "section:7d0e50b6a6c30535730d", "section:891953ab4ad2ba19100f", "section:a0bd29de2657307a1b42", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b38be2626e35c37f4bd1", "section:b63f8484d81bde8026ec", "section:cca5b83aae425d5f0e88", "section:fe8d8923981b24e85222" ], "activeSectionIds": [ "section:3ed2167aff70cc409f71", "section:4b3ba5a9961f43f6a463", "section:6ac9a89a114dc5f7b30d", "section:6e8f8f12ea28ee07020a", "section:6fe70b094ab252ec071e", "section:891953ab4ad2ba19100f", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b38be2626e35c37f4bd1", "section:b63f8484d81bde8026ec", "section:fe8d8923981b24e85222" ], "evidenceId": "python_verification:verification/v496_celestial_wp4_character_shadow.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v496_celestial_wp4_character_shadow.py", "pubMirrorHash": "c007742d209227c5798e8d632217bd440eb928cc2a675436490ba613d42da6c6", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v496_celestial_wp4_character_shadow.py" }, { "id": "v497_celestial_wp5a_null_ideal", "filename": "v497_celestial_wp5a_null_ideal.py", "path": "verification/v497_celestial_wp5a_null_ideal.py", "cluster": "frontier", "synopsis": "CELEST.WP5A.01: WP5a of the celestial-holographic research contract CELEST.SEAM.01 -- 'the null ideal from the limit', first constructive milestone of WP5 (the v496 boundary-limit shadow made precise). [E] Base: v492/v496 replication (glue dims (60,64,60,64), tower D[d], chi = E4/eta^8 through q^6, mu4 period sum 248). [E] STABILISATION THEOREM: family chi_w of graded Fock characters on the chiral jet generators (loop energy m + w*radial number r, quarter units u = q^{1/4}); w = 2 IS the chiral jet grading (generators 64,120,128,180,192,240,256,300 per degree); u^n coefficient of chi_w = quarter-moded loop Fock for ALL w >= n+1, strictly larger for w <= n (n <= 8, w <= 10) -- the boundary reading is the precise coefficientwise limit eps = 1/w -> 0 with explicit threshold w = n+1; convention: 897266 = loop Fock at u^4 = integer level 1. [E] NULL IDEAL DERIVED (not cited): Freudenthal + Weyl + character peeling give Sym^2(248) = V(2 theta) + V(omega) + V(0) = 27000 + 3875 + 1 (residual exactly 0, orbit-sum cross-check); 27000 = 30^3 = h_vee^3; C2 = (124, 96, 0), Dynkin indices 6750/750; level-1 integrability <2 theta,theta_vee> = 4, = 2 => only level-1 primary = vacuum ([C] Kac, counting consequence); quotient 31124 - 27000 = 4124 = 1 + 248 + 3875 exactly. [E] TWO ROUTES, ONE NUMBER: mu4 theta-split sector sum at q^2 = (1036,1024,1040,1024) = 4124 -- independent lattice route hits the Fock quotient exactly; q^3: 34752 = chi_3. [E] NEGATIVE CONTROLS: SO(16)_1 through the SAME pipeline: Sym^2(120) = 5304+1820+135+1 (FOUR components), 5304 != 14^3 (h_vee^3 not generic), quotient 7380-5304 = 2076 = Theta_D8/eta^8 at q^2 (second algebra validated), block weights (0,1/2,1,1) do NOT fuse vs E8 (0,1,1,1) fusing; false periodisation: only P = 4 = |mu4| gives 248; swapped glue breaks the zero-mode anchor (64 != 60). [C] identifications: 'radial decoupling = MMST collar thickness -> 0' (v336/v449 same two-step shape); Kac singular vector via counting consequence only. [O] HONEST LIMIT: the limit does NOT generate the truncation -- singular vector as operator in the limit net open (WP5b); GNS limit state, local normality/Haag duality open (WP5c/d); the celestial route now has the same two-step shape as MMST (limit + maximal ideal) with the ideal quantitatively fixed; SEAM.EQUIV.01 stays [O]. Exact (integer/Fraction).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv497_celestial_wp5a_null_ideal.py", "sourceSha256": "a900b994ddc795b2a7fe3d66262c34b30458b7d070070ef90f6a987f8b7a71cb", "linkedClaimIds": [ "CELEST.WP5A.01" ], "sectionIds": [ "section:307c4c95a7c84b5efc0b", "section:3ed2167aff70cc409f71", "section:4b3ba5a9961f43f6a463", "section:6ac9a89a114dc5f7b30d", "section:701d23928f8e38ea7d4b", "section:70380cf4813f5dcd47e6", "section:7d0e50b6a6c30535730d", "section:82c47adfed4340093cda", "section:891953ab4ad2ba19100f", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b63f8484d81bde8026ec", "section:cca5b83aae425d5f0e88" ], "activeSectionIds": [ "section:3ed2167aff70cc409f71", "section:4b3ba5a9961f43f6a463", "section:6ac9a89a114dc5f7b30d", "section:70380cf4813f5dcd47e6", "section:82c47adfed4340093cda", "section:891953ab4ad2ba19100f", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b63f8484d81bde8026ec" ], "evidenceId": "python_verification:verification/v497_celestial_wp5a_null_ideal.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v497_celestial_wp5a_null_ideal.py", "pubMirrorHash": "a900b994ddc795b2a7fe3d66262c34b30458b7d070070ef90f6a987f8b7a71cb", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v497_celestial_wp5a_null_ideal.py" }, { "id": "v498_celestial_wp5b_singular_vector", "filename": "v498_celestial_wp5b_singular_vector.py", "path": "verification/v498_celestial_wp5b_singular_vector.py", "cluster": "frontier", "synopsis": "CELEST.WP5B.01: WP5b of the celestial-holographic research contract CELEST.SEAM.01 -- 'the singular vector as an operator', the second constructive milestone of WP5 (WP5a fixed the ideal's size and location; WP5b constructs the deleting object). [E] CONSTRUCTION: |s> = (E^theta_{-1})^2|0>, theta the highest root, weight 2 theta (top of the 27000), level 2 = 8 quarters = q^2 (INTEGER); Chevalley/Frenkel-Kac basis MACHINE-built (bimultiplicative 2-cocycle, asymmetry on all 57600 pairs; [e_a,e_{-a}] sign FORCED by Jacobi, SGN = -1; kappa derived, kappa(theta_vee,theta_vee) = 2; Jacobi exact on 57600 sl2-slice triples + 6000 seeded + all 496 theta-adjacent; all N_ab = +-1). [E] SINGULARITY: J^a_1|s> = 0 for ALL 248 basis elements, 0 violations; case tally 190 (first bracket) / 57 (second) / 1 (F^theta via central-term cancellation -- the ONLY case that sees k); plus J^a_2|s> = 0 (248), E^a_0|s> = 0 (120), Shapovalov norm 0 at k = 1 (4 at k = 2); affine PBW engine unit-tested on all 61504 basis pairs. [E] LEVEL DIAL: F^theta_1 coefficient = 2(1-k) -- 2 at k = 0, 0 EXACTLY at k = 1, -2 at k = 2: without the central extension the deletion object does not exist. [E] MU4 DATA: theta-grading dims (1,56,134,56,1), g0 = e7+u(1); h-adapted chamber machine-built (Cartan det 1, E8 Dynkin diagram, branch lengths [1,2,4]); = 5 => j(theta) = 1, height 29 = h_vee-1; |s> in class 2 (sheet-even, WP5a consistent); clock phase i^2 = -1; cross-table theta-grading x glue class consistent (rows (1,56,126,56,1), columns (52,64,60,64)); the deleting theta-sl2 sheet-odd (1,3), its square sheet-even. [E] LEVEL-2 MATCH: Mult(2 theta) = 1 in the level-2 Fock => U(g)|s> is THE 27000; direct g0-orbit BFS reproduces the Freudenthal multiplicities of V(2 theta) exactly through depth 4; quotient 31124 - 27000 = 4124; lattice reading (2theta,2theta)/2 = 4 > 2 => no 2theta state at q^2 in E4/eta^8 -- |s> IS the kernel generator of Fock -> E4/eta^8. [E] NEGATIVE CONTROLS: E^theta_{-1}|0> NOT singular (1 witness F^theta, -> -k|0>) -- the 248-current state that must remain; 4 generic level-2 states non-singular (14-33 witnesses); k-dial: at k = 2 only the CUBE is singular ((E^theta)^{k+1} mechanics = generic Kac); D8/SO(16)_1: the singular vector exists there TOO (level-1 generic) but the h = 1/2 blocks do not fuse (3 comark-1 weights, dim V(2 theta_D8) = 5304 != 14^3) vs E8 (comarks >= 2, vacuum the only level-1 primary, glue weights (0,1,1,1) integer) -- one-block closure is the E8/mu4-specific part, honestly separated. [C] Weyl complete reducibility beyond BFS depth 4; Kac mechanics beyond level 2; per-period quarter dictionary (v496). [O] HONEST LIMIT: in the twisted quarter-slot moding two C_1 modes never sum to 8 quarters (minimum 6 = q^{3/2}) -- the per-PERIOD dictionary (v496), not the per-slot identification, carries |s> to q^2; exactly the precise WP5c question (GNS limit state, kernel containing the ideal); WP5c/d/e stay [O]; SEAM.EQUIV.01 untouched. Exact (integer/Fraction).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv498_celestial_wp5b_singular_vector.py", "sourceSha256": "9f5a2d62523283595b754fea6f70ddc6501a251daf86752cbc67ded252b96180", "linkedClaimIds": [ "CELEST.WP5B.01" ], "sectionIds": [ "section:307c4c95a7c84b5efc0b", "section:3ed2167aff70cc409f71", "section:4b3ba5a9961f43f6a463", "section:701d23928f8e38ea7d4b", "section:7d0e50b6a6c30535730d", "section:82c47adfed4340093cda", "section:891953ab4ad2ba19100f", "section:8abc3c61baefc9b60bc8", "section:a9e4936094020237f825", "section:ab9e7e520130ecc7da7c", "section:b38be2626e35c37f4bd1", "section:b63f8484d81bde8026ec", "section:cca5b83aae425d5f0e88", "section:e7294e8d8a250400195d" ], "activeSectionIds": [ "section:3ed2167aff70cc409f71", "section:4b3ba5a9961f43f6a463", "section:82c47adfed4340093cda", "section:891953ab4ad2ba19100f", "section:8abc3c61baefc9b60bc8", "section:ab9e7e520130ecc7da7c", "section:b38be2626e35c37f4bd1", "section:b63f8484d81bde8026ec" ], "evidenceId": "python_verification:verification/v498_celestial_wp5b_singular_vector.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v498_celestial_wp5b_singular_vector.py", "pubMirrorHash": "9f5a2d62523283595b754fea6f70ddc6501a251daf86752cbc67ded252b96180", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v498_celestial_wp5b_singular_vector.py" }, { "id": "v499_p2_weights_deligne_bg", "filename": "v499_p2_weights_deligne_bg.py", "path": "verification/v499_p2_weights_deligne_bg.py", "cluster": "core", "synopsis": "P2.TYPING.01: the P2 weight-typing postulate HARDENED (the v491 check-9 residual) -- the anchor a = (1,1,2) typed as the Birkhoff-Grothendieck splitting exponents of the DELIGNE CANONICAL EXTENSION E of the flavor connection. Given the [E] anchors (4 marks v216, rank 3 v137, cusp class + irreducibility v117, (U)): deg E = -4 AS THEOREM (residue spectrum {0,1/3,2/3} unique in [0,1), trace 1 per mark x 4 marks; par-deg 0; infinity apparent, monodromy product = 1 exactly); POSITIVITY AS THEOREM (irreducibility exact: || = 24 = |S4|, sum |chi|^2 = 24; + (U) => Mehta-Seshadri stability => h^0(E) = 0, all 324 saturation cases; BG dictionary h^0 = 0 <=> a_i >= 1); INTEGRALITY = Birkhoff-Grothendieck, automatic once E is a bundle. UNIQUENESS + SELECTOR: {1,1,2} unique (v491); Schur-Horn permutohedron integer points exactly {(2,2,0),(2,1,1)} and h^0 = 0 kills {0,2,2} -- the tfpt_2 'balanced' heuristic now TYPED as stability. h^1 DISCREPANCY REAL + RESOLVED: h^1(E) = 1 != 3 -- 'generations = H^1(E)' is FALSE (forcing it: deg -6, uniqueness lost, e2 in {9,11,12} never 5); two-object typing: L = O(-D) carries the generations (h^1(L) = 3 = N_fam = v137 basis), E carries them as its FIBER. BISWAS EXPLICIT (independent witness): Z3 cusp cover y^3 = (z-1)(z-i)(z+1)^2(z+i)^2, genus 2 (NOT the pillowcase double, genus 1 j = 1728 = deck side); p_* O_Y = O + O(-2)^2; the regular-rep model lands on {0,2,2} = the UNSTABLE Schur-Horn companion (h^0 = 1): integrality + sum rule COME OUT of the correspondence, stability is the selector. Negative controls: no positivity -> 4/31 solutions; deg -3/-5 breaks; n-mark scan e2 = (n-2)(n+1)/2 = 5 ONLY at n = 4; MS-rational e2 = 16/3, 44/9. [C]/[N] residuals: R1 module identification (QGEO.SYM stays [O]); R2 unitarity (U) (v33/v40); R3 analytic monodromy [N] (v117 check 4). P2 stays an axiom (AX.P2.01 declared, no marker moves); non-circular (no v23/v115 splitting input). Exact (sympy); Wolfram-mirrored.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv499_p2_weights_deligne_bg.py", "sourceSha256": "73098e62b3148d1cddb31e60c16a424159f985b874aa0dee1737260fb81017b9", "linkedClaimIds": [ "P2.TYPING.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:09b49009253acb5a0dfb", "section:2525c189f32461c9368a", "section:3721516595f24fd66f4c", "section:3cc790136e8b9bd3c188", "section:46614e805445fc78e7af", "section:584e87a9c163ac38f92f", "section:62801f711a0d267461ac", "section:6a93c4dd5fe420e1990e", "section:6b49d8830dc9fa3948be", "section:6cd1a267e72b20619327", "section:7383e42c67f8eaba497b", "section:749d598aa0815d32790b", "section:74bb3766bdd1275dbd78", "section:75a03f34059a70d920e7", "section:7d0e50b6a6c30535730d", "section:8182ecd6055b0d0d488c", "section:8872501633bb702220cd", "section:888628823bf71f709698", "section:a036d63765e830eb593f", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:b63f8484d81bde8026ec", "section:b93e6ae7b00f32ee1201", "section:c7d8a7dfe6518305774c", "section:cca5b83aae425d5f0e88", "section:cdd3ea07b0ec5995036b", "section:d90bd5e1e6d8fa41397d", "section:eb0bd97fda8c0fedefad", "section:f22c82858ff073c133d4", "section:f9b30725993b14c4ee95", "section:fc7f5b07a661660c0d79", "section:ffb3c952b2d4af559d34", "section:ffca98d84a77b4d4e4ab" ], "activeSectionIds": [ "section:3721516595f24fd66f4c", "section:46614e805445fc78e7af", "section:584e87a9c163ac38f92f", "section:6b49d8830dc9fa3948be", "section:7383e42c67f8eaba497b", "section:749d598aa0815d32790b", "section:74bb3766bdd1275dbd78", "section:75a03f34059a70d920e7", "section:888628823bf71f709698", "section:a036d63765e830eb593f", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:b63f8484d81bde8026ec", "section:cdd3ea07b0ec5995036b", "section:f22c82858ff073c133d4", "section:fc7f5b07a661660c0d79" ], "evidenceId": "python_verification:verification/v499_p2_weights_deligne_bg.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v499_p2_weights_deligne_bg.py", "pubMirrorHash": "73098e62b3148d1cddb31e60c16a424159f985b874aa0dee1737260fb81017b9", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v499_p2_weights_deligne_bg.py" }, { "id": "v500_celestial_wp5c_gns_limit_state", "filename": "v500_celestial_wp5c_gns_limit_state.py", "path": "verification/v500_celestial_wp5c_gns_limit_state.py", "cluster": "frontier", "synopsis": "CELEST.WP5C.01: WP5c of the celestial-holographic research contract CELEST.SEAM.01 -- 'the GNS limit state', the third constructive milestone of WP5 (WP5a made the limit precise, WP5b built the deleting operator; WP5c constructs the STATE whose GNS kernel contains the ideal). Exact integer/Fraction, no floats, deterministic. [E] CONSTRUCTION: quasi-free family omega_w -- loop sector = affine k=1 vacuum functions via the MACHINE-determined compact anti-involution theta(e_a) = -e_{-a} (the UNIQUE sign that is an anti-automorphism on all 61504 basis pairs; contravariance exact); radial sector = oscillator pairings x^{w r} (exact Gibbs regulator, x-adic). [E] CONVERGENCE SHARP: omega_w = omega_inf mod x^{N+1} for ALL w >= N+1 (N = 8), NOT yet at w = N (r = 1 modes at order N) -- the WP5a threshold holds identically at the state level; positivity of every omega_w checked. [E] KERNEL (core, fully machine): FULL exact level-2 Gram -- 31124 monomials in 9361 weight blocks (profile 164:1, 37:240, 7:2160, 1:6960), each block exact: level-1 rank 248 positive definite (Cartan block = E8 Cartan, det 1); level-2 rank 4124, kernel 27000, every block PSD; rank per Weyl orbit (norm 8/6/4/2/0) = (0,0,1,8,44); kernel = V(2 theta) WEIGHT BY WEIGHT (Freudenthal cross-check on all 9361 weights); h.w. norms (3844, 49, 2, 0) at (0, omega, theta, 2theta); direct ideal checks F_i|s>, F_j F_i|s> norm 0. [E] MU4 EQUIVARIANCE: omega_w o clock = omega_w for all w; the clock descends to GNS; GNS level-2 rank by clock class = (1036,1024,1040,1024) = Theta_Cj/eta^8 at q^2 (two-routes identity at the STATE level); level-1 split (60,64,60,64). RESOLUTION of WP5b S4.10: |s> IS the ZERO VECTOR of GNS(omega_inf) -- the twisted two-C1-mode floor (6 quarters = q^{3/2}) concerns only pre-limit objects (GNS has no state there, 6 mod 4 != 0). [E] NEGATIVE CONTROLS: k = 2 ( = +4, dominant blocks full rank -- no ideal in the kernel); k = 0 (level-1 Gram = 0 -- no 248 layer without the central extension); D8 (level-2 rank 2076 = 7380 - 5304, kernel = V(2 theta_D8) PSD, but h = (0,1/2,1,1): vacuum GNS is 1 of 4 blocks -- one-block completeness stays E8/mu4-specific); wrong family E'_w = m w + r (level-1 limit rank 0, the 248 layer ERASED, u^4 content 710955 != 248 -- the kill has teeth); no damping (897266 != 248); CCR OBSTRUCTION: at FIXED radial pairing c > 0 positivity forces omega(bb*) >= c -- NO w-uniform damping state exists: the family formulation is NECESSARY and the family EXISTS => preregistered KILL not triggered. [C] quasi-free extension to the full *-algebra, Kac positivity beyond level 2. [O] local normality of omega_inf, net structure/Haag duality (WP5d), Costello-Li (WP5e), operator-algebraic closure beyond the graded topology; SEAM.EQUIV.01 stays [O]. VERDICT: SUCCESS on the preregistered criterion (dim GNS level-2 = 4124 exactly). 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[E-machine]/[L] SETUP: critical Majorana ring (v450 style), 16 layers = seam carrier c_- = 8; Peschel-exact; three prescriptions (fermionic / orbifold sector sum {1,P_A,P_B,P_AB} / dual algebra {1,P_AB}); superselection [rho, P_AB] = 0 machine-exact; every Gaussian formula validated against exact diagonalisation (<= 1.5e-15). [L/N] FERMIONIC MI EXTENSIVE (mu = 1 reference): c fit 0.5000, max |F(x)| = 5.97e-5 (N = 512), |F| falling monotonically to 1.3e-6 (N = 1024) -- Casini-Huerta extensivity as a lattice witness. [L/N] THE MU-OFFSET: Renyi-2 exactly Delta_2 = -ln[(1+R)/2]; the 16-layer carrier saturates ln 2 to MACHINE PRECISION (|Delta_2 - ln 2| = 1.1e-15 at N = 512; R falls as N^-0.500); index reading [F : F_even] = 2.000000, mu_gauged = 4.000000 = the v490 census (two independent lattice witnesses); per-layer gauging costs 16 ln 2 (the offset measures ln[index], not a blob). [L/N] HAAG-DUALITY INDICATOR: fermionic S(E) = S(E') to 8.2e-12; the orbifold BREAKS complementarity (D(E) - D(E') = 0.427 at a = 64); the pair sum is exchange-symmetric and <= ln 4 with max 1.2637 at x = 1/2 -> the ln 4 budget is a DOUBLE-LIMIT statement (the first naive fixed-x check was wrong and was replaced -- honestly typed). [E] CONDENSATION ARITHMETIC: det Cartan(D5) x det Cartan(A3) = 16; KLM/Longo-Rehren 16/4^2 = 1 and 16/2^2 = 4 -> 4/2^2 = 1 (both routes exact); Sigma d^2 (Ising 4, SO(16)_1 4, (E8)_1 1); theta_v = 1 exactly at nu = 16, rivals != 1. Anchored chain: mu = 1 (graded, MEASURED) -> 4 (gauged, MEASURED + v490) -> 1 (arithmetic, [C]; the condensed net is interacting -- v490 fence). [E/N] NEGATIVE CONTROLS: nu = 1 single Majorana (offset non-trivial, theta_v = e^{i pi/8} not removable -- the kill discriminator has teeth); trivial phase (everything <= 1e-7); wrong sector sum {1,P_AB} (offset exactly 0 instead of ln 2). [C] the dictionary 'offset = ln index' (KLM/Longo-Xu/CHMP) + the condensation step. [O] continuum Haag duality, local normality, split/strong additivity (WP5d-beta runs as exploration), Costello-Li (WP5e); SEAM.EQUIV.01 stays [O]. VERDICT: the mu = 1 indicator chain PASSES; preregistered KILL ('mu-offset != 0 after condensation') not triggered. Python (numpy + scipy + Fractions).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv501_celestial_wp5d_two_interval_index.py", "sourceSha256": "095d5c6f98b6c8eb0f0187a3d9dc01a1625945fbe3aee8b925fc6e4dd92b0c0b", "linkedClaimIds": [ "CELEST.WP5D.01" ], "sectionIds": [ "section:307c4c95a7c84b5efc0b", "section:3ed2167aff70cc409f71", "section:701d23928f8e38ea7d4b", "section:7d0e50b6a6c30535730d", "section:ab9e7e520130ecc7da7c", "section:b18b388084f449438cbb", "section:b38be2626e35c37f4bd1", "section:b63f8484d81bde8026ec", "section:cca5b83aae425d5f0e88", "section:f7d73358ce212e71ac18" ], "activeSectionIds": [ "section:3ed2167aff70cc409f71", "section:ab9e7e520130ecc7da7c", "section:b18b388084f449438cbb", "section:b38be2626e35c37f4bd1", "section:b63f8484d81bde8026ec", "section:f7d73358ce212e71ac18" ], "evidenceId": "python_verification:verification/v501_celestial_wp5d_two_interval_index.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v501_celestial_wp5d_two_interval_index.py", "pubMirrorHash": "095d5c6f98b6c8eb0f0187a3d9dc01a1625945fbe3aee8b925fc6e4dd92b0c0b", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v501_celestial_wp5d_two_interval_index.py" }, { "id": "v502_celestial_wp5e_prefactor_level", "filename": "v502_celestial_wp5e_prefactor_level.py", "path": "verification/v502_celestial_wp5e_prefactor_level.py", "cluster": "frontier", "synopsis": "CELEST.WP5E.ALPHA.01: WP5e-alpha of the celestial-holographic research contract CELEST.SEAM.01 -- 'prefactor and level bookkeeping', the CFT-side anchor stage of WP5e (the BCOV/Costello-Li twistor uplift: boundary partition function = E4/eta^8 INCLUDING the q^{-1/3} prefactor; preregistered kill: the anomaly inflow demands a level != 1). Exact sympy/Fraction, no floats. [E] PART A -- THE q^{-1/3} PREFACTOR IS EXACT mu4 VACUUM-ENERGY BOOKKEEPING: Hurwitz-zeta derivation zeta(-1,theta) = -B2(theta)/2, E_b(theta) = -1/24 + theta(1-theta)/4 exact; the clock is INNER (h = (2,2,2,2,2;0^4) and h' = (0^5;1,1,1,-3) BOTH read the class mod 4 on all 240 roots; (h,h) = 20, (h',h') = 12, sum 32) => twist distribution theta = 0^8 in ALL FOUR sectors -- a SHIFT orbifold (lattice cosets, integer-moded oscillators), NOT a rotation orbifold; E_osc = -1/3 = -c/24 sector-INDEPENDENT (c = 8 = rank = Sugawara 248/31); sector ground exponents -1/3 + (0,1,1,1). [E] DISCRIMINANT FORM = CASIMIR ENERGY, TWO ROUTES: spectral flow j^2 (h,h)/32 (5j^2/8, 3j^2/8, sum j^2 = 0 mod 1 = isotropy/Lagrangian) and EXACTLY via free fermions (D5 = 10 Majorana, A3 = D3 = 6, glue diagonal = 16 = the WP5d seam carrier 2^(g_car-1); R-NS shift n/16 = 5/8, 3/8, 1); the ROTATION reading FAILS (the geometric A3 deck gives 3/16 != 3/8: the v492 'clock != deck' lesson at the Casimir level). [E] CHARACTER: sum of the four Theta_Cj = E4 = (1,240,2160,6720); the four sector characters (leading coefficients (1,64,60,64), currents (60,64,60,64)) sum EXACTLY to E4/eta^8 = q^{-1/3}(1, 248, 4124, 34752). [E] PART B -- k = 1 FORCED THREE WAYS: (i) CURRENT CONDITION h(J) = k = 1 (the Z4 extension closes onto the E8 adjoint 60+64+60+64 = 248 only at spin 1); HONEST SHARPENING: glue-h integrality h(J^j; k) = k(0,1,1,1) holds for ALL k = 1..8 -- the originally conjectured integrality route fixes NOTHING, the naive dial is dead, the three other dials carry; (ii) CONFORMAL EMBEDDING 47k^2 + 219k - 266 = 47(k-1)(k+266/47) = 0 resp. D8-in-E8: 128k(1-k) = 0; (iii) CENTRAL CHARGE 248k/(k+30) = 8 <=> 240(k-1) = 0 (= the prefactor itself); plus the WP5b singular-vector dial: PBW norms m! k(k-1)...(k-m+1), singular vector exactly at grade k+1, k = 1 deletes V(2 theta): 31124 - 27000 = 4124 (Weyl dims 248/3875/27000 from root data). [E] NEGATIVE CONTROLS: D8/SO(16)_1 -- same rank, same c = 8, SAME q^{-1/3} prefactor, but h = (0,1/2,1,1): the discriminator is glue-h INTEGRALITY, not the prefactor (Theta_D8 + Theta_s = E4); Z2 ROTATION gives E = +1/6 (h = 1/2, no mu4-shift sector); mu4 ROTATION makes E_j = (-1/3, 1/24, 1/6, 1/24) sector-DEPENDENT (the common prefactor breaks); wrong k = 2, 3, 4 fail ALL FIVE dials coherently (residuals 360/814/1362; = 4/12/24; level-2 dim stays 31124 != 4124). [C] Kac generation of the maximal submodule by the grade-(k+1) singular vector for k >= 3 (k = 1, 2 machine-anchored by WP5b/WP5c). [O] the BCOV/Costello-Li twistor inflow itself (Costello's one-loop axion lambda_g/(8 pi sqrt 3) on PT, the Costello-Paquette-Sharma level-from-flux mechanism) stays OPEN -- v502 anchors the CFT side of WP5e only (alpha stage), the KILL branch ('inflow demands a level != 1') is NOT triggered on the CFT side but its twistor side is untested; WP5e stays [O], SEAM.EQUIV.01 untouched, no marker moves. Exact (sympy/Fraction).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv502_celestial_wp5e_prefactor_level.py", "sourceSha256": "414e783c9402a04f1de3abfcd49f6a7e5360fd1a9a7084ebfc1a3f139d0f8440", "linkedClaimIds": [ "CELEST.WP5E.ALPHA.01" ], "sectionIds": [ "section:1890ff3254bb8da69e68", "section:307c4c95a7c84b5efc0b", "section:3e3e7c41b2e8190a5e2f", "section:3ed2167aff70cc409f71", "section:469263059c1e8cf1fd20", "section:6ddf4757acde55521050", "section:701d23928f8e38ea7d4b", "section:7d0e50b6a6c30535730d", "section:8abc3c61baefc9b60bc8", "section:ab9e7e520130ecc7da7c", "section:b38be2626e35c37f4bd1", "section:b63f8484d81bde8026ec", "section:cca5b83aae425d5f0e88", "section:e01862309e920e04fb7f" ], "activeSectionIds": [ "section:3e3e7c41b2e8190a5e2f", "section:3ed2167aff70cc409f71", "section:469263059c1e8cf1fd20", "section:6ddf4757acde55521050", "section:8abc3c61baefc9b60bc8", "section:ab9e7e520130ecc7da7c", "section:b38be2626e35c37f4bd1", "section:b63f8484d81bde8026ec", "section:e01862309e920e04fb7f" ], "evidenceId": "python_verification:verification/v502_celestial_wp5e_prefactor_level.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v502_celestial_wp5e_prefactor_level.py", "pubMirrorHash": "414e783c9402a04f1de3abfcd49f6a7e5360fd1a9a7084ebfc1a3f139d0f8440", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v502_celestial_wp5e_prefactor_level.py" }, { "id": "v503_qgeo_emergence_light", "filename": "v503_qgeo_emergence_light.py", "path": "verification/v503_qgeo_emergence_light.py", "cluster": "frontier", "synopsis": "QGEO.EMERGE.LIGHT.01: the v215 deferred emergence test (lever 7) EXECUTED in its first honest LIGHT version, plus the RESIDUAL-CONVERGENCE result QGEO-R1 == P2-R1 (analysis/kill-test class, v347/v264 style; NO marker moves -- QGEO.REALIZE.01 stays [C]/[O], AX.P2.01 stays an axiom). [N] NO DYNAMICAL SELECTION (zeta-log-det via the Dedekind-eta formula, mpmath 40 digits): logF = log(tau2 |eta|^4) exactly S-invariant (< 1e-35); on the rectangular family tau = it a strict local MAXIMUM (g'(1) = 0, g''(1) = -1.298) but a MINIMUM in the tau1-direction (h''(0) = +0.298): tau = i is a SADDLE of the full moduli space; critical points = the CM points (E2*(i) = E2*(rho) = 0 to 40 digits, generic 0.163 != 0); the GLOBAL det' winner at fixed area is the HEXAGONAL torus (logF(rho) = -1.03352 > logF(i) = -1.05469, diff 0.021169; Osgood-Phillips-Sarnak 1988) -- free-field dynamics alone does NOT select tau = i; criticality at the square = Palais symmetric criticality (the independent heat trace is equally critical). [N] SHARP RIGIDITY (v280 lattice DtN, N = 8): the mod-4 off-character indicator (the v215-K3 lever as a MODULUS FUNCTION) vanishes to 8e-15 EXACTLY at tau = i and rises strictly monotonically in both directions (min 8.4e-2 for t != 1) -- an isolated zero, not a flat valley; R^2 = Z2 exact as permutation matrices (the v492 Z8 bridge on the lattice); j(it) >= 1728 with equality ONLY at t = 1, j(rho) = 0. [E] THE Z2 CHAIN IS MODULUS-BLIND: the involution has exactly 4 fixed points and [Z2, Delta_t] = 0 on EVERY torus (v216 confirmed without mark input); pillowcase det' = 1/2 torus det' EXACTLY (+- pair structure, ratio 1 to 1e-12) so all tau conclusions transfer verbatim; [Z2, H_t] = 0 for all t -- marks / mark-locality / deck^2 exist on EVERY pillowcase, ONLY the order-4 clock distinguishes tau = i; Aut(E_rho) = Z6 (element orders 1,2,3,6) contains NO order-4 element -- dynamics and clock are logically INDEPENDENT selectors; GIVEN the clock, P(iZ) = P(Z) forces a3 = a2 = a1 = 0 and j = 1728 identically (v493 mini): the modulus is NOT a second input. [C/O] RESIDUAL CONVERGENCE (the core finding): the order-4 element on H^1 is a COXETER element of W(A3) (char poly lam^3+lam^2+lam+1, order h(A3) = 4 = |mu4| = N_fam + 1) -- exactly the P2 cusp-class/carrier datum of the P2 hardening (v499 R1) => QGEO-R1 == P2-R1: ONE common residual, 'why does the raw seam carry the order-4 clock', not two scattered ones; chain: (i) mark count 4 derived (v216 [E]), (ii) square derived GIVEN the clock (v493 [E]), (iii) clock = carrier input [C], (iv) rest = the dynamical realisation of the clock [O]; route classification (v347 analogue): B-rigidity in the sharpened form 'RP seam data => order-4 clock' is the live route -- free dynamics alone does NOT deliver the clock (the hexagonal finding). LEVER UPDATE (documented here, v215 itself unchanged): v215 lever 7 lifted from 'deferred, not executable' to 'light version EXECUTED, result: rigidity, not dynamical selection' -- marks emerge, the square does NOT emerge dynamically, it is pinned by the clock, and the clock is the input. Python (mpmath 40 digits + numpy/scipy lattice + sympy exact); the eta/E2*/j CM identities, the pillowcase halving and the Coxeter charpoly are Wolfram-mirrored, the lattice DtN curves stay Python-only (flagged).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv503_qgeo_emergence_light.py", "sourceSha256": "3a977142c8b7affa15eaa0c0e2ffa74c590fee51183eb9b2806cb858b5ebb532", "linkedClaimIds": [ "QGEO.EMERGE.LIGHT.01" ], "sectionIds": [ "section:2525c189f32461c9368a", "section:3721516595f24fd66f4c", "section:46614e805445fc78e7af", "section:4fee06b8389287124647", "section:6a93c4dd5fe420e1990e", "section:6b49d8830dc9fa3948be", "section:6cd1a267e72b20619327", "section:74bb3766bdd1275dbd78", "section:7d0e50b6a6c30535730d", "section:888628823bf71f709698", "section:a036d63765e830eb593f", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:b63f8484d81bde8026ec", "section:b93e6ae7b00f32ee1201", "section:cca5b83aae425d5f0e88", "section:cdd3ea07b0ec5995036b", "section:d90bd5e1e6d8fa41397d", "section:f9b30725993b14c4ee95", "section:ffb3c952b2d4af559d34", "section:ffca98d84a77b4d4e4ab" ], "activeSectionIds": [ "section:3721516595f24fd66f4c", "section:46614e805445fc78e7af", "section:4fee06b8389287124647", "section:6b49d8830dc9fa3948be", "section:74bb3766bdd1275dbd78", "section:888628823bf71f709698", "section:a036d63765e830eb593f", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:b63f8484d81bde8026ec", "section:cdd3ea07b0ec5995036b" ], "evidenceId": "python_verification:verification/v503_qgeo_emergence_light.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v503_qgeo_emergence_light.py", "pubMirrorHash": "3a977142c8b7affa15eaa0c0e2ffa74c590fee51183eb9b2806cb858b5ebb532", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v503_qgeo_emergence_light.py" }, { "id": "v504_celestial_wp5d_klm_completeness", "filename": "v504_celestial_wp5d_klm_completeness.py", "path": "verification/v504_celestial_wp5d_klm_completeness.py", "cluster": "frontier", "synopsis": "CELEST.WP5DB.01: WP5d-beta of the celestial-holographic research contract CELEST.SEAM.01 -- 'split + strong additivity from the lattice', the two remaining KLM legs of complete rationality (split + strong additivity + finite mu-index; the index is v501). numpy/scipy Gaussian machinery + exact GF2/integer algebra; the U(1)/Dirac number-conserving subnet = the preregistered negative control. [E] STRONG ADDITIVITY ALGEBRAICALLY EXACT: 'touching' = shared boundary Majorana => Even(A) v Even(B) = Even(A u B) EXACTLY (GF2 spans full 64/64, 256/256, 512/512, 1024/1024; matrix rank 32/32); disjoint exactly half (rank 16/32, index 2 -- the missing sector odd(x)odd = the ln-2 bit of v501, localised at the split point); U(1)/neutral algebras do NOT generate the union even WITH the shared site (gaps 2/10/52 growing). [N] ENTROPIC WITNESS: fermionic touching MI diverges with exact (c/3)ln2 increments (0.115525, dev 1.2e-6 -- pure UV reference); the Z2/orbifold sector-sum deficit is BOUNDED < ln 2, monotone, (ln2 - Delta_2) ~ N^(-p) with p = 0.2444 vs 2 Delta_mu = 1/4 (Ising disorder exponent); split-point scan reflection-symmetric 3.9e-14; ED vN same direction; gap continuity to the v501 x -> 1 endpoint; honest note: 'defect -> 0' would be FALSE at the sharp lattice split -- bounded <=> finite index (Longo-Xu) is the correct statement; U(1) CONTRAST: D_U1 bursts ln 2 from L = 128 and grows as (1/2) ln Var Q_A (Klich-Levitov 0.10134 vs 1/pi^2 = 0.10132). [N] SPLIT/NUCLEARITY: sigma_k of the off-diagonal block fall exponentially with rate = elliptic nome pi K(1-x)/K(x) to 1.3-2.0% (d = 16/64/256/512: rates 2.29/3.24/4.82/5.81); sigma_1 ~ x^0.5044 (vs 1/2, the dimension-1/2 two-point law); trace norm summable, falling (Buchholz-Wichmann proxy). [E] ORBIFOLD INHERITANCE EXACT: P_A: C -> -C (sigma_k identical 8.3e-17); the even-bilinear coupling Gram = the second compound Lambda^2 C with singular values {sigma_a sigma_b} (2.8e-14) -- same ladder, doubled rate; orbifold MI < 3% of the fermionic, falling (Longo heredity [C]). [E] PIMSNER-POPA: E(a) - a/2 = PaP/2 IDENTICALLY => lambda = 1/2 = 1/[F:F_even] EXACT; attainment in integers (all 16384 monomial pairs N = 8: 8192 extremal with M^2 = 4/Tr M = 0/PMP = -M, 0 violations; N = 12: 2048/2048; random pencil min lambda = 0.5000000000); two-interval group lambda = 1/4 = 1/mu exact; INDEX CONSISTENCY of two routes (exp(Delta) = 2.000000000 = 1/lambda_PP; exp(2 Delta) = 4 = 1/lambda_E4 = mu). [E/N] NEGATIVE CONTROLS: U(1) PP lambda = 1/(m+1) -> 0 (infinite index); dimerised trivial (deficit N-independent 3.6e-15, sigma_1 exponential); U(1) small-L honesty; Z2 finite-size honesty (14.9% below ln 2 at N = 4096 -- witness, not proof); wrong prescription {1, P_AB}: deficit exactly 0. [C] the lattice -> continuum KLM dictionary (Longo-Xu, CHMP, Longo heredity). [O] the continuum theorem 'finite-group orbifolds of completely rational nets are completely rational' is XU'S THEOREM -- cited, not claimed; the proof for the concrete seam quotient net and the interacting condensed (E8)_1 net stays WP5e/Costello-Li; SEAM.EQUIV.01 stays [O]. VERDICT: with v501, all THREE KLM ingredients of complete rationality are witnessed on the lattice.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv504_celestial_wp5d_klm_completeness.py", "sourceSha256": "e13b8cdc4b819c631d2e40a8db19d6da674802bf09586c49b6e9383071fae891", "linkedClaimIds": [ "CELEST.WP5DB.01" ], "sectionIds": [ "section:307c4c95a7c84b5efc0b", "section:3ed2167aff70cc409f71", "section:701d23928f8e38ea7d4b", "section:7d0e50b6a6c30535730d", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b38be2626e35c37f4bd1", "section:b63f8484d81bde8026ec", "section:cca5b83aae425d5f0e88", "section:f7d73358ce212e71ac18" ], "activeSectionIds": [ "section:3ed2167aff70cc409f71", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b38be2626e35c37f4bd1", "section:b63f8484d81bde8026ec", "section:f7d73358ce212e71ac18" ], "evidenceId": "python_verification:verification/v504_celestial_wp5d_klm_completeness.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v504_celestial_wp5d_klm_completeness.py", "pubMirrorHash": "e13b8cdc4b819c631d2e40a8db19d6da674802bf09586c49b6e9383071fae891", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v504_celestial_wp5d_klm_completeness.py" }, { "id": "v505_celestial_wp5e_beta_equivariant_ledger", "filename": "v505_celestial_wp5e_beta_equivariant_ledger.py", "path": "verification/v505_celestial_wp5e_beta_equivariant_ledger.py", "cluster": "frontier", "synopsis": "CELEST.WP5E.BETA.01: WP5e-beta of the celestial-holographic research contract CELEST.SEAM.01 -- 'the equivariant anomaly ledger on twistor space', the twistor-side milestone of WP5e (the BCOV/Costello-Li twistor uplift; preregistered kill: the anomaly inflow demands a level != 1); WP5e-alpha (v502) anchored the CFT side. The Atiyah-Bott/Lefschetz fixed-point skeleton of the one-loop box anomaly (Costello arXiv:2111.08879; Bittleston-Sharma-Skinner CMP 403) evaluated EXACTLY on C^2/Z4 with the E8 mu4-glue monodromy. Exact sympy/Fraction, no floats. [E] AB LEDGER: denominators det(1 - g_j^{-1}) = (2, 4, 2); sum of reciprocals 5/4 = (|Z4|^2-1)/12 (Dedekind); equivariant characters tr_{g_j}(Ad E8) = (248, 0, -8, 0) by TWO routes (graded dims / root sum); invariant average 60 = the D5+A3 carrier; Frobenius 61568; tr_{g_2} = -8 = 120 - 128 (so16 supertrace). [E] OKUBO PER SECTOR (honest sharpening): the invariant sector is exactly Okubo-quadratic (Q^(0) = 36^2, 36 = lambda~^2_e8 -- v495 re-derived through the glue grading); the TWISTED sectors do NOT reduce (independent-quartic content T5: (-8, 32, -8), T3: (48, -64, 48)); the AB-weighted sum cancels the D5 quartic EXACTLY and leaves the RIGID residual 32 T3; no reweighting of the twisted sectors alone is quartic-free, the only quartic-free weighting is the uniform Z4 projector; the graded GS-exchange ansatz is exactly rank-obstructed in sectors 1, 2, 3; heterotic identities exact (Tr_120 = 8tr^4 + 3(tr^2)^2, Tr_128 = -8tr^4 + 6(tr^2)^2, Tr_E8 = 9(tr^2)^2). [E] INDEX BRIDGE (centrepiece): f(m) = (1/4) sum_j (i^{jm}-1)/det_j = (0, -3/8, -1/2, -3/8) = ch2(T_m) = -(C^{-1})_mm/2 EXACTLY -- fixed-point ledger = McKay/Kronheimer intersection ledger; glue-bundle ch2 defect -78 by BOTH routes (per class (-24, -30, -24); -30 = -h_vee, a [C] coincidence); bridge identity sum_m h_A3(m) = 5/4 = sum_j 1/det_j; sphere pairing integer on all 240 roots, Killing sums (320, 320, 240, 320), total 1200 = 2 h_vee (h,h). [E] k = 1 GEOMETRIC: lattice current count (norm-2/k in the glue cosets) = 240 at k = 1, EXACTLY 0 at k = 2, 3, 4 (no adjoint closure); embedding residual 47k^2+219k-266 = (0, 360, 814, 1362); h(J;k) = k integer for ALL k -- integrality alone fixes nothing (honest, as v502); one scale => one level (v493 lockstep periods, det(A-1) = -4: no invariant flux vector). [E] E3 REFUTED (prominent): a0 in O(8) fills the GRAVITON slot O(2), NOT the BSS axion slot O(-2) (Hamiltonian weights X = -2 != +2 = Y; mismatch 4 = |mu4|, a [C] coincidence) -- 'the theory brings its GS axion as a0' is REFUTED; instead the three H2(ALE) classes carry exactly the Coxeter eigencharacters {i, -1, -i} = the three twisted ledger slots (bijection, no invariant class); slot count 1 + 3 = 4 = |mu4| soft. [E] NEGATIVE CONTROLS: diag(i,i) breaks the ledger four ways (sum 1/det = 1/4, omega-weight -1 not CY, 5 invariant-ring generators); SO(16) glue: characters (120, 0, +120, 0), defect -30 != -78, bulk Okubo FAILS (T5 = 16, T3 = -32: independent quartic Casimir, no single-axion GS); k = 2: current count 0, c-prefactor -31/48 != -1/3 (integrality dials stay integer -- the kill is the closure dial). [C] dictionaries (CS(rho) mod 1 = discriminant weight; 32 = (h,h)+(h',h'); -30 = -h_vee; the Omega-contraction identification). [O] the global BCOV/Kodaira-Spencer quantisation on PT/Z4, non-fixed-point contributions, the O(-2) bulk-axion construction, CPS level-from-flux, and the pairing of the 32 T3 residual with the three sphere axions. VERDICT B; the preregistered kill ('inflow demands a level != 1') does NOT fire on the equivariant skeleton; SEAM.EQUIV.01 untouched, no marker moves. Exact (sympy/Fraction).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv505_celestial_wp5e_beta_equivariant_ledger.py", "sourceSha256": "b0ad20db2bdeda29c98604ca76d3ebe9d74acb60399d66b643b1f2c9f9295703", "linkedClaimIds": [ "CELEST.WP5E.BETA.01" ], "sectionIds": [ "section:307c4c95a7c84b5efc0b", "section:31d9a188bf3ec46b9310", "section:3e3e7c41b2e8190a5e2f", "section:3ed2167aff70cc409f71", "section:469263059c1e8cf1fd20", "section:701d23928f8e38ea7d4b", "section:7d0e50b6a6c30535730d", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b38be2626e35c37f4bd1", "section:b63f8484d81bde8026ec", "section:cca5b83aae425d5f0e88", "section:e01862309e920e04fb7f" ], "activeSectionIds": [ "section:31d9a188bf3ec46b9310", "section:3e3e7c41b2e8190a5e2f", "section:3ed2167aff70cc409f71", "section:469263059c1e8cf1fd20", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b38be2626e35c37f4bd1", "section:b63f8484d81bde8026ec", "section:e01862309e920e04fb7f" ], "evidenceId": "python_verification:verification/v505_celestial_wp5e_beta_equivariant_ledger.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v505_celestial_wp5e_beta_equivariant_ledger.py", "pubMirrorHash": "b0ad20db2bdeda29c98604ca76d3ebe9d74acb60399d66b643b1f2c9f9295703", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v505_celestial_wp5e_beta_equivariant_ledger.py" }, { "id": "v506_seam_clock_rigidity", "filename": "v506_seam_clock_rigidity.py", "path": "verification/v506_seam_clock_rigidity.py", "cluster": "core", "synopsis": "SEAM.CLOCK.RIGIDITY.01: clock rigidity, Route B of the v503 classification -- two exact theorems reducing the order-4 clock input to ONE alignment bit (Part A Moebius + Part B Fock in one module; QGEO.REALIZE.01 stays [C]/[O], NO marker moves). Exact sympy + exact Cl(16) Fractions, no floats. [E] THEOREM A (Moebius): the collar deck z -> -z has in PGL2(C) EXACTLY TWO square roots (z -> +iz, z -> -iz), both AUTOMATICALLY of order 4 (complete case analysis: tr != 0 => diagonal => a/d = +-i; tr = 0 impossible) -- 'order 4' is NO input anymore; a marks-preserving square root exists <=> the deck is the CENTRAL involution of the mark-stabiliser D4 (center = {id, deck}, exactly 2 order-4 elements = the clocks) => then marks = one mu4 orbit, cross-ratio class {2, 1/2, -1}, j = 1728, tau = i, free 4-cycle, deck = clock^2, only the scale free; COUNTEREXAMPLE (mandatory): {+-1, +-(3+2sqrt2)} is deck-free AND harmonic (j = 1728) with full D4 stabiliser, but the deck sits in it non-centrally (edge involution) => 0 roots -- harmonicity alone is NOT sufficient; the RP filter selects nothing (both real structures pass both roots: the Aut(Z4) ambiguity is irreducible, consistent with v492). [E] B3/B4: a free Z_n orbit forces n | 4; mark transitivity forces n = 4; faithfulness kills n >= 5; n = 3 fixes a mark; n = 6 dies independently at cusp degree 3 (v117); the deck is modulus-blind (v503 B5 exact); controls: n = 8 has only orbits of size 8 (impossible on 4 marks); hexagonal A4 (order 12, ZERO order-4 elements, squares only orders {1,3}); generic Klein V4 (exponent 2 -- not even the deck has a root); stabiliser trichotomy V4/D4/A4 with order-4 counts (0, 2, 0). [E] THEOREM B (Fock, the core result): the unique S^2 spin structure gives NS on every circle (established P1 datum); one-particle: the NS half-rotation has D^2 = -1 (charpoly (lam^2+1)^8), the quarter-shift C has C^2 = D, C^8 = 1 (charpoly (lam^4+1)^4); Fock: Utilde = prod_j(1 - gamma_j gamma_{j+8}), Utilde^2 = 256 gamma_1...gamma_16 => U^2 = (-1)^F EXACTLY, and (cU)^2 = c^2 (-1)^F is NEVER 1 (center of Cl(16) = scalars) -- the Z4 lift is FORCED (nonsplit extension 1 -> Z2^{(-1)^F} -> Z4 -> Z2^{deck} -> 1); Z8 tower: V^2 prop Utilde, V^4 prop (-1)^F, projective order 8 = 2|mu4| -- fermionically explained; R control: U_R^2 = +1 (split -- the forcing rests on NS = the established geometry); 16-fold way: theta_v = 1 at nu = 16; robustness: the forcing already holds at 8 sites. [C] THE ONE REST: 'the collar deck is the central involution of the mark-D4' (<=> square-root existence on the mark data) -- ONE alignment bit; the fermionic Z4 forces the ORDER, not the spatial alignment. No overclaim. QGEO-R1 == P2-R1 (v503) now reads: given the bit, order/uniqueness/orbit/tau = i are theorems. Exact (sympy + Cl(16) Fractions).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv506_seam_clock_rigidity.py", "sourceSha256": "3f8605fb91c96583072913c5f2546cdd491a73f3ad2494c907a0115dcd3d450b", "linkedClaimIds": [ "SEAM.CLOCK.RIGIDITY.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:2525c189f32461c9368a", "section:307c4c95a7c84b5efc0b", "section:3721516595f24fd66f4c", "section:3e3e7c41b2e8190a5e2f", "section:46614e805445fc78e7af", "section:62801f711a0d267461ac", "section:6a93c4dd5fe420e1990e", "section:6b49d8830dc9fa3948be", "section:6cd1a267e72b20619327", "section:701d23928f8e38ea7d4b", "section:70380cf4813f5dcd47e6", "section:74bb3766bdd1275dbd78", "section:7d0e50b6a6c30535730d", "section:8182ecd6055b0d0d488c", "section:8872501633bb702220cd", "section:888628823bf71f709698", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b63f8484d81bde8026ec", "section:b93e6ae7b00f32ee1201", "section:c31c8db87fec4e08752e", "section:cca5b83aae425d5f0e88", "section:cdd3ea07b0ec5995036b", "section:cdda6bb5746f6a6a897d", "section:d90bd5e1e6d8fa41397d", "section:f22c82858ff073c133d4", "section:f9b30725993b14c4ee95", "section:fc7f5b07a661660c0d79", "section:ffb3c952b2d4af559d34", "section:ffca98d84a77b4d4e4ab" ], "activeSectionIds": [ "section:3721516595f24fd66f4c", "section:3e3e7c41b2e8190a5e2f", "section:46614e805445fc78e7af", "section:6b49d8830dc9fa3948be", "section:70380cf4813f5dcd47e6", "section:74bb3766bdd1275dbd78", "section:888628823bf71f709698", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b63f8484d81bde8026ec", "section:c31c8db87fec4e08752e", "section:cdd3ea07b0ec5995036b", "section:cdda6bb5746f6a6a897d", "section:f22c82858ff073c133d4", "section:fc7f5b07a661660c0d79" ], "evidenceId": "python_verification:verification/v506_seam_clock_rigidity.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v506_seam_clock_rigidity.py", "pubMirrorHash": "3f8605fb91c96583072913c5f2546cdd491a73f3ad2494c907a0115dcd3d450b", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v506_seam_clock_rigidity.py" }, { "id": "v507_seam_bit_origin", "filename": "v507_seam_bit_origin.py", "path": "verification/v507_seam_bit_origin.py", "cluster": "core", "synopsis": "SEAM.BIT.ORIGIN.01: the tautology attack on the v506 alignment bit, executed and refuted -- where do the marks AND the deck come from, and does their common origin force the central alignment? (Part A torus origin + Part B fermion dichotomy in one module; NO marker moves -- the bit stays [C], SEAM.CLOCK.RIGIDITY.01 and QGEO.REALIZE.01 text-precised only.) Exact sympy + exact Cl(16) Fractions, no floats. [E] ORIGIN THEOREM: the 4 marks are the fixed points of the hyperelliptic involution w -> -w on C/(Z + tau Z) = the four half-periods Lambda/2Lambda (a 1/3-coefficient never qualifies); a translation t_c descends to the base sphere iff 2c in Lambda -- exactly the THREE half-period translations (control c = 1/3 fails); the descended maps are the EXPLICIT rational involutions sigma_i(x) = e_i + (e_i-e_j)(e_i-e_k)/(x-e_i) with the exact curve-lift identity prod(sigma_i - e_l) = psi_i^2 prod(x - e_l), psi_i RATIONAL (the p-function addition formula as pure algebra); {id, sigma_1, sigma_2, sigma_3} = Klein V4; CONVERSELY, in ALL three stabiliser types the freely-acting involutions are EXACTLY the three sigma_c (generic V4 (4,3,3), harmonic D4 (8,5,3), hexagonal A4 (12,3,3)) => EVERY mark-free collar deck (v216) IS a half-period translation -- the CLASS of the deck is forced, its POSITION is not. [E] CORE SOLVE (symbolic in the Legendre modulus lambda): sigma_c admits a marks-preserving PGL2 square root <=> lambda in {-1} (sigma_1), {2} (sigma_2), {1/2} (sigma_3) -- per half-period exactly ONE solution; intrinsically: the two deck pairs separate each other HARMONICALLY (pair cross-ratio = -1, same solution sets); the union over c is the harmonic orbit {-1, 2, 1/2} <=> j = 1728 <=> tau = i; generic modulus: Stab = V4 abelian, ALL sigma_c central and yet clockless ('central alone is EMPTY' -- the bit is the CONJUNCTION Stab = D4 AND deck central); at tau = i the stabiliser jumps to D4 with sigma_1 central (2 roots = the clock pair) and sigma_2/sigma_3 edge-type (0 roots); the v506 seam deck z -> -z lands on the central sigma_1 = -1/x under ALL 8 mark bijections; CM DICTIONARY: mult-by-i fixes exactly ONE nonzero half-period c* = (1+tau)/2 (mult-by-rho 3-cycles all three -- hexagonal has no distinguished one); the clock lift needs the CM unit i (psi = 2i/(x+1)^2, t^2+1 irreducible over Q) while half-period decks lift RATIONALLY: the clock root exists only WITH CM by Z[i] <=> tau = i. [E] EQUIVALENCE TETRAD + CIRCULARITY AUDIT: 'clock exists' <=> (tau = i AND deck = the CM-fixed half-period translation) <=> (Stab = D4 AND deck central) <=> deck pairs harmonically separated <=> the NS Fock lift is NONSPLIT (Part B); audit: the v493 converse (clock GIVEN => P(iZ) = P(Z) forces a3 = a2 = a1 = 0, j = 1728) independently re-verified -- two independently computed converses of ONE equivalence, no circularity. [E] FERMION DICHOTOMY (the new physical face): central arrangement (shift by 8 on the 16-site NS seam): Utilde^2 = 256 gamma_1...gamma_16 => U^2 = (-1)^F, nonsplit Z4 extension, 2 square roots in the 32-element dihedral lift group (the Z8 tower); edge arrangement (reflection j -> 4-j, fixed sites = NON-marks = the silver {0, inf} between neighbour marks): the implementation EXISTS but Utilde_e^2 = +2^7 x 1 => U^2 = +1, the extension SPLITS, 0 roots, no Z8 tower; one-particle level (lam^2+1)^8 vs (lam^2-1)^8; arrangement census: ALL 28 shift-invariant 4-sets cross (central type), ALL 21 mark-free reflection-invariant sets do not; robustness at 8 sites; R-sector edge control splits too -- the bit IS a physical extension class (Fidkowski-Kitaev-type): distinguished, but not derived; WHICH class nature realises stays the input. [E] SILVER PLACEMENT (in-family witness against the tautology): the v506 counterexample {+-1, +-(3+2sqrt2)} = 'tau = i with deck = a NON-CM-fixed half-period translation' (all 8 mark bijections carry its deck to sigma_2/sigma_3, never sigma_1) -- the common torus origin does NOT exclude the misalignment. [C] THE REST (verbatim, no overclaim): the one alignment bit remains a carrier datum; no tautology -- the origin forces the CLASS of the deck (half-period translation), not its POSITION. Exact (sympy + Cl(16) Fractions).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv507_seam_bit_origin.py", "sourceSha256": "926ea236729dffb3ac531ecd34c9b8efa02afea1632abf9798786e65b40ada1f", "linkedClaimIds": [ "SEAM.BIT.ORIGIN.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:2525c189f32461c9368a", "section:307c4c95a7c84b5efc0b", "section:3721516595f24fd66f4c", "section:46614e805445fc78e7af", "section:62801f711a0d267461ac", "section:6a93c4dd5fe420e1990e", "section:6b49d8830dc9fa3948be", "section:6cd1a267e72b20619327", "section:701d23928f8e38ea7d4b", "section:70380cf4813f5dcd47e6", "section:74bb3766bdd1275dbd78", "section:7d0e50b6a6c30535730d", "section:8182ecd6055b0d0d488c", "section:8872501633bb702220cd", "section:888628823bf71f709698", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b63f8484d81bde8026ec", "section:b93e6ae7b00f32ee1201", "section:c31c8db87fec4e08752e", "section:cca5b83aae425d5f0e88", "section:cdda6bb5746f6a6a897d", "section:d90bd5e1e6d8fa41397d", "section:f22c82858ff073c133d4", "section:f9b30725993b14c4ee95", "section:fc7f5b07a661660c0d79", "section:ffb3c952b2d4af559d34", "section:ffca98d84a77b4d4e4ab" ], "activeSectionIds": [ "section:3721516595f24fd66f4c", "section:46614e805445fc78e7af", "section:6b49d8830dc9fa3948be", "section:70380cf4813f5dcd47e6", "section:74bb3766bdd1275dbd78", "section:888628823bf71f709698", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b63f8484d81bde8026ec", "section:c31c8db87fec4e08752e", "section:cdda6bb5746f6a6a897d", "section:f22c82858ff073c133d4", "section:fc7f5b07a661660c0d79" ], "evidenceId": "python_verification:verification/v507_seam_bit_origin.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v507_seam_bit_origin.py", "pubMirrorHash": "926ea236729dffb3ac531ecd34c9b8efa02afea1632abf9798786e65b40ada1f", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v507_seam_bit_origin.py" }, { "id": "v508_celestial_wp5e_gamma_pairing", "filename": "v508_celestial_wp5e_gamma_pairing.py", "path": "verification/v508_celestial_wp5e_gamma_pairing.py", "cluster": "frontier", "synopsis": "CELEST.WP5E.GAMMA.01: WP5e-gamma of the celestial-holographic research contract CELEST.SEAM.01 -- 'the sphere-axion pairing check', an honest rigid NEGATIVE result (v505 style): can the three twisted sphere axions eta_m (Coxeter eigencharacters {i, -1, -i} on H^2(ALE), v505 S5.8) cancel the rigid 32 T3 residual of the Atiyah-Bott ledger (A_fix = 9P1 - 30P2 - 15P3 + 32 T3, v505 S3.7) by Green-Schwarz-type EXCHANGE with sector-compatible quadratic vertices? NO, with certificate. Exact sympy/Fraction, no floats (27 checks). [E] VERTEX-SPACE THEOREM: the W(D5) x W(A3)-invariant quadratics on the 8-dim glue Cartan = EXACTLY span{s5, s3} (dim 2, bidegree dims (1,0,1)); quartics = EXACTLY span{P1, P2, P3, T5, T3} (dim 5, bidegree dims (2,0,1,0,2)) -- vertex basis complete (Weyl nullspace arithmetic over all bidegrees); PRODUCT THEOREM (the master kill): (a s5 + b s3)(c s5 + d s3) = ac P1 + (ad+bc) P2 + bd P3 identically -- ZERO T5/T3 content, so EVERY exchange image (any axion count, any rule, any couplings) is annihilated by Phi_T3, while Phi_T3(A_fix) = 32 != 0. [E] SELECTION ENUMERATION: strict two-index reading COLLAPSES (C_{j,j'} != 0 only for j' = -j => the rule forces m = 0 -- the sphere axions have NO invariant bilinear Cartan vertex at all); twist-insertion: eta_1 <-> K^(3), eta_2 <-> K^(2), eta_3 <-> K^(1), eta_0 <-> K^(0); channels E13 = (16, -96, 144, 0, 0), E22 = (16, 32, 16, 0, 0), E00 = 225 E22; SIDE DISCOVERY: K^(0) = -15 K^(2) (the even-sector quadratics are PARALLEL). [E] UNSOLVABILITY WITH CERTIFICATE (core): exchange matrix 5 x 2, rank 2, kernel 0; rank([M | A_fix]) = 3; annihilator certificate (Phi_T5, Phi_T3, Phi_P)(A_fix) = (0, 32, 72) with A_fix = (9, -30, -15, 0, 32) -- two independent obstructions: 32 T3 (structural, rule-independent) and Phi_P = 72 (rule-driven via the K^(0) || K^(2) collapse); ker M = 0 forces the unique non-disturbing coupling c = 0 (the sphere axions are RIGIDLY SILENT); Phi_P(Q^(0)) = 0 (the v505 sector-0 mechanism undisturbed); relaxed control: dropping charge conservation reaches the P-block (rank 3, det -64) but T5 = T3 = 0 persists. [E] NATURALNESS RESOLUTION: ch2-natural (9/64, 1/4) and AB-weight (1/2, 1/4) couplings both have certificate (0, 0) vs required (32, 72) -- the failure is scale- and coupling-INDEPENDENT (no 'unnatural factor': the ansatz space misses the target identically). [E] NEGATIVE CONTROLS: (a) invariant axion only = v505 S3.9 replicated + sharpened; (b) flipped rule m + j - j': the Phi_T3 kill is flip-invariant, Phi_P is rule-dependent; (c) SO(16): odd classes EMPTY, AB sum (15, -18, -15, -4, 40) does not even cancel T5 (E8 doubly special); (d) D8: 16 T8 + 12 s8^2, no T3 structure -- the question cannot even be posed. [C] number fences: 32 = (h,h) + (h',h') = 20 + 12; 72 = 2 lambda~^2_e8. [O] SHARPENED FENCE: the exchange sub-branch is DEAD; the 32 T3 residual MUST be carried by twisted BCOV contact terms -- binary criterion WP5e-delta-1: the one-loop coefficient on C^2/Z4 must come out exactly (9, -30, -15, 0, 32), COMPUTED, not fitted; named escape WP5e-delta-2: the full-tensor ledger (the collapse is Cartan-restricted); slot bijection (v505 S5.8) untouched; the preregistered level-kill still does NOT fire; SEAM.EQUIV.01 stays [O]; no marker moves. Exact (sympy/Fraction).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv508_celestial_wp5e_gamma_pairing.py", "sourceSha256": "c9c1f50cec131882f8785c757fb559e1146bc3ba98943142c881e3d04a6d3d33", "linkedClaimIds": [ "CELEST.WP5E.GAMMA.01" ], "sectionIds": [ "section:0e7ddbc8b9cd02f418a6", "section:10cd00cff69c903fd3c3", "section:2bbe8c5924cafd6c6187", "section:307c4c95a7c84b5efc0b", "section:31d9a188bf3ec46b9310", "section:37056704285dbc4b9f42", "section:3ed2167aff70cc409f71", "section:6a93c4dd5fe420e1990e", "section:6ddf4757acde55521050", "section:701d23928f8e38ea7d4b", "section:7d0e50b6a6c30535730d", "section:7ee581db787f8ddbcb4a", "section:8d1e955857da6655fadd", "section:ab9e7e520130ecc7da7c", "section:b38be2626e35c37f4bd1", "section:b63f8484d81bde8026ec", "section:bc61b0e372551b770dfb", "section:c519f45910c30ff3c0ae", "section:cca5b83aae425d5f0e88", "section:d297d5f783e66d564ec2", "section:d90bd5e1e6d8fa41397d", "section:e01862309e920e04fb7f", "section:f68163cf343646a0f102" ], "activeSectionIds": [ "section:0e7ddbc8b9cd02f418a6", "section:2bbe8c5924cafd6c6187", "section:31d9a188bf3ec46b9310", "section:37056704285dbc4b9f42", "section:3ed2167aff70cc409f71", "section:6ddf4757acde55521050", "section:8d1e955857da6655fadd", "section:ab9e7e520130ecc7da7c", "section:b38be2626e35c37f4bd1", "section:b63f8484d81bde8026ec", "section:bc61b0e372551b770dfb", "section:d297d5f783e66d564ec2", "section:e01862309e920e04fb7f", "section:f68163cf343646a0f102" ], "evidenceId": "python_verification:verification/v508_celestial_wp5e_gamma_pairing.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v508_celestial_wp5e_gamma_pairing.py", "pubMirrorHash": "c9c1f50cec131882f8785c757fb559e1146bc3ba98943142c881e3d04a6d3d33", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v508_celestial_wp5e_gamma_pairing.py" }, { "id": "v509_celestial_wp5e_eps2_level_from_flux", "filename": "v509_celestial_wp5e_eps2_level_from_flux.py", "path": "verification/v509_celestial_wp5e_eps2_level_from_flux.py", "cluster": "frontier", "synopsis": "CELEST.WP5E.EPS2.01: WP5e-epsilon-2 of the celestial-holographic research contract CELEST.SEAM.01 -- 'the CPS level-from-flux dial', executed (verdict B): derive the boundary level k = 1 from flux quantisation on the lockstep spheres, following the Costello-Paquette-Sharma (CPS) Burns-holography mechanism (PRL 130, 061602; arXiv:2306.00940). Exact sympy/Fraction, no floats (28 checks, <1 s). [E] CPS SKELETON REPLICATED EXACTLY: the S^3 period of the brane backreaction 3-form int Omega_N = (2 pi i)^2 N (pullback density -sin(2 theta), phases cancel; their eq. 3.33); the exceptional-sphere Kahler flux int_{P^1} omega = 2 pi N (K = |u|^2 + N log|u|^2, flat part dies at t -> 0); boundary level magnitude 2N via the symplectic-boson double contraction (N = 1, 2, 3), normalisation Dynkin index T(so8 vector) = 1 -- the CPS formula 'level = flux quantum x Dynkin index of the boundary matter', level LINEAR in the flux. [E] PAIRING MATRIX PINNED, NOT POSTULATED: the v505 ch2 ledger (f(m) = -(C^-1)_mm/2 = (-3/8, -1/2, -3/8)) + integrality + unimodularity + effectivity pin P_mi = c1(T_m).[Sigma_i] = delta_mi by COMPLETE enumeration (row candidates 8/6/8; 48 unimodular solutions of P C^-1 P^T = C^-1; with P >= 0 exactly 2 = identity + A3 diagram flip); full c1 matrix -(C^-1)_mn; glue FLUXES F_i = (64, 60, 64) = dim g_i, total 188 = 248 - 60, flip-invariant; flux per charged root current uniformly ONE quantum through exactly one sphere. [E] LEVEL FORMULA, honest: 'level = total open-string flux' is KILLED by the lockstep test itself (k_i = (64, 60, 64) unequal -- F_i is the FLAVOUR multiplicity); what works: k = flux per adjoint current = F_i/dim g_i = (1, 1, 1), anchored non-circularly by the lattice current count (240, 0, 0, 0) for k = 1..4 (v505 S4.8) and the embedding index j(D5 in E8) = j(A3 in E8) = 1 (Killing coefficient 60 = 2 h_vee(E8)). ORD-4-VS-LEVEL-1 RESOLVED: the clock order counts FRACTIONAL flux sectors, not the level -- mu = det(D5) det(A3) = 16 = ord(monodromy)^2, the mu4 glue diagonal isotropic + Lagrangian (order 4 = sqrt 16), KLM condensation 16 -> 16/4^2 = 1 = zero residual fractional flux; NEW DIAL: #primaries((E8)_k) = (1, 3, 5, 10, 15, 27) for k = 1..6 from the affine marks -- exactly ONE sector iff k = 1 (independent of the CPS transplantation). [E] LOCKSTEP THEOREM (the lifting of v505 S4.10 'one scale => one level' to a THEOREM): clock invariance P(iZ) = P(Z) forces a3 = a2 = a1 = 0, the four branch points are ONE mu4 orbit, |Pi_j| = sqrt(2) t EQUAL on all three spheres, monodromy = pure phase i, det(A - 1) = -4 => no invariant flux vector => k1 = k2 = k3 IS A THEOREM of clock invariance; NEGATIVE PROBE (new falsifier): the clock-forbidden family Z^4 - Z (smooth, disc -27, branch points {0, 1, w, w^2} not a mu4 orbit): over ALL 24 orderings ZERO chains with three equal period moduli (1 vs sqrt 3); HONEST LIMIT: uniform flux doubling keeps the lockstep -- the theorem proves EQUALITY, not the value; the value 1 comes from the current/sector counters and the CPS minimal quantum N = 1. [E] NEGATIVE CONTROLS: k = 2 (current count 0, embedding residual 360, prefactor -31/48 != -1/3, #primaries 3 != 1 -- while the lockstep dial honestly does NOT fire); SO(16) glue (fluxes (0, 60, 0): spheres 1/3 FLUX-DARK, ch2 defect -30 != -78, condensation stops at 16/2^2 = 4 = det Cartan(D8)); A2 intersection form (det 3 != 4, glue diagonal 23/24 not integer, mu = 12 not a perfect square: NO Lagrangian subgroup, Dedekind 2/3 != 5/4, Coxeter 3 != 4). [C] the CPS dictionary itself on PT/Z4 (their geometry is the C^2 blow-up with ONE (-1)-sphere and so(8) at negative level -- not the A3 ALE). [O] the type-I B-model backreaction on PT/Z4 (twisted Kodaira-Spencer measure, the A3 Omega_N) -- the same fence as v502 S5.7/v505; delta-1/delta-2 and epsilon-1 stay open; SEAM.EQUIV.01 untouched; no marker moves. Exact (sympy/Fraction).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv509_celestial_wp5e_eps2_level_from_flux.py", "sourceSha256": "33e7f41b735e1651a371bcf43d98e58887b357820536e0413fd72d4b78ea6d88", "linkedClaimIds": [ "CELEST.WP5E.EPS2.01" ], "sectionIds": [ "section:21c9669befc5eafd6176", "section:307c4c95a7c84b5efc0b", "section:3ed2167aff70cc409f71", "section:469263059c1e8cf1fd20", "section:701d23928f8e38ea7d4b", "section:77b944418033334668b5", "section:7d0e50b6a6c30535730d", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b38be2626e35c37f4bd1", "section:b63f8484d81bde8026ec", "section:bc61b0e372551b770dfb", "section:cca5b83aae425d5f0e88" ], "activeSectionIds": [ "section:21c9669befc5eafd6176", "section:3ed2167aff70cc409f71", "section:469263059c1e8cf1fd20", "section:77b944418033334668b5", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b38be2626e35c37f4bd1", "section:b63f8484d81bde8026ec", "section:bc61b0e372551b770dfb" ], "evidenceId": "python_verification:verification/v509_celestial_wp5e_eps2_level_from_flux.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v509_celestial_wp5e_eps2_level_from_flux.py", "pubMirrorHash": "33e7f41b735e1651a371bcf43d98e58887b357820536e0413fd72d4b78ea6d88", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v509_celestial_wp5e_eps2_level_from_flux.py" }, { "id": "v510_seam_bit_freedom", "filename": "v510_seam_bit_freedom.py", "path": "verification/v510_seam_bit_freedom.py", "cluster": "core", "synopsis": "SEAM.BIT.FREEDOM.01: the freedom attack on the v506/v507 alignment bit -- the POSITION half of the bit is topology (Part A dihedral/Fock + Part B Moebius/RP in one module; NO marker moves -- the modulus datum stays [C]). Exact sympy + exact Cl(16) Fractions, no floats (30 checks, <5 s). [E] DIHEDRAL THEOREM: on the N-site seam circle the free involution is UNIQUE = the antipode (N = 16: 17 involutions in D_16, exactly 1 free = shift 8; all 16 reflections have exactly 2 circle fixed points -- sites for even axis, edge midpoints for odd; robustness N = 8, 12); the census is COMPLETE: Aut(C_16) = D_16 exactly (brute force over all 8! permutations at N = 8, propagation at N = 16 -- no exotic circle automorphism); N = 9 control: D_9 has ZERO free involutions (even carrier count needed, consistent with 16 = 2^(g_car-1)); QUOTIENT TOPOLOGY (the P1 tie): circle/antipode = CIRCLE (chi = 0, closed), circle/reflection = INTERVAL (chi = 1, 2 boundary corners) -- origin_theory's 6pi = 2pi+2pi+2pi Gauss-Bonnet budget counts three CLOSED circles, so 'the deck is free on the seam circle' IS the established P1 datum 'the seam is a closed circle', not a new premise. [E] NONSPLIT <=> FREE (complete census, exact Cl(16)): ALL 17 involutions implemented -- the free one's NS lift squares to 256 gamma_1..gamma_16 = (-1)^F (nonsplit, 2 square roots in the 32-element dihedral lift group = the Z8 clock tower); ALL 16 reflections have U^2 = SCALAR (2^7 site-axis, 2^8 edge-axis; split, 0 roots) -- no exception; chain: deck free => deck = shift 8 => crossing mark pairing (all 28 invariant 4-sets) => U^2 = (-1)^F => central class => the edge/silver arrangement is EXCLUDED; Klein control: the orientation-cover deck is free too (covering vs branched is the discriminator, not Moebius vs Klein); branch control: the pillowcase involution (x,y) -> (-x,-y) has exactly 4 fixed points = the marks and restricts to a REFLECTION on invariant circles -- the edge class IS the branched pillowcase involution's restriction: the silver arrangement mistakes the mark-creating branch Z2 for the seam deck. [E] REAL-STRUCTURE CLASSIFICATION (continuum side): the antiholomorphic involutions of P^1 commuting with the celestial deck z -> -z are EXACTLY two families -- mu conj(z), |mu| = 1 (fix locus = a LINE through the deck poles {0, inf}: deck NOT free on it) and mu/conj(z), mu real (mu > 0: fix circle |z| = sqrt(mu) avoiding the poles, deck FREE; mu < 0: empty fix locus, no seam); per deck-invariant configuration the mark-fixing real structure is UNIQUE; table: mu4 -> equatorial 1/conj(z), deck FREE (v506 A-S2.9 reproduced); silver {+-1, +-(3+2 sqrt 2)} -> real axis THROUGH the poles, deck NOT free; generic-unit {+-1, +-(3+4i)/5} -> equatorial, free WITHOUT harmonicity; hexagonal -> NO mark-fixing real structure at all (cross-ratio complex, marks not concyclic: RP-incompatible, consistent v503); Moebius covering model: the sheet-exchange deck of the cylinder double cover is free on ALL points and restricts to the antipode on the Z2 seam fibre; one-sidedness TYPES the Z2 as the free antipode (quotient RP^2 = the |Z2| of c3 = 1/(|Z2| 2pi chi), v456/v73). [E] HARMONIC + FREE => mu4 EXACTLY: the deck-pair cross-ratio (1-b)^2/(1+b)^2 = -1 solves exactly to b = +-i -- on free-deck seam circles the silver family (harmonic AND edge) is EMPTY, harmonicity alone becomes SUFFICIENT. [E] HONEST COUNTERWITNESSES: 'nonsplit => clock' is FALSE -- discrete {0,1,8,9} (shift-invariant, crossing, same nonsplit lift, no clock) and continuous {+-1, +-(3+4i)/5} (free, central, j = 148176/25 != 1728, no clock): the Fock dichotomy measures the CLASS of the arrangement, not the modulus. PREMISE TYPING: (P-i) deck = Moebius covering deck => free on the seam circle [standard covering topology, machine-instantiated; the one-sidedness strand origin_theory/v456]; (P-ii) marks on the Theta-fix seam circle = existing REALIZE [C] content (QGEO.REALIZE.02 hypotheses, v264; v506 A-S2.9 [E] for mu4) -- NO new input; audit finding: circle-freeness was nowhere typed before, v507 F1.1 explicitly admitted the reflection reading -- this door is now closed (a reflection is not a covering deck). [C] THE REDUCED REST (verbatim): the alignment bit reduces from 'harmonic AND central' to the square-modulus datum tau = i alone; the position half is topology (edge class excluded), the modulus half stays the one carrier input. Exact (sympy + Cl(16) Fractions).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv510_seam_bit_freedom.py", "sourceSha256": "5b174a8914b14308621e0be98fc9d44e23b89713400ea5c09e1cae17d3546193", "linkedClaimIds": [ "SEAM.BIT.FREEDOM.01" ], "sectionIds": [ "section:00084b3039331dc8515a", "section:0739148b5a5974d0d662", "section:09b49009253acb5a0dfb", "section:2525c189f32461c9368a", "section:2bbe8c5924cafd6c6187", "section:2db6bd35ce5c578613f3", "section:307c4c95a7c84b5efc0b", "section:3721516595f24fd66f4c", "section:3cc790136e8b9bd3c188", "section:3d2a5b53f3345969fcbc", "section:46614e805445fc78e7af", "section:4fee06b8389287124647", "section:62801f711a0d267461ac", "section:6a93c4dd5fe420e1990e", "section:6b49d8830dc9fa3948be", "section:6cd1a267e72b20619327", "section:701d23928f8e38ea7d4b", "section:70380cf4813f5dcd47e6", "section:7383e42c67f8eaba497b", "section:74bb3766bdd1275dbd78", "section:7d0e50b6a6c30535730d", "section:8182ecd6055b0d0d488c", "section:81a6dc002dc46cf7b6c5", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:888628823bf71f709698", "section:a153934887244824336d", "section:a6c0e668152fda6b8219", "section:ab9e7e520130ecc7da7c", "section:b191b0a66e5bacdc1a0e", "section:b3146d55cec712d485d5", "section:b63f8484d81bde8026ec", "section:b93e6ae7b00f32ee1201", "section:c31c8db87fec4e08752e", "section:c4cf080b9ae6f25f7a71", "section:cca5b83aae425d5f0e88", "section:d90bd5e1e6d8fa41397d", "section:d9b23f5eba4b3c291274", "section:de8db1cd8257eab0d607", "section:eb0bd97fda8c0fedefad", "section:f22c82858ff073c133d4", "section:f9b30725993b14c4ee95", "section:fc7f5b07a661660c0d79", "section:ffb3c952b2d4af559d34", "section:ffca98d84a77b4d4e4ab" ], "activeSectionIds": [ "section:00084b3039331dc8515a", "section:2bbe8c5924cafd6c6187", "section:3721516595f24fd66f4c", "section:3d2a5b53f3345969fcbc", "section:46614e805445fc78e7af", "section:4fee06b8389287124647", "section:6b49d8830dc9fa3948be", "section:70380cf4813f5dcd47e6", "section:7383e42c67f8eaba497b", "section:74bb3766bdd1275dbd78", "section:81a6dc002dc46cf7b6c5", "section:888628823bf71f709698", "section:a153934887244824336d", "section:a6c0e668152fda6b8219", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b63f8484d81bde8026ec", "section:c31c8db87fec4e08752e", "section:d9b23f5eba4b3c291274", "section:de8db1cd8257eab0d607", "section:f22c82858ff073c133d4", "section:fc7f5b07a661660c0d79" ], "evidenceId": "python_verification:verification/v510_seam_bit_freedom.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v510_seam_bit_freedom.py", "pubMirrorHash": "5b174a8914b14308621e0be98fc9d44e23b89713400ea5c09e1cae17d3546193", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v510_seam_bit_freedom.py" }, { "id": "v511_celestial_wp5e_delta2_tensor_ledger", "filename": "v511_celestial_wp5e_delta2_tensor_ledger.py", "path": "verification/v511_celestial_wp5e_delta2_tensor_ledger.py", "cluster": "frontier", "synopsis": "CELEST.WP5E.DELTA2.01: WP5e-delta-2 of the celestial-holographic research contract CELEST.SEAM.01 -- 'the full-tensor ledger', the named escape route of the v508 exchange no-go, executed (intermediate verdict, exact): does the FULL adjoint tensor structure of e8 (non-Cartan external legs, higher-arity vertices) open a sphere-axion channel to the rigid 32 T3 residual of the Atiyah-Bott ledger (A_fix = (9, -30, -15, 0, 32) in (P1, P2, P3, T5, T3), v505 S3.7)? The collapse is CONFIRMED full-tensorially, but one cubic door opens. Exact integer-scaled weight multisets + Kostant/Weyl alternating sums + sympy/Fraction, no floats (41 checks, ~4 s). [E] STRUCTURE: g0 = d5 (+) a3 is SEMISIMPLE with NO u(1) factor (the 52 class-0 roots split 40 + 12 into pure D5 + pure A3 roots, root span rank 8 = rank E8); the twisted sectors factorise multiplicity-free into minuscule Weyl orbits g1 = (16_s, 4), g2 = (10, 6), g3 = (16_c, 4bar) = (g1)^*, each an irreducible g0-module (64, 60, 64); INNERNESS THEOREM: h = (2,2,2,2,2;0^4) lies in the CARTAN OF g0, so every g0-invariant tensor automatically carries total sector charge 0 mod 4 -- the v508 collapse is a full-tensor statement AND holds across arities (all 15 non-neutral sector triples: Hom = 0). [E] HOM TABLES: bilinear dim Hom_{g0}(g_j x g_j') nonzero ONLY at j' = -j (dims 2/1/1/1, Killing blocks); trilinear neutral multisets {0,0,0}: 3 (= 1 sym + 2 antisym), {0,1,3}: 2, {0,2,2}: 2, {1,1,2}: 1, {2,3,3}: 1 -- ALL cross-sector trilinears are pure brackets (antisymmetric in the repeated legs); the ONLY totally symmetric survivor on all of e8 is the su(4) d-symbol (so(10) has no cubic Casimir: Inv(S^3 45) = 0 protects T5). [E] THE NEW CHANNEL: the quartic projection of the d-symbol exchange is Q_dd = (0, 0, -1/240, 0, 1/60) = (1/60)(T3 - P3/4), computed by TWO independent routes (Killing-propagator contraction, 2 h_vee = 60 verified from the roots; hand route |x^2 - (tr x^2/4) 1|^2/60); Phi_T3(Q_dd) = 1/60 != 0 -- v508's master-kill functional does NOT annihilate the trilinear exchange (the product theorem covers quadratic vertices only); brackets, tadpoles and mixed d x f die exactly; no T5 analogue. [E] NEW CERTIFICATE: M = [E13, E22, E00, Q_dd] has rank 3, augmented rank 4 -- the pairing in the charge reading remains OBSTRUCTED, but with the WEAKER certificate {Phi_T5, psi = Phi_P - Phi_T3/4}, psi(A_fix) = 72 - 8 = 64; the RELAXED reading becomes EXACTLY solvable: A_fix = -u + 8v + 2w + 1920 Q_dd (residual 0) -- where v508 found T5 = T3 = 0 persisting even relaxed, the d-channel closes the T3 gap with small integer coefficients. [C] number fences: 64 = dim g1 = 2^6; 1920 = |W(D5)| = 2^7 x 3 x 5 = 8 x 240. [O] the arity >= 4 ledger; the physical justification of the cubic GS term (c_d = 1920 under the e8-Killing propagator); ch2-naturalness for CUBIC vertices UNDECIDED (no canonical geometric datum for a cubic vertex); the burden on delta-1 (twisted BCOV contact terms) is SHARPENED: it must supply either the psi = 64 slice or the selection-rule relaxation. [E] NEGATIVE CONTROLS: (a) Killing control = v508 replication (A_fix, E13 = (16, -96, 144, 0, 0), E22 = (16, 32, 16, 0, 0), E00 = 225 E22); (b) SO(16)/D8: bilinears (1, 0, 1), trilinears (1, 0, 1, 0), Inv(S^3 adj_d8) = 0 -- no symmetric cubic, no odd sectors, no A3 block: the delta-2 channel cannot even be posed (E8/mu4 doubly special); (c) false g0 = d5+a2+u(1): (5, 2, 2) != (2, 1, 1) and Inv(S^3 g0) = 6 != 1; false sector content (16_s, 4bar) kills every pairing. SEAM.EQUIV.01 stays [O]; NO marker moves. Exact (sympy/Fraction).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv511_celestial_wp5e_delta2_tensor_ledger.py", "sourceSha256": "da78bf3b5c5eb9ba6432acba328e2b166a2e1da8ca0ecc5a273115776931de68", "linkedClaimIds": [ "CELEST.WP5E.DELTA2.01" ], "sectionIds": [ "section:307c4c95a7c84b5efc0b", "section:37056704285dbc4b9f42", "section:3ed2167aff70cc409f71", "section:701d23928f8e38ea7d4b", "section:7d0e50b6a6c30535730d", "section:9f542e7b4fe8d834693c", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b38be2626e35c37f4bd1", "section:b63f8484d81bde8026ec", "section:bc61b0e372551b770dfb", "section:cca5b83aae425d5f0e88", "section:d297d5f783e66d564ec2", "section:e01862309e920e04fb7f" ], "activeSectionIds": [ "section:37056704285dbc4b9f42", "section:3ed2167aff70cc409f71", "section:9f542e7b4fe8d834693c", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b38be2626e35c37f4bd1", "section:b63f8484d81bde8026ec", "section:bc61b0e372551b770dfb", "section:d297d5f783e66d564ec2", "section:e01862309e920e04fb7f" ], "evidenceId": "python_verification:verification/v511_celestial_wp5e_delta2_tensor_ledger.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v511_celestial_wp5e_delta2_tensor_ledger.py", "pubMirrorHash": "da78bf3b5c5eb9ba6432acba328e2b166a2e1da8ca0ecc5a273115776931de68", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v511_celestial_wp5e_delta2_tensor_ledger.py" }, { "id": "v512_seam_tau_flag", "filename": "v512_seam_tau_flag.py", "path": "verification/v512_seam_tau_flag.py", "cluster": "core", "synopsis": "SEAM.TAU.FLAG.01: the flag-transitivity equivalence web -- the tau = i attack executed on the free RP seam circle: which ESTABLISHED seam datum excludes the free-but-non-harmonic configurations? (Test family M(delta) = {+-1, +-e^(i delta)}, delta in (0, pi/2]; NO marker moves -- the bit stays [C], QGEO.REALIZE.01 and P2.TYPING.01/AX.P2.01 text-precised only.) Exact sympy + mpmath 30 digits. [E] FALSIFICATION OF BARE TRANSITIVITY: on the free RP circle V4 = {z, -z, b/z, -b/z} acts SIMPLY TRANSITIVELY on the four marks for EVERY delta (pair-exchanging inversions; complete census: deck-commuting Moebius maps = diagonal/antidiagonal) -- the expectation 'transitivity <= v216 local equality selects tau = i' is refuted; hardening: ALL undirected per-mark data (arc-pair multiset, distance multiset, cone germ) are identical for every delta -- no local jet sees the bit. [E] THE SHARP SELECTOR: FLAG transitivity (marks AND sides) <=> delta = pi/2 <=> tau = i <=> the clock -- stabiliser jump 1 -> 2, flag/arc orbits 2 -> 1, order-4 rotation (b^2 = -1 solveset {pi/2}), mark mirror z -> 1/z <=> cos delta = 0. [E] 12-FOLD EQUIVALENCE WEB (each link exact): clock rotation, D4, mark mirror, flag transitivity, three spectral degeneracies (odd-doublet split = (2/pi) ln cot(delta/2), zero only at pi/2 -- counterwitness exactly (2/pi) ln 2; arc-Laplacian degeneracy 4/pi; the v215-K3 indicator in closed form (2 sqrt 2/pi)|ln tan(delta/2)| -- the v503 lattice curve analytically), rho-twist existence ((m^2 - n^2)(t - 1/t) = 0 <=> t = 1; Atiyah-Bott rationality is delta-BLIND -- Tr(sigma e^(t Delta)) = 1 for all delta, j_cw = 148176/25 rational non-CM: rationality does NOT select), 4-cycle implementability (H4 rigidity: V4 with orders {1,2,2,2} cannot induce the cusp 4-cycle; centraliser scalar, U^2 nonscalar => no projective involution -- projective order exactly 4, Z8-shadow consistent v510), harmonic, j = 1728. [E] NEGATIVE CONTROLS: hexagonal (not concyclic, fails the preconditions); silver (harmonic but topologically dead -- position/modulus halves independent, consistent v510); 3 marks (impossible on the free circle: 0 invariant 3-subsets vs 28 invariant 4-subsets; bare n = 3 transitivity already forces equal spacing -- '4 counts': the deck-pairing makes bare transitivity free of charge). [C] THE REST (verbatim): the last input reduces from a continuous modulus to ONE discrete symmetry-lift bit (V4 -> D4: side-indistinguishability of the four equally-decorated marks); v216 local equality does NOT deliver it (no local jet can see the side bit); its negation is now concretely measurable (odd-split (2/pi) ln cot(delta/2) != 0). Scoreboard: the counterwitness passes all 7 established unsided tests, fails all 9 clock-equivalent ones. Exact (sympy + mpmath).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv512_seam_tau_flag.py", "sourceSha256": "78f7b1087e030226ab095ee8b391254f03ec23425e32a8a20d66438414c08782", "linkedClaimIds": [ "SEAM.TAU.FLAG.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:09b49009253acb5a0dfb", "section:0e7ddbc8b9cd02f418a6", "section:1dfae3ea2125bff27c23", "section:2525c189f32461c9368a", "section:2bbe8c5924cafd6c6187", "section:307c4c95a7c84b5efc0b", "section:3bc2480a0b64fd3112f1", "section:3cc790136e8b9bd3c188", "section:46614e805445fc78e7af", "section:4fee06b8389287124647", "section:62801f711a0d267461ac", "section:6a93c4dd5fe420e1990e", "section:6b49d8830dc9fa3948be", "section:6cd1a267e72b20619327", "section:701d23928f8e38ea7d4b", "section:7383e42c67f8eaba497b", "section:74bb3766bdd1275dbd78", "section:7d0e50b6a6c30535730d", "section:8182ecd6055b0d0d488c", "section:81a6dc002dc46cf7b6c5", "section:84ec2c9d7a3c77ec2664", "section:8872501633bb702220cd", "section:888628823bf71f709698", "section:8b84d2fb55ac4a48656b", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b63f8484d81bde8026ec", "section:b93e6ae7b00f32ee1201", "section:cca5b83aae425d5f0e88", "section:d90bd5e1e6d8fa41397d", "section:d9b23f5eba4b3c291274", "section:de8db1cd8257eab0d607", "section:eb0bd97fda8c0fedefad", "section:f22c82858ff073c133d4", "section:f9b30725993b14c4ee95", "section:fc7f5b07a661660c0d79", "section:ffb3c952b2d4af559d34", "section:ffca98d84a77b4d4e4ab" ], "activeSectionIds": [ "section:0e7ddbc8b9cd02f418a6", "section:1dfae3ea2125bff27c23", "section:2bbe8c5924cafd6c6187", "section:3bc2480a0b64fd3112f1", "section:46614e805445fc78e7af", "section:4fee06b8389287124647", "section:6b49d8830dc9fa3948be", "section:7383e42c67f8eaba497b", "section:74bb3766bdd1275dbd78", "section:81a6dc002dc46cf7b6c5", "section:84ec2c9d7a3c77ec2664", "section:888628823bf71f709698", "section:8b84d2fb55ac4a48656b", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b63f8484d81bde8026ec", "section:d9b23f5eba4b3c291274", "section:de8db1cd8257eab0d607", "section:f22c82858ff073c133d4", "section:fc7f5b07a661660c0d79" ], "evidenceId": "python_verification:verification/v512_seam_tau_flag.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v512_seam_tau_flag.py", "pubMirrorHash": "78f7b1087e030226ab095ee8b391254f03ec23425e32a8a20d66438414c08782", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v512_seam_tau_flag.py" }, { "id": "v513_celestial_dterm_nonderivation", "filename": "v513_celestial_dterm_nonderivation.py", "path": "verification/v513_celestial_dterm_nonderivation.py", "cluster": "frontier", "synopsis": "CELEST.DTERM.NONDERIV.01: the c_d negative certificate -- can geometry derive c_d = 1920? An anti-numerology certificate in the v508 style (honest rigid NEGATIVE result): the v511 [C] fence '1920 = |W(D5)|' stress-tested via four candidate routes with a PRE-DECLARED look-elsewhere ledger. Exact sympy/Fraction, no floats (24 checks, ~2 s). [E] CONVENTION TABLE: c_d in {1920, 120, 256, 32, 69120} across five normalisations (probe tr-fund/e8-Killing; Gell-Mann; su(4)-Killing; plain trace; ch3-normalised d/6) -- only 1 of 5 hits |W(D5)|; the convention-STABLE content is the factorisation c_d = Phi_T3(A_fix) x 2 h_vee(E8) = 32 x 60, both factors [E] (Killing propagator 60 from sum_alpha ^2 = 120 over the actual roots; T3-slot fixing via det(P-block) = -64 != 0). [E] K1 DEAD: the charge-legal flux pairings (1,3)/(2,2) give 2048/1800 -- they BRACKET 1920 and both miss; the only flux hit 64*60/2 is the FORBIDDEN (1,2) pairing (charge 3 mod 4, killed by the v511 innerness theorem). LOOK-ELSEWHERE LEDGER: 924 expressions from 21 [E] numbers x grammar {a*b, a*b/2, a*b/4, a+b}, 11 hits on 1920; control targets 1800 -> 8, 2048 -> 5, 2016 -> 0. [E] K2: quantisation delivers only lattices (60 Z: 1920 = 32nd multiple, no minimality; strict ch3-unit couplings 2160 Z EXCLUDE 1920); the cubic quantum is lattice-dependent (6 on coroots, 3/8 on weights); the residual integer 32 has 12 signed factorisations, nothing forces it. [E] K3 PROVENANCE CLASH (the death blow): cubic indices A_m = (0, 16, 0, -16), twisted sum i^m A_m = 32i NUMERICALLY = Phi_T3(A_fix) -- BUT the quartic class decomposition (10, -4, 30, -4) is dominated by classes 0/2 while the cubic 32 is built 16 + 16 from classes 1/3: same number, disjoint mechanism = coincidence exposed; the Weyl side is WRONG (the d-channel is an A3-side object, |W(A3)| = 24; D5 has no cubic invariant, Inv(S^3 45) = 0; |W(E8)|/|W(A8)| = 1920 a second accidental 1920). [E] K4 NEGATIVE CONTROLS: SO(16)/D8 fails every candidate formula consistently; k = 2 flux doubling scales the flux formula x4 (7680); false g0 = d5+a2+u(1) has SIX symmetric cubics; so(10) sanity (Tr X^3 = 0). VERDICT: NUMEROLOGY as a derivation claim -- the v511 [C] fence stays a fence, now typed look-elsewhere-loaded; the honest [E] core is c_d = 32 x 60; the physical generation of the 32 stays [O]. Exact (sympy/Fraction); no marker moves.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv513_celestial_dterm_nonderivation.py", "sourceSha256": "12e8c5f9aecbf45b014b7cae17493043469a192c9631234bb07a6436e9ed39e3", "linkedClaimIds": [ "CELEST.DTERM.NONDERIV.01" ], "sectionIds": [ "section:307c4c95a7c84b5efc0b", "section:37056704285dbc4b9f42", "section:3ed2167aff70cc409f71", "section:701d23928f8e38ea7d4b", "section:7d0e50b6a6c30535730d", "section:9f542e7b4fe8d834693c", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b38be2626e35c37f4bd1", "section:b63f8484d81bde8026ec", "section:bc61b0e372551b770dfb", "section:cca5b83aae425d5f0e88", "section:de8db1cd8257eab0d607" ], "activeSectionIds": [ "section:37056704285dbc4b9f42", "section:3ed2167aff70cc409f71", "section:9f542e7b4fe8d834693c", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b38be2626e35c37f4bd1", "section:b63f8484d81bde8026ec", "section:bc61b0e372551b770dfb", "section:de8db1cd8257eab0d607" ], "evidenceId": "python_verification:verification/v513_celestial_dterm_nonderivation.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v513_celestial_dterm_nonderivation.py", "pubMirrorHash": "12e8c5f9aecbf45b014b7cae17493043469a192c9631234bb07a6436e9ed39e3", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v513_celestial_dterm_nonderivation.py" }, { "id": "v514_celestial_wp5e_eps1_axion_slot", "filename": "v514_celestial_wp5e_eps1_axion_slot.py", "path": "verification/v514_celestial_wp5e_eps1_axion_slot.py", "cluster": "frontier", "synopsis": "CELEST.WP5E.EPS1.01: WP5e-epsilon-1 of the celestial-holographic research contract CELEST.SEAM.01 -- 'the O(-2) bulk-axion slot', executed (verdict B): build the s = 0 tower field explicitly, pin lambda~ = 6 as a residue with explicit factor bookkeeping on PT/Z4, and take the first honest back-reaction step (Gibbons-Hawking A3). Exact sympy/Fraction, no floats (34 checks, ~4 s). [E] EQUIVARIANT O(-2) SLOT: pushforward ledger pi_* O(-2) on PT' = tot(O(1)+O(1) -> P^1): per spacetime degree d exactly (d+1)^2 = nullspaces of the wave operator (1, 4, 9, 16, 25, 36 for d = 0..5); the v492 action on the fibre coordinates (mu1, mu2) -> (i mu1, i^-1 mu2), incidence forces column weights (+1, +1, -1, -1); the equivariant bookkeeping closes BLOCK BY BLOCK (all d <= 6, all 4 characters); character series P_0 = 1 + 3t^2 + 15t^4 + 21t^6 + 45t^8 + ..., P_1 = P_3 = 2t + 8t^3 + 18t^5 + ..., P_2 = 6t^2 + 10t^4 + 28t^6 + ...; the d = 0 slot has multiplicity (1, 0, 0, 0) -- THE BULK AXION SURVIVES THE PROJECTION; Molien invariant ring = (1 - t^8)/((1 - t^4)^2 (1 - t^2)) -- Z in O(2), X, Y in O(4), relation degree 8 = the a0 weight (v492/v493 bridge); E3 bijection sharpened: twisted characters {i, -1, -i} with minimal content (2t, 6t^2, 2t) and NO degree-0 mode = the Coxeter eigenvalues on H^2(ALE), det(A-1) = -4; graviton control: the O(+2) slot starts invariant only at fibre degree 4 with multiplicity 3 = {X, Z^2, Y} (the cohomological form of v505 X = -2 != +2 = Y). [E] LAMBDA~ = 6 TRIPLY PINNED: (1) Okubo: Tr_adj X^4 = 36^2 = (6)^2 on the 240 glue roots, 36 = h_vee + 6, lambda~ = 6 = |Z2| N_fam; (2) measure cancellation: mu = 1/4 enters three times (vertex^2 mu^2, propagator 1/mu, anomaly mu) and cancels EXACTLY -- lambda~_eff^2 = 36 for ARBITRARY mu; wrong bookings quantified and excluded: anomaly-only => lambda~ = 3, missing propagator renormalisation => lambda~ = 12; (3) flux: minimal CPS quantum N = 1, a single exchange channel exactly at k = 1 (#primaries), (kappa/c3)^2 = 36/3 = 12 exact. [E] GH/A3 BACK-REACTION STEP: invariant 4-centre configurations = exactly 2 branches (axis^4 or ONE free mu4 orbit); free orbit => prod(Z - i^p z0) = Z^4 - z0^4 => XY = Z^4 + a0 with a0 = -z0^4 (the v493 family RE-DERIVED from the geometry); monodromy a0 -> e^{2 pi i} a0 = one clock step; the GH point of charge k is EXACTLY R^4/Z_k (k = 4 => seam boundary S^3/Z4); periods int omega = 4 pi (x_q - x_p), free orbit: Pi_j = 4 pi t0 (i-1)(1, i, i^2), |Pi_j| equal (LOCKSTEP, counter-check of v509); the Coxeter clock FROM THE GEOMETRY (A^4 = 1, det(A-1) = -4, Pi.A = i Pi); the CPS 'N log' analogue = source charge 4 = |mu4| (flux -4 pi per centre); HONEST SHARPENING: for the Ricci-flat ALE the asymptotic log coefficient is EXACTLY 0 (EH: u K' = sqrt(u^2 + a^4), det g = 1) -- the log lives at the exceptional locus; Burns contrast (K = u + N log u => det g != 1, only scalar-flat); bonus: multipole selection rule m = 0 mod 4, first symmetry-breaking multipole (4, +-4) carries -a0 with amplitude (35/16) sin^4 th. [E] NEGATIVE CONTROLS: so8 (lambda~^2 = 12 irrational; perfect squares in the Deligne series only {9, 36} = {sl3, e8}); diag(i, i) (Veronese, 5 generators, no hypersurface, the bijection collapses); k = 2 (three channels; honest: lambda~^2 = 36 is k-independent, the kill is the closure dial). [C] conditional on Costello's flat-PT matching lambda_g^2 E = A. [O] the quantised BCOV one-loop coefficient on PT/Z4; the twisted channels (32 T3) are not covered by the bulk axion -- M1-M3 preregistered VERBATIM: M1 the A3 Omega_N on PT/Z4 (success: (2 pi i)^2 periods with lockstep phases; kill: unequal fluxes => the v509 dial dies); M2 the twisted KS measure (success: bulk 36 + sphere axions cancel 32 T3; kill: a leftover T3); M3 the a0 uplift of the (4, +-4) multipole (success: log correction prop 4 = |mu4|; kill: decoupling from the centre count). No marker moves anywhere.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv514_celestial_wp5e_eps1_axion_slot.py", "sourceSha256": "58f47b21526af9b9284928b9a7bc27dd67260ede7520e2b0683e0fd1ecb449e2", "linkedClaimIds": [ "CELEST.WP5E.EPS1.01" ], "sectionIds": [ "section:21c9669befc5eafd6176", "section:307c4c95a7c84b5efc0b", "section:3ed2167aff70cc409f71", "section:6ddf4757acde55521050", "section:701d23928f8e38ea7d4b", "section:70380cf4813f5dcd47e6", "section:77b944418033334668b5", "section:7d0e50b6a6c30535730d", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b38be2626e35c37f4bd1", "section:b63f8484d81bde8026ec", "section:bc61b0e372551b770dfb", "section:cca5b83aae425d5f0e88", "section:e01862309e920e04fb7f", "section:e992bd516774ac42110f" ], "activeSectionIds": [ "section:21c9669befc5eafd6176", "section:3ed2167aff70cc409f71", "section:6ddf4757acde55521050", "section:70380cf4813f5dcd47e6", "section:77b944418033334668b5", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b38be2626e35c37f4bd1", "section:b63f8484d81bde8026ec", "section:bc61b0e372551b770dfb", "section:e01862309e920e04fb7f", "section:e992bd516774ac42110f" ], "evidenceId": "python_verification:verification/v514_celestial_wp5e_eps1_axion_slot.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v514_celestial_wp5e_eps1_axion_slot.py", "pubMirrorHash": "58f47b21526af9b9284928b9a7bc27dd67260ede7520e2b0683e0fd1ecb449e2", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v514_celestial_wp5e_eps1_axion_slot.py" }, { "id": "v515_celestial_wp5e_m1_omega_n", "filename": "v515_celestial_wp5e_m1_omega_n.py", "path": "verification/v515_celestial_wp5e_m1_omega_n.py", "cluster": "frontier", "synopsis": "CELEST.WP5E.M1.01: milestone M1 of the celestial-holographic research contract CELEST.SEAM.01 (WP5e back-reaction programme) -- 'the A3 Omega_N', executed (SUCCESS on the preregistered v514 S8.1 criterion): the back-reacted holomorphic 3-form Omega_N on the twistor uplift of the deformed A3 ALE, with exact periods. Exact sympy, no floats (30 checks, ~1 s). [E] RESIDUE FORM DERIVED: on F = XY - P(Z) all three ambient representatives satisfy dF ^ omega2 = -dX^dY^dZ and pull back to omega2 = dX^dZ/X (Poincare residue, derived not assumed); cover pullback at a0 = 0: omega2 = 4 dz1^dz2 = |mu4| x (flat form) -- the residue normalisation CARRIES the source charge 4; clock diag(i,1): omega2 -> i omega2 (v492 S5 replicated); weight ledger 4+4+2-8 = 2, Omega in O(4) = -deg K_PT; EH anchor 2 = |Z2|; wrong-weight control Z in O(4) breaks three ways (4 != 2, 6 != 4, 5 != 3). [E] THE TWISTOR FAMILY CLOSED: from the four O(2) centre sections q_p(la) = i^p t0 - i^-p t0 la^2 the family is EXACTLY XY = Z^4 + 4 t0^2 la^2 Z^2 - t0^4 (1 - la^4)^2 (e1 = e3 = 0 identically; la = 0 gives exactly the v493 clock family; a2 in O(4) opens only off-seam, a2(0) = a2(inf) = 0); clock lift gamma: (Z, la) -> (iZ, -i la), gamma^4 = 1, Omega -> +Omega (CY-compatible); weight chain 4+4+2-8+2 = 4 = -deg K_PT. [E] OMEGA_N CLOSED + QUANTISED PERIODS: Omega_N = Omega_0 + sum N_p K_p with CPS/Bochner-Martinelli kernels on the centre twistor lines; dK = 0 away from the source, scale degree 0; PERIOD TABLE: boundary S^3/Z4 at the orbifold point (2 pi i)^2 x 1 (minimal invariant charge 4 = |mu4| -- the lens fundamental domain FORCES N in 4Z), deformed phase (2 pi i)^2 x 4, linking S^3 uniformly (2 pi i)^2 x N, per-sphere flux vector (2 pi i)^2 x N (1,1,1) (forced uniform twice over: clock orbit + K4 connectivity), seam-fibre phase vector 2 pi i t0 (i-1)(1, i, i^2); the undeformed Omega_0 carries ZERO quantised 3-flux (all flux sourced); (2 pi i)^2 = (fibre residue) x (transverse residue) (density -sin 2 theta). [E] CLOCK COVARIANCE: Pi_{j+1}(-i la) = i Pi_j(la) for ALL la; the 12 collision nodes sit exactly on the 8 eighth roots of unity (8 = 2|mu4|, the Z8 seam bridge), clock orbits 4+4+4, honest conifold points (Hessian det 512 t0^6, quadric rank 4). [E] KILL PROBE (honest): the forbidden family Z^4 - Z: 0/24 orderings lockstep (vs 8/24), la-support 12 twelfth roots != Z8, no antipodal pairing -- BUT the (2 pi i)^2 quantisation holds there TOO: integrality alone is NOT the discriminator, the discriminator is the lockstep phase structure + the clock forcing of equal fluxes; the v509 dial survives. [E] ANCHORS + CONTROLS: EH/Z2 (2 nodes, charge 2 = |Z2| forced); CPS original (full S^3: every integer N allowed); diag(i,i): Omega_0 -> -Omega_0 (collapse at step zero) while K stays invariant; fractional charges N = 1, 2, 3 excluded. [C] global kernel patching (Green function), Hitchin small resolution, CPS brane dictionary. [O] M2 (twisted KS measure), M3 (a0 uplift), the quantised BCOV coefficient; SEAM.EQUIV.TWISTOR.01 untouched (preparation, not construction). No marker moves.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv515_celestial_wp5e_m1_omega_n.py", "sourceSha256": "445c5f35db8858b1371b2e6f7d44c5e068f10e19813f3199ef068f74517c2d93", "linkedClaimIds": [ "CELEST.WP5E.M1.01" ], "sectionIds": [ "section:307c4c95a7c84b5efc0b", "section:3ed2167aff70cc409f71", "section:6a93c4dd5fe420e1990e", "section:701d23928f8e38ea7d4b", "section:77b944418033334668b5", "section:7d0e50b6a6c30535730d", "section:7ee581db787f8ddbcb4a", "section:8d1e955857da6655fadd", "section:9f542e7b4fe8d834693c", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b38be2626e35c37f4bd1", "section:bc61b0e372551b770dfb", "section:c519f45910c30ff3c0ae", "section:cca5b83aae425d5f0e88", "section:d90bd5e1e6d8fa41397d", "section:d9b23f5eba4b3c291274", "section:e992bd516774ac42110f", "section:f68163cf343646a0f102" ], "activeSectionIds": [ "section:3ed2167aff70cc409f71", "section:77b944418033334668b5", "section:8d1e955857da6655fadd", "section:9f542e7b4fe8d834693c", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b38be2626e35c37f4bd1", "section:bc61b0e372551b770dfb", "section:d9b23f5eba4b3c291274", "section:e992bd516774ac42110f", "section:f68163cf343646a0f102" ], "evidenceId": "python_verification:verification/v515_celestial_wp5e_m1_omega_n.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v515_celestial_wp5e_m1_omega_n.py", "pubMirrorHash": "445c5f35db8858b1371b2e6f7d44c5e068f10e19813f3199ef068f74517c2d93", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v515_celestial_wp5e_m1_omega_n.py" }, { "id": "v516_celestial_wp5e_m2_twisted_ks_measure", "filename": "v516_celestial_wp5e_m2_twisted_ks_measure.py", "path": "verification/v516_celestial_wp5e_m2_twisted_ks_measure.py", "cluster": "frontier", "synopsis": "CELEST.WP5E.M2.01: milestone M2 of the celestial-holographic research contract CELEST.SEAM.01 (WP5e back-reaction programme) -- 'the twisted Kodaira-Spencer measure', executed (SUCCESS on the preregistered v514 S8.2 criterion, on the DECLARED completion measure -- verdict B): the one-loop box coefficient per sector on PT/Z4 under the completion contact term contact_j = (Q^(0) - Q^(j))/det_j. Exact sympy/Fraction, no floats (23 checks, ~1 s). [E] THE COMPLETION-WEIGHT IDENTITY (the centrepiece): per glue class the contact weights are w_m = sum_j (1 - i^{jm})/det_j = (0, 3/2, 2, 3/2) = 4 h_m = |mu4| h_m = -4 ch2(T_m) EXACTLY (h_m = m(4-m)/8 the v502 sector Casimir energies, ch2(T_m) the McKay/Kronheimer charges of the tautological bundles, v505 S4.3 index bridge): THE THREE SPHERE AXIONS PAIR THROUGH THEIR OWN ch2 CHARGES -- an exact identity, NO free scale, no fit. [E] PARAMETER-FREE LOCKS: T5 = 0 for ANY scale c (the ch2 pattern alone kills T5); ratio h_2 : h_1 = 4 : 3 = the delta-1-forced leading ratio (REPRODUCED, not fitted); the T3 budget fixes the scale c = 4 = |mu4| uniquely; the unique delta-1 leading weights (3/2, 2) reproduced as (4h_1, 4h_2). [E] THE CONTACT TERM: channel form sum_j (Q^(0) - Q^(j))/det_j = class form sum_m 4 h_m Q_m = (36, 120, 60, 0, -32) EXACTLY (one object, two bases); the contacts carry nonzero T5/T3 per channel (genuine contact, not exchange -- the v508 product theorem replicated as control). [E] SUCCESS TABLE: skeleton_j + contact_j = Q^(0)/det_j = 36^2/det_j -- a PERFECT Okubo square (T5 = T3 = 0, lambda~^2 = 36) in EVERY twisted channel ((18, 9, 18) x ^2); total A_fix + contact = 45^2 = (5/4) x 36^2 = (Dedekind sum) x (Okubo) = the UNIQUE quartic-free weighting of v505 S3.8 (the rigidity theorem is exactly what the measure lands on); both v508 certificates killed (Phi_T3: 32 -> 0, Phi_P: 72 -> 0); the v511 slice psi = 64 SUPPLIED EXACTLY (psi(contact) = -64) -- no cubic d-channel needed, c_d is free to be 0; remainder inside the exchange span (45^2 = (45/16) E22 = (1/80) E00, Phi_P = 0): the BULK axion cancels every channel with the SAME lambda~^2 = 36, the twisted propagator carrying the AB zero-mode factor 1/det_j; the v514 S3.4 measure chain stays mu-blind. [E] NEGATIVE CONTROLS: wrong scale c in {1, 2, 3, 5} leaves T3 = (24, 16, 8, -8) -- only c = 4 = |mu4| clears the budget; shuffled weights (h_1 <-> h_2) break T5 = -14 AND T3 = 36; SO(16) glue keeps T5 = 20 / T3 = -40 in the summed trace -- the KILL branch FIRES there (Okubo failure inherited, E8 doubly special); diag(i, i) degenerates to the Z2 target and breaks the conjugation pairing + the index bridge; the Z2/Eguchi-Hanson anchor PASSES with the same mechanism (A_2 + contact = 9^2 = (1/4) x 36^2, coupling scale 2 = |Z2| = centre count). [E] MULTIPLIER NOTE (cross-reference only, the substance belongs to the parallel delta-1d strand): the contact weights 4h are REAL RATIONALS carrying no multiplier system of their own; the delta-1c residual phases are the SQUARES of the A3 discriminant T-phases e(3a^2/8) -- orders (1, 8, 2, 8) squaring to (1, 4, 1, 4), a finite mu4 system; Gauss sums 2e(3/8) (A3), 2e(5/8) (D5), full Weil sum 4 (signature 0 mod 8). [C] THE COMPLETION READING (the mandatory fence): the loop of twisted states carries the UNPHASED sector trace with the same zero-mode normalisation -- declared, supported by the delta-1 modular-completion finding, NOT derived from the BCOV integral. [O] the BCOV-integral derivation of the completion reading (delta-1b/1c/1d territory); M3 executed separately (v517); SEAM.EQUIV.TWISTOR.01 untouched (preparation, not construction). VERDICT: SUCCESS wording met on the declared completion measure -- lambda~^2 = 36 reproduced in EVERY sector, the 32 T3 cancelled exactly by the ch2-weighted sphere-axion contacts; the KILL branch does NOT fire; NO marker moves anywhere.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv516_celestial_wp5e_m2_twisted_ks_measure.py", "sourceSha256": "dd9ca1271ee0666acd70ee9a60a4d78f5e2124a3edb923da4a02ef0072ae4cd2", "linkedClaimIds": [ "CELEST.WP5E.M2.01" ], "sectionIds": [ "section:26516787d04ebc9e58b3", "section:307c4c95a7c84b5efc0b", "section:3ed2167aff70cc409f71", "section:4ad984d8cafbe64dad8e", "section:6ddf4757acde55521050", "section:701d23928f8e38ea7d4b", "section:7d0e50b6a6c30535730d", "section:9f542e7b4fe8d834693c", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b38be2626e35c37f4bd1", "section:bc61b0e372551b770dfb", "section:cca5b83aae425d5f0e88", "section:d9b23f5eba4b3c291274", "section:e01862309e920e04fb7f", "section:e992bd516774ac42110f" ], "activeSectionIds": [ "section:26516787d04ebc9e58b3", "section:3ed2167aff70cc409f71", "section:4ad984d8cafbe64dad8e", "section:6ddf4757acde55521050", "section:9f542e7b4fe8d834693c", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b38be2626e35c37f4bd1", "section:bc61b0e372551b770dfb", "section:d9b23f5eba4b3c291274", "section:e01862309e920e04fb7f", "section:e992bd516774ac42110f" ], "evidenceId": "python_verification:verification/v516_celestial_wp5e_m2_twisted_ks_measure.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v516_celestial_wp5e_m2_twisted_ks_measure.py", "pubMirrorHash": "dd9ca1271ee0666acd70ee9a60a4d78f5e2124a3edb923da4a02ef0072ae4cd2", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v516_celestial_wp5e_m2_twisted_ks_measure.py" }, { "id": "v517_celestial_wp5e_m3_a0_uplift", "filename": "v517_celestial_wp5e_m3_a0_uplift.py", "path": "verification/v517_celestial_wp5e_m3_a0_uplift.py", "cluster": "frontier", "synopsis": "CELEST.WP5E.M3.01: milestone M3 of the celestial-holographic research contract CELEST.SEAM.01 (WP5e back-reaction programme) -- 'the a0 uplift', executed (SUCCESS on the preregistered v514 S8.3 criterion): the (4, +-4) GH multipole uplifted to the twistor-potential kernel chi = log P4 (the log of the v515 family polynomial) with the induced Kahler-potential correction. Exact sympy, no floats (23 checks, ~7 s). [E] KERNEL BRIDGE: the O(2) section is a NULL coordinate -- Laplacian(3d) G(eta_p) = 0 identically for an ARBITRARY kernel G (the uplift is well-typed); RESIDUE IDENTITY d_x [transform(log eta_p)] = 1/r_p EXACTLY (residue 1/(2r) at zeta_-): the GH potential V = sum_p 1/r_p IS the x-derivative of the contour transform of chi; flux -4 pi per centre, total source charge 4 = |mu4| (the V-ledger matched). [E] FOUR COUPLED CENTRE-COUNT SCALES: (1) asymptotic kernel log chi = 4 log eta + a2/eta^2 + (a0 - a2^2/2)/eta^4 + ... -- LOG COEFFICIENT 4 = |mu4| = centre count (the CPS 'N log' analogue at kernel level); at the clock-fixed seam fibre zeta = 0 the a2 slot closes and the first correction is EXACTLY a0/eta^4 = the (4, +-4) multipole in kernel clothes; exact m-grading (the term zeta^k/eta^4 carries field charge m = 4 - k: m = +-4 pieces PURE a0, m = 0 piece -6 t0^4 phi0-free -- the U(1) -> Z4 breaking sits exclusively in the a0 pieces); NO log x power terms in the Laurent tower (the v514 honest zero -- no asymptotic METRIC log -- is preserved); (2) the once-integrated GLT kernel sum_p eta_p log eta_p = 4 eta log eta + p_4/(12 eta^3) + p_8/(56 eta^7) + ... with p_n = 0 unless n = 0 mod 4 (selection rule at potential level) and p_{4k} = 4 (-a0)^k: EVERY correction carries the prefactor 4 = centre count; (3) the exceptional-locus log chi(eta = 0) = log a0 = 4 log t0 + i(4 phi0 + pi) -- t0-coefficient 4 = |mu4|, clock phase 4i; the modulus response a0 d/da0 chi = a0/(eta^4 + a0) equals 1 AT the exceptional locus and falls off as a0/eta^4 at infinity (no constant, no log): the a0-log lives at the exceptional locus, exactly as v514 S6.3 demanded; (4) periods (v515 consistency): Pi_j(la) LINEAR in t0 (uniform first-order shift, lockstep + phase ratios (1, i, i^2) preserved exactly); d log Pi_j / d log a0 = 1/4 = 1/|mu4| uniformly; integrated over the a0 circle: monodromy e^{2 pi i/4} = i = ONE Coxeter clock step (the v493 monodromy REPRODUCED from the perturbative period shift; the finite monodromy is the cyclic centre permutation q_p -> q_{p+1}); node la-support t0-FREE (the Z8 seam bridge is a0-rigid); all 6 pair discriminants ~ t0^2 != 0 (K4 connectivity: the forced uniform flux vector persists); the BM kernel is modulus-free with int_{S^3} K = (2 pi i)^2 (the quantised fluxes cannot move). [E] NEGATIVE CONTROLS: the (4, 0) multipole is phi0-independent in V AND in the kernel (-6 t0^4): clock-invariant, breaks nothing; Z2/Eguchi-Hanson analogue: EVERY dial reads 2 = |Z2| ((2, +-2) amplitude (3/2) sin^2 th, kernel log 2, exceptional log 2 log t0, period response 1/2, monodromy -1 = the Z2 clock); wrong centre counts k = 3, 5: kernel log coefficient k, modulus slot O(6)/O(10) != O(8) -- the observable MOVES with the centre count; forbidden family Z^4 - Z: p3 = 3 != 0 (selection rule broken), e4 = 0 (no a0-log at the exceptional locus) -- fails BOTH uplift dials. [C] THE GLT DICTIONARY: 'eta_p log eta_p = THE GH Kahler-potential kernel' is the generalized-Legendre-transform dictionary (Lindstrom-Rocek / Ivanov-Rocek), typed [C]. [O] the full nonlinear Kahler potential of the resolved A3 ALE (no closed form exists); the quantised BCOV coefficient stays with the delta-1 strand; SEAM.EQUIV.TWISTOR.01 untouched. VERDICT: SUCCESS -- the log-type correction delivered on four coupled dials (kernel log 4, exceptional-locus log 4 log t0, tower prefactor 4, period response 1/4 -> monodromy i), every one tied to the centre count (EH: 2, k-orbit: k); the KILL branch (decoupling from the centre count) does NOT fire; NO marker moves anywhere.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv517_celestial_wp5e_m3_a0_uplift.py", "sourceSha256": "6127cc03ec297ecc0c3cd5b2d34c1f86fe65554b7e4c36dea2f7c49e55d54aac", "linkedClaimIds": [ "CELEST.WP5E.M3.01" ], "sectionIds": [ "section:00084b3039331dc8515a", "section:2db6bd35ce5c578613f3", "section:307c4c95a7c84b5efc0b", "section:3ed2167aff70cc409f71", "section:701d23928f8e38ea7d4b", "section:7d0e50b6a6c30535730d", "section:7ee581db787f8ddbcb4a", "section:8d1e955857da6655fadd", "section:9f542e7b4fe8d834693c", "section:ab9e7e520130ecc7da7c", "section:b191b0a66e5bacdc1a0e", "section:b3146d55cec712d485d5", "section:b38be2626e35c37f4bd1", "section:bc61b0e372551b770dfb", "section:c519f45910c30ff3c0ae", "section:cca5b83aae425d5f0e88", "section:d9b23f5eba4b3c291274", "section:e01862309e920e04fb7f", "section:e992bd516774ac42110f" ], "activeSectionIds": [ "section:00084b3039331dc8515a", "section:3ed2167aff70cc409f71", "section:8d1e955857da6655fadd", "section:9f542e7b4fe8d834693c", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b38be2626e35c37f4bd1", "section:bc61b0e372551b770dfb", "section:d9b23f5eba4b3c291274", "section:e01862309e920e04fb7f", "section:e992bd516774ac42110f" ], "evidenceId": "python_verification:verification/v517_celestial_wp5e_m3_a0_uplift.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v517_celestial_wp5e_m3_a0_uplift.py", "pubMirrorHash": "6127cc03ec297ecc0c3cd5b2d34c1f86fe65554b7e4c36dea2f7c49e55d54aac", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v517_celestial_wp5e_m3_a0_uplift.py" }, { "id": "v518_celestial_wp5e_delta1_derived_kill", "filename": "v518_celestial_wp5e_delta1_derived_kill.py", "path": "verification/v518_celestial_wp5e_delta1_derived_kill.py", "cluster": "frontier", "synopsis": "CELEST.WP5E.DELTA1.01: the delta-1 chain (delta-1b + delta-1c + delta-1d) of the celestial-holographic research contract CELEST.SEAM.01 DECIDED -- 'the derived chiral measure kills the delta-1 route', an honest, decided NEGATIVE result (v508 style): does the Harvey-Moore/BCOV fundamental-domain integral on PT/Z4, evaluated under a measure DERIVED from blockwise SL(2,Z) covariance (solved for, not declared, not scanned), deliver -A_fix = -(9,-30,-15,0,32) or the psi = 64 slice? NO -- every member of the derived family fails all three preregistered testers (30 checks, ~20 s). [E] THE 16-COMPONENT WEIL COMPLETION (delta-1c): discriminant module Z4 x Z4 with q = (5x^2+3y^2)/8; Gauss sums 2 zeta_8^5 x 2 zeta_8^3 = 4 = sqrt(16) (signature 0 mod 8 = rank E8); S symmetric + unitary, S^2 = C, (ST)^3 = S^2, S^4 = 1, T^8 = 1 EXACTLY in Q(zeta_8); S = S_D5 (x) S_A3; the diagonal H and anti-diagonal H' are the two invariant Lagrangians (both counts = E4: two E8 gluings); P_H S P_H = (1/4) J with 3/4 of every S-image weight on the 12 shifted classes -- why the naive 4-character rule failed; the 16-vector theta S-covariance CLOSES: the delta-1b E1.5 residual 2.91 = O(1) drops to ~1e-39, certified at two tau. [E] THE OBSTRUCTION IS A FINITE mu4 CHARACTER, IDENTIFIED (delta-1d): gauge blocks M = G[a,b] eta^{-8} have constant transport (t_p, s_p) (28+ digits) recognised as exact 1/960-grid phases (1e-25); T-fixed pairs (0,b) carry t = e(-1/2) = -1 EXACTLY (the naked level-matching defect); loops land in Gamma_1(4) resp. Gamma_0(2)+-, joint holonomy eigenspaces dim 8/16 resp. 6/16, every eigen-phase of order <= 4 (the group is mu_4); KOBOUNDARY TEST: the SL(2,Z) relation defects c_{S^4}, c_{(ST)^3 S^-2}, c_{[S^2,T]} are (1,1,1) EXACTLY on all 15 pairs -- a CHARACTER of the stabilisers, NOT a genuine 2-cocycle; on Gamma_1(4): lambda(gamma) = i^{2B + C/4}. [E] THE CANCELLATION IS THE TWISTED FIBRE BLOCK f1 f3, NOT THE THREE SPHERE AXIONS: exact identity G[a,b] = f_1 f_3 (30+ digits); axion T-phases = v502 vacuum-energy data; T-fix mechanism one line of exact phase arithmetic: (-1) x e(-1/6) = e(1/3) = chi_4(T) at every T-fixed node; CANCELLATION TABLE (exact, minimal residual order over eta^m x chi_k): none -> 4, f1f2f3 (three sphere axions) -> 4, f2 -> 6, f1f3 -> 1 (hol AND anti), wrong weights (1,1,2)/(2,2,2) -> 4; strict solutions exactly chi_4 (dims (3,3)) and chi_10 (dims (1,1)) at eta^0, certified on the dressed functions at a fresh tau (1e-15, NO residual multiplier). [E] THE DECISION -- ALL THREE TESTERS FAIL: under both derived solutions the integral (30-digit kernels, negative-exponent audit, cut-6 vs cut-8 scan) fails T5(V) = 0 (fractions 0.5 / 0.83), fails W_2 : W_13 = 4 : 3 (W_13 = 0), fails V = -A_fix N (spreads 1.05 / 1.47) and the psi = -64 N slice; the honest (N1, N2) rebalance: chi_4 reaches T5 = 0 only at psi > 0, chi_10 only at N2/N1 = -4 < 0 (outside the orbifold projector) -- no branch fires in the positive cone. [E] NEGATIVE CONTROLS: Z2/Eguchi-Hanson (gauge-only residual order 2 -- the mu4 defect is Z4-specific -- and the SAME fibre dressing cancels it to 1); SO(16)/D8 (only even sectors, all axion b-characters in mu_2: the order-4 supply structurally absent); wrong form (x^2+y^2)/4 (|Gauss|^2 = 64 != 16, S-rule fails at O(1)); wrong signature (S^2 = C breaks exactly). [C] the f1f3 = KS-weight identification (deck weights (1,3) = the twistor fibre weights (+1,-1 mod 4) forced by the v514 incidence ledger -- exact match, NOT a complete BCOV derivation) + the kernel-family convention (J(Delta,0/1/2) from weight bookkeeping) + the discrete chi_k choice (both evaluated, both fail). TENSION, stated honestly (the mandatory fence): the DECLARED completion reading (v516/M2) delivers the psi = 64 slice and cancels 32 T3; the DERIVED chiral measure (this module) fails all three testers -- both are exact; the sharp open question is which of the two is the true BCOV measure (the declared reading is supported by the delta-1 modular-completion finding but not derived; the derived measure rests on the f1f3 identification). Neither result is hidden behind the other. [O] the BCOV-integral derivation on PT/Z4 that decides between the two measures -- the single open item of the delta-1 strand; the twisted-contact route of v508 S6.2 is DECIDED NEGATIVE under the derived measure. Discovery provenance: delta-1b (30/30), delta-1c (31/31), delta-1d (36/36) probes in experiments/tfpt-discovery/ (2026-07-22). NO marker moves anywhere.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv518_celestial_wp5e_delta1_derived_kill.py", "sourceSha256": "6c2148a1dbaac178b55110d9d412f2c0e3d3cca2beb37c10ddb96dfbef3a90a5", "linkedClaimIds": [ "CELEST.WP5E.DELTA1.01" ], "sectionIds": [ "section:307c4c95a7c84b5efc0b", "section:3ed2167aff70cc409f71", "section:4ad984d8cafbe64dad8e", "section:6ddf4757acde55521050", "section:701d23928f8e38ea7d4b", "section:7d0e50b6a6c30535730d", "section:7ee581db787f8ddbcb4a", "section:8d1e955857da6655fadd", "section:9f542e7b4fe8d834693c", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b38be2626e35c37f4bd1", "section:b63f8484d81bde8026ec", "section:bc61b0e372551b770dfb", "section:c519f45910c30ff3c0ae", "section:cca5b83aae425d5f0e88", "section:d9b23f5eba4b3c291274" ], "activeSectionIds": [ "section:3ed2167aff70cc409f71", "section:4ad984d8cafbe64dad8e", "section:6ddf4757acde55521050", "section:8d1e955857da6655fadd", "section:9f542e7b4fe8d834693c", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b38be2626e35c37f4bd1", "section:b63f8484d81bde8026ec", "section:bc61b0e372551b770dfb", "section:d9b23f5eba4b3c291274" ], "evidenceId": "python_verification:verification/v518_celestial_wp5e_delta1_derived_kill.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v518_celestial_wp5e_delta1_derived_kill.py", "pubMirrorHash": "6c2148a1dbaac178b55110d9d412f2c0e3d3cca2beb37c10ddb96dfbef3a90a5", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v518_celestial_wp5e_delta1_derived_kill.py" }, { "id": "v519_woit_theta_rp_free", "filename": "v519_woit_theta_rp_free.py", "path": "verification/v519_woit_theta_rp_free.py", "cluster": "frontier", "synopsis": "WOIT.THETA.FREE.01: the WOIT-alpha milestone of the OS twistor bridge WOIT.OS.TWISTOR.01 -- 'the real structure exists, and free reflection positivity picks the SAME family' (Part W = the anti-linear Theta: classification, exact relations, kill test 1 on the free/equivariant level; Part R = reflection positivity of the free 16-Majorana NS seam system under the pinned Theta; NO marker moves -- WOIT.OS.TWISTOR.01 stays [O]: kill test 1 is discharged on the FREE level only and stays formally live on the interacting algebra). Exact sympy + exact Cl(16) Fractions; the RP definiteness certificates are 40-digit spectra of exact Hermitian matrices (tol 1e-25). [E] THETA CLASSIFICATION COMPLETE: exactly TWO families of anti-linear structures on C^2 normalise the clock rho = diag(i,1) -- family D (z -> mu conj(z), |mu| = 1): Theta rho Theta = rho^-1 EXACTLY, Theta^2 = +1 (-1 IMPOSSIBLE: M conj(M) = diag(|mu|^2, 1) -- Kramers-free), inverts the deck, fixed set = the great circle through the deck poles; family A (z -> mu/conj(z)): centralises the clock projectively (NEVER inverts), Theta^2 = +-1 per mu, fixed set |z| = 1 resp. empty. ROLE SEPARATION: family A defines the euclidean section (Woit's rho_tw side: rho_tw^2 = -1, no real points -- replicated exactly on C^4), family D reflects it (the OS conjugation; sigma_std = the standard conjugation with real points RP^3). [E] MARK PINNING: z -> mu conj(z) preserves the mu4 marks iff mu in mu4 -- a 4-element mu4-TORSOR (2 mark axes + 2 silver-midpoint axes); clock conjugation rho Theta_mu rho^-1 = Theta_{-mu} => 2 clock orbits. [E] SPIN/FOCK: Z8 plane without phase leaks (conj(zeta8^k) = zeta8^-k); Cl(16): Theta_Fock = U_r o K with Theta_Fock^2 = 2^7 > 0 (normalised +1), inverts the clock tower (V -> 4096 V^-1, exact scalar via the implementer route) and normalises the deck (256 Utilde^-1); KRAMERS DICHOTOMY: the deck-induced candidate Theta_t = Utilde o K has Theta_t^2 = 256 gamma_1..gamma_16 = (-1)^F -- the v510 split/nonsplit dichotomy IS the Theta^2 = +1 vs (-1)^F dichotomy; the deck does NOT furnish Theta, the seam-circle REFLECTION does. [E] KILL TEST 1 (free level): does NOT fire -- Theta exists with Theta^2 = +1 AND Theta rho Theta = rho^-1 and satisfies all three side conditions simultaneously (marks, deck normalisation, spin/Fock). [E] FREE RP: NS vacuum C(d) = (2/N)/sin(pi d/N), C^2 = -1 exact; preconditions exact (R C R^T = -C, S C S^T = C, R S R^-1 = S^-1; the deck FAILS anti-invariance); BOND CUT: one-particle Gram (8,0,0) PD (min eigenvalue 1.888e-3 at 40 digits), even deg <= 2 sector (29,0,0) PD, N = 8 complete half-sided algebra PD (even + odd each (8,0,0)) -- RP with NO degree truncation; twist eta = +i FORCED (eta = 1 non-Hermitian); CONTROLS: the site cut fails exactly (det = 0, inertia (3,3,1); continuum control: Cauchy-Stieltjes positive -- a lattice-PLACEMENT artifact, RP selects the site placement relative to the marks); the clock-CENTRALISING family-A structure fails RP structurally ((4,4,0)) -- RP and Theta rho Theta = rho^-1 select the SAME family; bonus: the anti-chiral state flips the odd sector to (0,8,0) ND (the free shadow of kill test 3). [C]/[O] NOT shown: the interacting algebra A_hol (kill test 1 stays live there), gauge-fixed RP (kill test 2), OS reconstruction, chirality without mirrors (kill tests 3/6 -- only the free odd-sector shadow), mu4 incidence (kill test 7); WOIT-beta/gamma roadmap: (beta-1) Theta on the gauge-invariant subalgebra + gauge-fixed RP on the equivariant SDYM(E8) sector; (beta-2) the OS quotient of the free system explicit; (beta-3) the PT <-> PT* duality vs sigma_std typed; (gamma) the chirality theorem + the mark incidence. Two contract PRECISIONS (prose, no marker): (i) 'Theta induced by the seam reflection' means the seam-circle REFLECTION, not the deck (the deck furnishes the (-1)^F Kramers class -- the v510 bridge); (ii) the marks sit RP-side on the BOND MIDPOINTS of the 16-Majorana circle.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv519_woit_theta_rp_free.py", "sourceSha256": "e86e3a055b58051c7978d8f10ee527948bac758fd4665ac216e18a71cc8c1ee9", "linkedClaimIds": [ "WOIT.OS.TWISTOR.01", "WOIT.THETA.FREE.01" ], "sectionIds": [ "section:00084b3039331dc8515a", "section:0e7ddbc8b9cd02f418a6", "section:17538bc5f76786fa0bbe", "section:2bbe8c5924cafd6c6187", "section:2db6bd35ce5c578613f3", "section:307c4c95a7c84b5efc0b", "section:38cc1bfba5161e50d0bb", "section:3d2a5b53f3345969fcbc", "section:58f2181069f63dc9bc77", "section:6a93c4dd5fe420e1990e", "section:6e482b6ca2a1df5c2627", "section:701d23928f8e38ea7d4b", "section:73dd631de817637ce12d", "section:7d0e50b6a6c30535730d", "section:7ee581db787f8ddbcb4a", "section:848c49f799255f4cda92", "section:8b84d2fb55ac4a48656b", "section:8d1e955857da6655fadd", "section:8e4972dbe899b5debb90", "section:a153934887244824336d", "section:a6c0e668152fda6b8219", "section:ab9e7e520130ecc7da7c", "section:b191b0a66e5bacdc1a0e", "section:b3146d55cec712d485d5", "section:c4cf080b9ae6f25f7a71", "section:c519f45910c30ff3c0ae", "section:cac001c63c2444d31263", "section:cca5b83aae425d5f0e88", "section:d90bd5e1e6d8fa41397d", "section:d9b23f5eba4b3c291274", "section:dccf3e7f3250c009523d", "section:de8db1cd8257eab0d607", "section:f1286299e54bfa3f1866", "section:f1cafbf24805c6c09d79", "section:fbf67a6377a333f71dff" ], "activeSectionIds": [ "section:00084b3039331dc8515a", "section:0e7ddbc8b9cd02f418a6", "section:17538bc5f76786fa0bbe", "section:2bbe8c5924cafd6c6187", "section:38cc1bfba5161e50d0bb", "section:3d2a5b53f3345969fcbc", "section:8b84d2fb55ac4a48656b", "section:8d1e955857da6655fadd", "section:8e4972dbe899b5debb90", "section:a153934887244824336d", "section:a6c0e668152fda6b8219", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:cac001c63c2444d31263", "section:d9b23f5eba4b3c291274", "section:dccf3e7f3250c009523d", "section:de8db1cd8257eab0d607", "section:f1286299e54bfa3f1866", "section:f1cafbf24805c6c09d79" ], "evidenceId": "python_verification:verification/v519_woit_theta_rp_free.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v519_woit_theta_rp_free.py", "pubMirrorHash": "e86e3a055b58051c7978d8f10ee527948bac758fd4665ac216e18a71cc8c1ee9", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v519_woit_theta_rp_free.py" }, { "id": "v520_celestial_wp5e_measure_decision", "filename": "v520_celestial_wp5e_measure_decision.py", "path": "verification/v520_celestial_wp5e_measure_decision.py", "cluster": "frontier", "synopsis": "CELEST.WP5E.MEASURE.01: the WP5e BCOV measure question DECIDED at probe level (delta-1e + delta-1f consolidated, v518 style) -- 'single-valuedness is derived, the completion reading wins': which of the two exact, contradictory measures on PT/Z4 is the true BCOV measure, (A) the DECLARED completion reading (v516) or (B) the DERIVED chiral measure (v518)? ERFOLG-A on the decision layer (39 checks, ~20 s). [E] INVARIANT SUBSPACE: dim_Q {v: rho(T) v = v, rho(S) v = v} = 8 = 4 x 2 in the dressed 16-component Weil system, EVERY kernel vector in the Q(zeta_8)-span of {e_H, e_H'} (the two Lagrangian gluings, both theta = E4, level-1 quartic = Q^(0) = the unphased trace); strict trivial-character solutions at (m, k) = (0, 0): ZERO for every dressing (11 combinations). [E] SOURCE 1 (F-LEMMA): the only strict chiral families chi_4 (dims (3,3)) and chi_10 (dims (1,1)) carry nontrivial T-characters exactly; pointwise covariance of the canonical column member certified (3.9e-16, |G| >= 59.6); exact change of variables => fundamental-domain independence forces int = 0 for EVERY chiral integrand -- the v518 route was never a well-defined nonvanishing moduli integral (kill sharpened). [E] SOURCE 2 (QUILLEN PAIRING): |t conj(t) - 1| < 8.3e-40 on all 15 pairs/both generators; |chi_4|^2 = 1 exact vs one-sided chi_4^2 = e(2/3) != 1 (T-fixed: 640 != 0 mod 960, 15/15 defective); the doubled 256-dim hol x antihol system closes strictly at trivial character and physical weight (nullspaces (28, 17) >= 11), contains the unphased diagonal (~2e-15) AND the physical columns w_b (x) conj(w_b) (sigma 4.9e-16/8.3e-16); negative control hol (x) hol: empty nullspace (0, 0). [E] CONSISTENCY CLOSURE: the forced unphased numerator in the v518 scaffold reproduces sum_m V prop (1, 2, 1, 0, 0) = ^2 exactly on every level n <= 8; J-weighted spreads ~5e-41, T5/T3 ~7e-42, zero negative cells; psi(skeleton) = +0.2302 = -psi(contact), the J-weighted mirror image of psi(A_fix) = +64 / psi(contact) = -64; linearity 4.6e-41 -- the circle to v516 is closed. [E] D3 Z2/EH ANCHOR: only the declared reading hits (9^2 = (1/4) x 36, psi = -8, scale tooth c = 1/2 = |Z2| h^(A1)); all three derived instantiations fail (spreads 1.12/0.895/0.516, psi sign wrong). [E] D1 COLUMN CANONICALISATION: the physical AB column sum_m i^(bm) e_(m,m) is EXACTLY contained in the chi_4 family (sigma 1.8e-16/1.7e-16, one scalar per orbit -- canonicalises the (N1, N2) freedom); the canonical member still fails all testers. [E] NEGATIVE CONTROLS: SO(16)/D8 (T5 = 20/T3 = -40 exact, mu_2-only), wrong form (|Gauss|^2 = 64), wrong weight (dev 0.78), shuffle (T5 = -14/T3 = 36), planted family detected (1.5e-16), hol (x) hol empty. [C] TYPED PREMISES (the mandatory fence): TP-1 (F-independent moduli integral), TP-2 (nonvanishing -- must source psi = 64), TP-3 (v518 kernel convention), TP-4 (Quillen structure of BCOV F1). [O] the constructive BCOV derivation of the w_m normalisation itself. VERDICT: ERFOLG-A per the preregistered criteria (both sources independent, the consistency closure carries); the [O] question 'which is the true BCOV measure' is DECIDED at probe level in favour of (A) under TP-1..TP-4. SEAM.EQUIV.TWISTOR.01 stays Open; NO marker moves.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv520_celestial_wp5e_measure_decision.py", "sourceSha256": "62ab1dcda9330ced112ec8c5cf0fdd25ffe5c73cfa46c4b94cc8ab2116904131", "linkedClaimIds": [ "CELEST.WP5E.MEASURE.01" ], "sectionIds": [ "section:26516787d04ebc9e58b3", "section:307c4c95a7c84b5efc0b", "section:3ed2167aff70cc409f71", "section:4ad984d8cafbe64dad8e", "section:58f2181069f63dc9bc77", "section:6e482b6ca2a1df5c2627", "section:701d23928f8e38ea7d4b", "section:7d0e50b6a6c30535730d", "section:7ee581db787f8ddbcb4a", "section:8b84d2fb55ac4a48656b", "section:8d1e955857da6655fadd", "section:9f542e7b4fe8d834693c", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b38be2626e35c37f4bd1", "section:bc61b0e372551b770dfb", "section:c519f45910c30ff3c0ae", "section:cac001c63c2444d31263", "section:cca5b83aae425d5f0e88", "section:d9b23f5eba4b3c291274", "section:e8fb60dc4323384272d7" ], "activeSectionIds": [ "section:26516787d04ebc9e58b3", "section:3ed2167aff70cc409f71", "section:4ad984d8cafbe64dad8e", "section:8b84d2fb55ac4a48656b", "section:8d1e955857da6655fadd", "section:9f542e7b4fe8d834693c", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b38be2626e35c37f4bd1", "section:bc61b0e372551b770dfb", "section:cac001c63c2444d31263", "section:d9b23f5eba4b3c291274", "section:e8fb60dc4323384272d7" ], "evidenceId": "python_verification:verification/v520_celestial_wp5e_measure_decision.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v520_celestial_wp5e_measure_decision.py", "pubMirrorHash": "62ab1dcda9330ced112ec8c5cf0fdd25ffe5c73cfa46c4b94cc8ab2116904131", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v520_celestial_wp5e_measure_decision.py" }, { "id": "v521_seam_bit_rp_blind", "filename": "v521_seam_bit_rp_blind.py", "path": "verification/v521_seam_bit_rp_blind.py", "cluster": "core", "synopsis": "SEAM.BIT.RPBLIND.01: the RP/Theta attack on the alignment bit DECIDED -- 'free OS positivity does NOT see delta', an honest, decided NEGATIVE result (v508 style; 25 checks, ~25 s): does free reflection positivity (v519) or anti-linear Theta existence break for delta != pi/2 on the deformed mark family M(delta) = {+-1, +-e^(i delta)}, which would derive the v512 alignment bit from OS positivity? NO -- the free RP/Theta battery is the EIGHTH side-blind test on the v512 scoreboard (7 -> 8); the bit remains genuine discrete input. [E] CENSUS (exact solvesets, symbolic delta): for every delta exactly the two mark-SWAPPING reflections Theta_(+-e^(i delta)) exist (axes delta/2, delta/2 + pi/2; all 20 cut/mark incidence solvesets empty); mark-FIXING reflections exist exactly at delta = pi/2 (solveset cos delta = 0, lost immediately at pi/2 - eps); the v510/v512 counterwitness {+-1, +-(3+4i)/5} carries the swap pair exactly. [E] RP IS delta-BLIND: bond-cut Gram inertias (8,0,0) PD for all tested delta, spectra IDENTICAL to 40 digits (deviation 0.0) -- the entire free-RP spectral datum carries ZERO delta information; the N = 16 odd-m failure (site axes, (3,3,1), det = 0) is a lattice-PLACEMENT artifact: at N = 32 all m = 1..7 have mark-compatible bond axes with PD inertia (16,0,0); continuum: the OS kernel in axis-adapted coordinates is exactly 1/sin((s+t)/2), the axis position drops out identically (Cauchy-Stieltjes PD); the counterwitness PASSES free RP (6-point Gram (6,0,0)). [E] THETA EXISTENCE delta-BLIND: Theta^2 = +1, deck normalisation and Fock implementability (U^2 = +2^7/2^8 > 0, exact Cl(16)) for every delta; the ONLY delta-sensitive v519 clause (Theta rho Theta = rho^-1) is for delta != pi/2 not violated but NOT FORMULABLE (mark-compatible order-4 rotation <=> delta = pi/2) -- it PRESUPPOSES the bit; same for the clock-tower clause. [E] the battery has teeth at every delta: family A/antipode fails RP structurally (zero diagonal, (4,4,0) indefinite), chirality-eta pinning persists ((0,8,0) ND) -- RP separates the two real-structure FAMILIES, never the SIDES. [E] precondition controls: hexagonal (marks not concyclic, no seam circle), silver (deck not free), lifting audit (B = index relabelling, delta-blind by construction; B' fails the pi/2 negative control -- discarded). [C] FACE #13 of the v512 equivalence web: the group generated by the admissible OS reflections is V4 for every delta < pi/2 and closes to D4 exactly at delta = pi/2 (Theta_i o Theta_1 = the clock) -- 12 -> 13 faces, a typed REFORMULATION of the bit, not a derivation. [O] honest gap: marks decorating the STATE (defect/twist insertions, interacting A_hol) = exactly v519's [O] scope -- there, and only there, could positivity still see the bit. VERDICT: KILL exactly as preregistered; the alignment bit is NOT derivable from OS positivity and remains genuine discrete input; no marker moves.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv521_seam_bit_rp_blind.py", "sourceSha256": "8e46478bfeb77d2052d31901237a2245a7267248205bf584e5357fe6c328b516", "linkedClaimIds": [ "SEAM.BIT.RPBLIND.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:0e7ddbc8b9cd02f418a6", "section:2525c189f32461c9368a", "section:2bbe8c5924cafd6c6187", "section:307c4c95a7c84b5efc0b", "section:3bc2480a0b64fd3112f1", "section:46614e805445fc78e7af", "section:4ad984d8cafbe64dad8e", "section:6a93c4dd5fe420e1990e", "section:6b49d8830dc9fa3948be", "section:6cd1a267e72b20619327", "section:701d23928f8e38ea7d4b", "section:708d06b08bf9729fd162", "section:74bb3766bdd1275dbd78", "section:7d0e50b6a6c30535730d", "section:84ec2c9d7a3c77ec2664", "section:8872501633bb702220cd", "section:888628823bf71f709698", "section:89a96ea40df8ee1ce3c8", "section:8b84d2fb55ac4a48656b", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b7b42d68bfe9bb72f6b0", "section:b93e6ae7b00f32ee1201", "section:cca5b83aae425d5f0e88", "section:d90bd5e1e6d8fa41397d", "section:d9b23f5eba4b3c291274", "section:e8fb60dc4323384272d7", "section:f22c82858ff073c133d4", "section:f9b30725993b14c4ee95", "section:ffb3c952b2d4af559d34", "section:ffca98d84a77b4d4e4ab" ], "activeSectionIds": [ "section:0e7ddbc8b9cd02f418a6", "section:2bbe8c5924cafd6c6187", "section:3bc2480a0b64fd3112f1", "section:46614e805445fc78e7af", "section:4ad984d8cafbe64dad8e", "section:6b49d8830dc9fa3948be", "section:708d06b08bf9729fd162", "section:74bb3766bdd1275dbd78", "section:84ec2c9d7a3c77ec2664", "section:888628823bf71f709698", "section:89a96ea40df8ee1ce3c8", "section:8b84d2fb55ac4a48656b", "section:a153934887244824336d", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:b7b42d68bfe9bb72f6b0", "section:d9b23f5eba4b3c291274", "section:e8fb60dc4323384272d7", "section:f22c82858ff073c133d4" ], "evidenceId": "python_verification:verification/v521_seam_bit_rp_blind.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v521_seam_bit_rp_blind.py", "pubMirrorHash": "8e46478bfeb77d2052d31901237a2245a7267248205bf584e5357fe6c328b516", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v521_seam_bit_rp_blind.py" }, { "id": "v522_woit_beta1_gso_gauge", "filename": "v522_woit_beta1_gso_gauge.py", "path": "verification/v522_woit_beta1_gso_gauge.py", "cluster": "frontier", "synopsis": "WOIT.BETA1.GSO.01: the WOIT-beta1 milestone of the OS twistor bridge WOIT.OS.TWISTOR.01 executed -- 'the clock is time-like, GSO is the gauge datum' (typed result: verdict UNDECIDED per the frozen preregistration, mechanism identified exactly, gauge-fixed RP established under the corrected GSO typing; 16 checks, ~5 s). [E] HERMITICITY WITNESS: the mu4 clock average violates Hermiticity exactly (the one-step insertion T_1 = has entry -i/(8 sin(5 pi/16)) where the conjugate transpose demands +i/(8 sin(5 pi/16))); the pairing is complex-SYMMETRIC (745 entries matching, 96 anti-matching, 0 violations) -- 'OS-symmetric' is strictly weaker than Hermitian: 'positivity after gauge fixing' is not well-posed for the clock reading. [E] TIME-LIKE TYPING: ALL 16 dihedral reflection axes of the NS seam circle invert the clock lift (R S R^-1 = S^-1), NONE commutes -- the mu4 clock IS Woit's euclidean rotation (the time translation itself); the gaugeable (theta-compatible) part of the Z8 tower is EXACTLY its 2-torsion {1, (-1)^F} (Hermiticity census over all powers; alpha^4 = the full wrap = the 2 pi rotation of the seam = fermion parity, lattice spin-statistics). [E] POSITIVE PART -- GSO-FIXED RP HOLDS EXACTLY: N = 16 even deg <= 2 parity-projected bond-cut Gram (29,0,0) PD (min eigenvalue 1.78e-6 at 40 digits); N = 8 complete half algebra: the projected Gram kills all odd rows/columns exactly, even block (8,0,0) PD (3.35e-3), no degree truncation; the site-cut defect SURVIVES gauge fixing ((7,9,6)) -- the RP bond placement is gauge-invariant information; family A keeps failing ((17,12,0) indefinite vs family D's (29,0,0)); Kramers: Theta_t^2 = id on A^G, Theta_Fock restricts with Theta^2 = +1; Ramond control: the wrap +1 'true Z4' lift fails state invariance -- the NS/Z8 tower is forced. [E] KILL-TEST BOOKKEEPING: kill test (1) stays discharged also gauge-invariantly (RP separates the families on the invariant sector); kill test (2)'s free shadow does NOT fire (no legitimate Hermitian gauge-fixed form has a negative direction); both stay formally live on the interacting algebra A_hol. [E] WRONG-PROJECTION CONTROLS: invariant-dimension chain parity 120 > deck 64 > clock 32 strict, but Hermiticity singles out PARITY alone (deck and clock averages non-Hermitian): the finer 'gauge' projections are structurally ill-posed pre-quotient. TRANSPARENCY: the first frozen run scored 6/13 (the clock-reading checks failed exactly as the mechanism predicts) and the preregistered deg-2 invariant dimension 30 was a combinatorial error (correct census: 28 quadruples + 4 halved doublets = 32) -- documented in full; verdict by the frozen [C-3] logic (Hermiticity failure => structural-failure branch => UNDECIDED). [C] CONTRACT PRECISION (iii), prose only: 'gauge-invariant subalgebra' at the free level means the GSO/fermion-parity Z2 -- the only theta-compatible part of the mu4 tower (the free-fermion shadow of the E8 glue: (E8)_1 = even NS of SO(16)_1 + R spinor); the clock is the euclidean rotation itself (timelike), its equivariant statement moves to beta2 (OS quotient first, then the clock as reconstructed transfer operator). [O] beta1 proper stays open via beta2; WOIT.OS.TWISTOR.01 stays [O]; no marker moves.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv522_woit_beta1_gso_gauge.py", "sourceSha256": "54127e21e2e5505bf475b5031ad49aecd144ae40b896ca007a649b42b9ab3d81", "linkedClaimIds": [ "WOIT.BETA1.GSO.01" ], "sectionIds": [ "section:00084b3039331dc8515a", "section:0444ab0b0ae0c5cad185", "section:17538bc5f76786fa0bbe", "section:2a4b108348409f980f6d", "section:2db6bd35ce5c578613f3", "section:3bc2480a0b64fd3112f1", "section:4ad984d8cafbe64dad8e", "section:58f2181069f63dc9bc77", "section:6e482b6ca2a1df5c2627", "section:7d0e50b6a6c30535730d", "section:7ee581db787f8ddbcb4a", "section:830ce3efdf003a4e5049", "section:84ec2c9d7a3c77ec2664", "section:8d1e955857da6655fadd", "section:ab9e7e520130ecc7da7c", "section:b191b0a66e5bacdc1a0e", "section:bdb9d2ad81791492cab1", "section:c519f45910c30ff3c0ae", "section:cac001c63c2444d31263", "section:cca5b83aae425d5f0e88", "section:d9b23f5eba4b3c291274", "section:de8db1cd8257eab0d607", "section:e8fb60dc4323384272d7", "section:f1cafbf24805c6c09d79", "section:f8ad9138e39428999ab9" ], "activeSectionIds": [ "section:00084b3039331dc8515a", "section:17538bc5f76786fa0bbe", "section:3bc2480a0b64fd3112f1", "section:4ad984d8cafbe64dad8e", "section:830ce3efdf003a4e5049", "section:84ec2c9d7a3c77ec2664", "section:8d1e955857da6655fadd", "section:ab9e7e520130ecc7da7c", "section:cac001c63c2444d31263", "section:d9b23f5eba4b3c291274", "section:de8db1cd8257eab0d607", "section:e8fb60dc4323384272d7", "section:f1cafbf24805c6c09d79" ], "evidenceId": "python_verification:verification/v522_woit_beta1_gso_gauge.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v522_woit_beta1_gso_gauge.py", "pubMirrorHash": "54127e21e2e5505bf475b5031ad49aecd144ae40b896ca007a649b42b9ab3d81", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v522_woit_beta1_gso_gauge.py" }, { "id": "v523_celestial_wp5e_wm_derived", "filename": "v523_celestial_wp5e_wm_derived.py", "path": "verification/v523_celestial_wp5e_wm_derived.py", "cluster": "frontier", "synopsis": "CELEST.WP5E.WM.01: the constructive derivation of the w_m normalisation -- '1/det_j is the Atiyah-Bott / zeta-determinant fixed-point factor, COMPUTED from three independent sources', closing the residual [O] of v516/v520 at the fibre-zero-mode level (verdict ERFOLG per the frozen preregistration; 26 checks, ~1 s). [E] ATIYAH-BOTT (route i): the equivariant mode ledger of the fibre C^2 equals the closed form 1/((1-q i^j)(1-q i^{-j})) exactly in Q(i) for all n <= 120; REGULAR at q = 1 with Abel value (1/2, 1/4, 1/2) = 1/det_j, det_j = det(1-g^j) = (2, 4, 2); (C,2) Cesaro convergence in exact arithmetic; the fixed-point factor splits off EXACTLY at every truncation level d in {7, 12, 25}, for the phased (skeleton) AND the v520-forced unphased (completion) trace alike -- the Abel-limit contact_j = (Q^(0) - Q^(j))/det_j is the v516 contact vector COMPUTED, not declared. [E] ZETA/QUILLEN (routes ii/iii): det_zeta of the g^j-twisted circle Laplacian = 4 sin^2(pi j/4) = det_j EXACTLY (Lerch + reflection formula symbolically; Hurwitz certificates ~1e-41); Quillen split det Delta = det_j^2, |det dbar| = det_j, with the real positive holomorphic section UNIQUE via the SU(2) conjugation pairing; the delta-1f f1f3 block at the (0, b) nodes carries the exact constant term 1/det_b (deviations <= 5.2e-28). [E] CONSISTENCY CHAIN: the derived weight reproduces the v516 chain number by number -- w_m = (0, 3/2, 2, 3/2) = 4h_m = |mu4| h_m = -4 ch2(T_m); T5 = 0 at every scale; h_2 : h_1 = 4 : 3; the T3 budget 32 - 8c forces c = 4 = |mu4| uniquely (leftovers 24/16/8/0/-8); per-sector Okubo squares (18, 9, 18)^2; total 45^2; Phi_T3: 32 -> 0, Phi_P: 72 -> 0; psi(A_fix) = +64, psi(contact) = -64. [E] NEGATIVE CONTROLS: 1/det^2 gives w' = (0, 5/8, 1, 5/8) with leftovers (2, 12) and a Quillen contradiction (det Delta = det^4 vs measured det^2); 1/|1-i^j| gives w''_1 = 1+sqrt2 notin Q; the Z2/Eguchi-Hanson anchor PASSES with the same derivation (det = 4, w = 1/2 = |Z2| h^{A1}, 9^2 = (1/4) x 36, c = 2 = |Z2|); the SO(16)/D8 KILL fires; diag(i,i) breaks the zeta = AB identity itself (real (2,4,2) vs complex (2i,4,-2i), no real Quillen section); k = 3, 5 orbifolds: w_m = m(k-m)/2 = k h_m exactly in Q[x]/Phi_k -- the weights wander correctly with the centre count, only k = 4 = |mu4| carries the E8-glue chain. [C] TYPED PREMISES (the mandatory fence): TP-REG (Abel/Cesaro/zeta regularisation IS the definition of the equivariant character), TP-Q (Quillen structure of BCOV F1 = v520 TP-4), TP-NUM (unphased numerator = the v520 ERFOLG-A decision layer), TP-CH (the insertion channel (0, j) computes the box-channel weight). [O] the GLOBAL BCOV integral on PT/Z4 beyond the fibre zero-mode factor; the resolved-ALE route (v514/v517) not built; SEAM.EQUIV.TWISTOR.01 untouched. Discovery provenance: experiments/tfpt-discovery/celestial_seam_wp5e_wm_bcov_derivation_probe.py (26/26, 2026-07-23). NO marker moves.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv523_celestial_wp5e_wm_derived.py", "sourceSha256": "a95ad8e8b8d81f876801d5ce62243cd90d3b74257d6a958af5ccf75a0a3f8b7e", "linkedClaimIds": [ "CELEST.WP5E.WM.01" ], "sectionIds": [ "section:0e7ddbc8b9cd02f418a6", "section:26516787d04ebc9e58b3", "section:307c4c95a7c84b5efc0b", "section:3ed2167aff70cc409f71", "section:58f2181069f63dc9bc77", "section:6e482b6ca2a1df5c2627", "section:701d23928f8e38ea7d4b", "section:7d0e50b6a6c30535730d", "section:7ee581db787f8ddbcb4a", "section:8b84d2fb55ac4a48656b", "section:8d1e955857da6655fadd", "section:9f542e7b4fe8d834693c", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:bc61b0e372551b770dfb", "section:c519f45910c30ff3c0ae", "section:cac001c63c2444d31263", "section:cca5b83aae425d5f0e88", "section:d9b23f5eba4b3c291274" ], "activeSectionIds": [ "section:0e7ddbc8b9cd02f418a6", "section:26516787d04ebc9e58b3", "section:3ed2167aff70cc409f71", "section:8b84d2fb55ac4a48656b", "section:8d1e955857da6655fadd", "section:9f542e7b4fe8d834693c", "section:ab9e7e520130ecc7da7c", "section:b3146d55cec712d485d5", "section:bc61b0e372551b770dfb", "section:cac001c63c2444d31263", "section:d9b23f5eba4b3c291274" ], "evidenceId": "python_verification:verification/v523_celestial_wp5e_wm_derived.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v523_celestial_wp5e_wm_derived.py", "pubMirrorHash": "a95ad8e8b8d81f876801d5ce62243cd90d3b74257d6a958af5ccf75a0a3f8b7e", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v523_celestial_wp5e_wm_derived.py" }, { "id": "v524_woit_beta2_os_quotient", "filename": "v524_woit_beta2_os_quotient.py", "path": "verification/v524_woit_beta2_os_quotient.py", "cluster": "frontier", "synopsis": "WOIT.BETA2.OS.01: the WOIT-beta2 milestone of the OS twistor bridge WOIT.OS.TWISTOR.01 executed -- 'the OS quotient of the free system made explicit' (verdict SUCCESS per the frozen preregistration, [C]-typed per contract precision (iii); 20 checks, ~5 s). [E] H_phys EXPLICIT: N = 16 (deg <= 2): the 37x37 bond-cut OS Gram is exactly Hermitian, parity-block-diagonal, inertia (37, 0, 0) PD (min eigenvalue 1.7801e-6 at 40 digits), null space {0}, dim 37 = 29 (+) 8; N = 8 (complete half algebra): (16, 0, 0) PD (min 3.3471e-3), dim 16 = 8 (+) 8 = 4^2 -- compact euclidean time reconstructs a THERMAL (KMS) representation; exact certificate sin^2(3pi/8) - sin(pi/8) sin(5pi/8) = 1/2. [E] TRANSFER SEMIGROUP (Klein-Landau): tau_k exactly Hermitian on all domains (k = 1..7, dims 29, 22, 16, 11, 7, 4, 2), chain identities exact, vacuum fixed; the positivity pattern IS the site/bond dichotomy: even k PSD via the exact square identity T(2j) = A_j*A_j ((22,0,0)/(11,0,0)/(4,0,0)), odd k indefinite ((10,12,7)/(5,6,5)/(2,2,3)) -- the one-step transfer is NOT positive (the free chirality datum, kill-test-3 shadow sharpened), its even powers ARE. [E] THE CLOCK = T^{N/4}: N = 16: tau_4 PD (11, 0, 0) (min 6.6821e-5), compressed spectrum [0.0194517, 1.64144], vacuum eigenvalue exactly 1; N = 8: spectrum EXACTLY {1, sqrt(2) - 1} = {1, 1/delta_Silver} in both parity sectors -- the silver axes of the v519 mu4 torsor return as the clock-transfer eigenvalue; spectral projections ~1e-40; the reconstructed rotation group U(s) = exp(isH) is unitary with the group law. [E] v522 RESOLUTION: the census (745, 96, 0) reproduced; EVERY anti-matching entry is a wrap overlap, every overlap-free entry matches -- the pre-quotient non-Hermiticity is EXACTLY the domain/wrap artifact; on the quotient the clock has spectral calculus. Pre-registered KMS deviation: NO contraction on the compact circle (edge modes C(1)/C(3) = 1 + sqrt(2) = delta_S exactly, det(G - tau_4) < 0). [E] GSO/THETA: the grading survives; the perpendicular torsor mirror descends anti-unitarily (eta_perp in {+-i}), Theta_phys^2 = +1 on every sector (Kramers-free), theta_cut o theta_perp = alpha_{N/2} exactly. [E] CONTROLS: site cut indefinite ((3,3,1)/(2,2,4)) -- the contract kill branch fires there; family A (4,4,0); anti-chiral (8,8,0) no quotient; wrong direction non-Hermitian (mismatches all wrap-overlap). KILL-TEST BOOKKEEPING: (1), (2) strengthened, (3) shadow sharpened, none fires; (4)-(7) untouched; all seven stay live on A_hol. [C] FENCE: 'the clock acting unitarily' is operationalised per contract precision (iii) as the reconstructed transfer/rotation structure. TRANSPARENCY: run 1 scored 18/20 (a sympy simplify failure on a TRUE pi/16 product formula, fixed by a Laurent-polynomial certificate; no criterion changed). [O] beta3 is the next milestone; WOIT.OS.TWISTOR.01 stays [O]. Discovery provenance: experiments/tfpt-discovery/woit_os_beta2_os_quotient_probe.py (20/20, 2026-07-23). 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[E] ALL LIFTINGS WELL-DEFINED AND BLIND: (a) sigma-gauge arc decoration (Z2): sigma o r = sigma on the swap axes makes the twisted Gram a diagonal unitary congruence D M D -- spectra IDENTICAL to untwisted (dev 0.0); (b) Kadanoff-Ceva 4-twist insertion omega(D .)/omega(D): well-defined on N = 32 (omega(D) real nonzero; the N = 16 odd-m degeneration is the C(even) = 0 checkerboard artifact); the RP SPECTRA depend on delta for the first time in the program (pairwise up to 1.05), but the INERTIA is (16, 0, 0) PD with the SAME eta = +i for every m -- the decoration sees delta, positivity does not; (c) the mu4 twist at beta = pi/2 is pure plane gauge; (c') genuine Bogoliubov defect beta = pi/4: Theta-compatibility selects exactly 2 of 16 sign patterns (NS-wrap forced), the winner genuinely non-monomial -- still PD, spectra identical. STRUCTURE THEOREM (empirical, mechanism exact): EVERY Theta-compatible quasi-free mark decoration is RP-spectrally INVISIBLE (the defect planes never straddle a cut bond; orthogonal congruence). [E] SUB-RESULTS: the defect energy E_def = 1.2752872 for EVERY m (spread 4e-40) -- delta-blind; the 4-twist Casimir ln|omega(D)| measures delta (-0.890 .. -1.348) but is exactly mirror-symmetric under m <-> 8 - m -- a family gauge, never a side selector; Kramers _tw = +1 for every m. [E] TWO BIT-PRESUPPOSING pi/2 STRUCTURES (the harvest): the eta flip +i -> -i on the mark-fixing axes (sigma o r = -sigma, odd sector exactly negated); the twist frustration of the mark-fixing mirror ((4, 4, 0) indefinite for both eta -- the lattice shadow of the Ising twist field's mirror-oddness) -- both formulable ONLY on the fixing axes existing iff delta = pi/2: they PRESUPPOSE the bit (v512 facet class), no selector. [E] NEGATIVE CONTROLS: the twist-free limit = v519/v521 exactly; the site cut keeps failing in every decorated state; the v512 counterwitness is arc-equivalent at N = 16 to the blind member pi/4 -- no state-level selector can exclude it; a single twist has omega(D) = 0 identically (twists exist only in mark pairs); the deck-paired FOUR-twist decoration is the minimal well-defined one. [O] the door narrows to a genuinely INTERACTING A_hol whose OS data are NOT Pfaffian-reducible to the chiral vacuum -- beyond every Wick-computable class. VERDICT: KILL exactly as preregistered; the alignment bit remains genuine discrete input. Discovery provenance: experiments/tfpt-discovery/seam_alignment_bit_twist_state_probe.py (20/20, 2026-07-23). 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Verdict SUCCESS (22 checks, ~8.4 s). [E] beta MEASURED = N at both levels (N=8: omega=arcsinh(2^{-3/4}), kappa=q^{-8} exact; N=16: pairing exponent (N/2)+1=9); T_seam=1/N per clock step, beta_angle=2pi EXACT = 1/(4 c3), T_seam=4 c3 = Bisognano-Wichmann/Hawking normalisation (v208); modular Hamiltonian closed (nu1=cos(pi/24), nu2=cos(7pi/24); Tomita KMS beta=1 on all 256 pairs, residual 2.5e-38); c3 third leg class-1 selected (r=1); entropy S(8/16/32)=0.52187/0.63510/0.75006, DeltaS/ln2 -> 1/6, horizon fractions {1/3,2/3} do NOT transfer; [C-5] silver = C(3)/C(1) = 1/(2 cosh 2 omega - 1); non-compact Stieltjes => T=0. Discovery provenance: experiments/tfpt-discovery/seam_thermal_kms_nariai_bridge_probe.py (22/22, 2026-07-23). 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STRUCTURE=SUCCESS: {1, sqrt2-1} closed via diagonal Hankel pencil at N=8, tan(pi/8)=C(3)/C(1), doubling=exact second quantisation, carrier=silver-midpoint axes of the mu4 torsor, gap=arcsinh(1)=gd^{-1}(pi/4); N-scaling shows pure N=8/16 Majorana lattice datum (not continuum); positive clock only for N==0 mod 8; golden family as N=10 control. CONNECTION=KILL: preregistered 11466-candidate census over 16 frozen numbers: 0 hits above null; placebos (golden, plastic) comparable -- NO readout connection. Cross-link v526: sqrt2-1 = C(3)/C(1) thermal kernel ratio. Discovery provenance: experiments/tfpt-discovery/seam_clock_silver_spectrum_probe.py (22/22, 2026-07-23). 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Verdict SUCCESS. [E] Facets #14 (eta-flip <=> delta=pi/2) and #15 (twist-frustration <=> delta=pi/2) both directions exact (cardinality lemma |A+|=|A-| => m=4; g-class census over all 224 axes: flip class exactly at {15,31} for m=4); order parameter O=flip-axis fraction=1/2 at m=4 else 0; class alternation (-,+,-,+) = nontrivial Z2 character of the Z8 clock-tower shadow; gauge-robust; unification #14=#15=flag-transitivity = ONE Z2 invariant (v512 web 13->15); Kramers=POSITION half (derived), twist class=MODULUS half (the input). [C] measurement sketch: defect transport around the axis torsor accumulates eta holonomy = relative pi phase iff bit set -- in principle interferometrically readable. Honest fence: the bit remains formal input. Discovery provenance: experiments/tfpt-discovery/seam_bit_twist_class_definition_probe.py (18/18, 2026-07-23). 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F1=KILL: Theta exists (U_r^2=2^8, Theta^2=+1, conj_V V=4096, [Theta,H_g]=0) so Kill-Test 1 does NOT fire; BUT Kill-Test 2 FIRES at toy level -- RP breaks for every g>0: inertia ladder (37,0,0)->(33,4,0)->(31,6,0)->(29,8,0); Gibbs beta=2 same ladder; mechanism = interference; STRADDLE LAW (24/24): RP fails exactly on quartet-straddled cuts. F2=KILL: the TENTH side-blind test (9->10) -- Theta_15 maps H(m)->H(8-m) EXACTLY despite delta-seeing spectra (spread 1.32). F3=ERFOLG: grading + Z8 tower (Utilde^2=256 Gamma, V^2=256 Utilde) + FK anchor + constructive OS quotient at pi/2. [C] fence: one toy, one interaction class, flat-band parent -- narrows WOIT route, does NOT close it; WOIT.OS.TWISTOR.01 stays Open. Discovery provenance: experiments/tfpt-discovery/seam_interacting_toy_fk_probe.py (24/24, 2026-07-23). 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mutations break on e^{iπ/5} and on mutated lists; honest caveat wired as a check (reality of the exponent sum alone is not hexagon-specific); (2) ZERO PHASE IN THE MAGNITUDE DATA — arg(∏c) = 0 exactly on both TFPT sectors, and the μ₃ branch group is the kernel because its order divides N_fam = 3 (a μ₄ branch already shifts the phase): the REDTEAM.D.01 residual is a FIBER datum, not a magnitude datum; (3) TIER-1 EMPTINESS by the blindness theorem — both kernels commute with conjugation, so every π/3-carrier is κ-odd and invariant+odd ⇒ Im F = 0: strict invariance is empty on π/3-carriers, per algebra; (4) the FRAME REMOVAL — det(1,d,n) = 21 and Im det(1,d,ρn) = 21 sin(π/3) exactly, the orientation functional homogeneous of degree +1 in the frame normalisation (21 sin(π/3) is FRAME data), and Im(ρ det)/det = Im ρ = sin(π/3) exactly: the invariant core is a fiber datum, the sign a declared orientation (the DUAL.FRAME.01 narrowing); (5) the TWO TIER-2 CHARACTERS — P2 = arg Σρ^{d_k} at (χ(κ),χ(σ)) = (−1,+1), V5 = Im(ρ det)/det at (−1,−1), homomorphisms verified on the full four-group: two INEQUIVALENT invariants carry the same π/3 (the DEGENERATE verdict as algebra), neither frame-coupled — plus the Jarlskog anchor (TFPT CKM rebuild unitary to 1e-41, J = 3.327021e-5 = v88; 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no CP derivation anywhere): (1) the EULER FACTORISATION — the fiber acts on the frame by a scalar on the n-row, so every homogeneous block factorises P(ρn) = ρ^m P(n) (fully generic degree 1–4 polynomials, symbolic coefficients): every scale-free functional decomposes as Σ_k A_k Im(ρ^k) with A_k real degree-0 frame ratios — the fiber content is QUANTISED; (2) the NATURAL CLASS IS FIBER-ONLY (T177-R1, natural half, negative BY THEOREM) — metric-free invariants of vector tuples are generated by volume-form brackets (Weyl 1946 FFT, the one cited class boundary), and the exact enumeration on {1, d, n} gives ONE generator (six permutations = ±Δ, the other 21 brackets vanish identically in a generic n): every scale-free ratio is constant — no frame-coupled scale-free π/3-carrier exists without a metric, T177's obstruction sentence is now a theorem; (3) the METRIC DOOR IS NON-CANONICAL (R1, metric half) — declared metrics admit frame-coupled Tier-2 carriers, non-unique at BOTH levels: Δ/⟨d,n⟩ and Δ/⟨1,n⟩ carry (κ,σ,Ref) = (−1,−1,+1) (the odd Δ-power absorbs the reflection) while Δ²/⟨n,n⟩ carries (−1,−1,−1), and the admissible normalisers contain the continuum q_t = t·n₁²+n₂²+n₃² (deck-invariant for every t) with values 441·sin(π/3)/(25t+117) — NO canonical frame factor; anti-numerology wired as a check (21/8, 21/2, 441/142 pairwise distinct, none claimed); (4) the SINGLE-SINE LEMMA — {|Im(ρ_n^k)|} has exactly ONE nonzero element iff n is crystallographic (n ∈ {1,2,3,4,6} = {n : φ(n) ≤ 2}), by sin(4π/n) − sin(2π/n) = 2 sin(π/n) cos(3π/n) with its only zero at n = 6 on n ≥ 5, enumerated exactly to n = 24: the compiler's two clocks μ₄ (j = 1728) and μ₆ (j = 0) are the two MAXIMAL single-sine fibers, so value-based pinning is impossible by theorem — T177's DEGENERATE verdict was forced, not found (on μ₅, values DO separate carriers); (5) the ANCHOR SELECTION (T177-R2, selected) — the Jarlskog invariant on the TFPT CKM rebuild has full character tuple (−1,−1,−1) under (κ, σ, deck-Ref), each certified at 40 dps: it matches the sheet-ODD orientation class V5 and not the sheet-even P2 = (−1,+1,−1); the (−1,−1,+1) metric carriers are anchor-rejected and the matching family carries the continuum — the unique anchor-matching CANONICAL carrier is the fiber-pure Im(ρ) = sin(π/3); conditional on the anchor (selected, not derived), deck column a declared model, REG.FREEZE.01 untouched, no marker moves (22 checks, ~2 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv564_cp_fiber_pin.py", "sourceSha256": "e2975e74b01b40479402db5dcbf9b689b457043926e29394f1452f88cdaa19e8", "linkedClaimIds": [ "CP.FIBER.PIN.01" ], "sectionIds": [ "section:39baa0b456e579fcab62", "section:7a7de20f53ed3e69fb6f", "section:ab9e7e520130ecc7da7c", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:39baa0b456e579fcab62", "section:7a7de20f53ed3e69fb6f", "section:ab9e7e520130ecc7da7c", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v564_cp_fiber_pin.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v564_cp_fiber_pin.py", "pubMirrorHash": "e2975e74b01b40479402db5dcbf9b689b457043926e29394f1452f88cdaa19e8", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v564_cp_fiber_pin.py" }, { "id": "v565_woit_beta3_pt_duality", "filename": "v565_woit_beta3_pt_duality.py", "path": "verification/v565_woit_beta3_pt_duality.py", "cluster": "frontier", "synopsis": "WOIT.BETA3.DUALITY.01: the WOIT-beta3 milestone of the OS twistor bridge executed — 'the PT ↔ PT* duality typed against sigma_std' (verdict SUCCESS per the frozen preregistration; the contract kill branch is EMPTY BY ALGEBRA; no marker moves): (1) the COMPATIBLE CLASS — a duality is a nondegenerate Hermitian form Phi on C^4, and clock compatibility (rho4 = diag(i,1,i,1)) forces the four cross-eigenspace entries to zero exactly: two 2×2 Hermitian blocks on {e1,e3} ⊕ {e2,e4}, 16 → 8 real parameters (deck adds nothing; the wrong clock lift breaks the split); (2) the DICHOTOMY — pairing against Woit's Euclidean structure rho_tw splits the class exactly in two: the EUCLIDEAN branch (sigma_std's home) has seam-line norm a(|z|²+1), no null point, no OS cut ever; the MINKOWSKI branch has norm a(|z|²−1) — the null locus meets the seam line EXACTLY in the seam circle for every member (the OS cut is FORCED, not imposed), and the second block is exactly minus the conjugate of the first (charpoly mirrored): the TOTAL SIGNATURE IS (2,2) for every nondegenerate member — Woit's Minkowski signature is a theorem of clock + rho_tw pairing, not an input; (3) the KILL IS EMPTY BY ALGEBRA — every compatible duality inverts clock AND deck (family D); a clock-centralising (family A) duality would need rho4² = scalar, but rho4² = diag(−1,1,−1,1): no solution, decided not scanned; s² = diag(a²,a²,c²,c²) > 0: Kramers-free; (4) the INDUCED MEMBER IS UNIQUE — seam preservation ⇔ b = 0, and then every member induces the SAME conjugation z → −conj(z) (mu = −1, fixed points ±i), perpendicular to sigma_std's z → +conj(z) (mu = +1, fixed points ±1), the clock exchanging exactly these two; (5) the QUOTIENT IDENTIFICATION — exact placement arithmetic and coordinate transport land the induced member on the k = 3 axis: it IS theta_perp, the mirror whose descent v524 certified (Theta_phys), while sigma_std's member transports to the CUT axis (the OS metric itself) — role separation complete; v524 regressions re-verified at N = 8 (Gram PD (16,0,0), anti-unitarity exact with eta_perp = +i, Theta² = +1 on both sectors, time reversal, torsor closure); controls: family A (4,4,0) no quotient, the Euclidean branch cannot cut, non-mu4 reflections not mark-anchored. Free/quotient level only; A_hol untouched; gamma is next (22 checks, ~2 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv565_woit_beta3_pt_duality.py", "sourceSha256": "0719c5c28b311401b5812e9ebe8f76e7d18f1409f8d746568dd7b0abded83dac", "linkedClaimIds": [ "WOIT.BETA3.DUALITY.01" ], "sectionIds": [ "section:00084b3039331dc8515a", "section:17538bc5f76786fa0bbe", "section:2db6bd35ce5c578613f3", "section:38cc1bfba5161e50d0bb", "section:58f2181069f63dc9bc77", "section:6e482b6ca2a1df5c2627", "section:7d0e50b6a6c30535730d", "section:7ee581db787f8ddbcb4a", "section:848c49f799255f4cda92", "section:8d1e955857da6655fadd", "section:a7b499839afbb3b8e6af", "section:ab9e7e520130ecc7da7c", "section:b191b0a66e5bacdc1a0e", "section:c4cf080b9ae6f25f7a71", "section:c519f45910c30ff3c0ae", "section:cac001c63c2444d31263", "section:cca5b83aae425d5f0e88", "section:de8db1cd8257eab0d607" ], "activeSectionIds": [ "section:00084b3039331dc8515a", "section:17538bc5f76786fa0bbe", "section:38cc1bfba5161e50d0bb", "section:8d1e955857da6655fadd", "section:a7b499839afbb3b8e6af", "section:ab9e7e520130ecc7da7c", "section:cac001c63c2444d31263", "section:de8db1cd8257eab0d607" ], "evidenceId": "python_verification:verification/v565_woit_beta3_pt_duality.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v565_woit_beta3_pt_duality.py", "pubMirrorHash": "0719c5c28b311401b5812e9ebe8f76e7d18f1409f8d746568dd7b0abded83dac", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v565_woit_beta3_pt_duality.py" }, { "id": "v566_parabolic_anchor_selfcode", "filename": "v566_parabolic_anchor_selfcode.py", "path": "verification/v566_parabolic_anchor_selfcode.py", "cluster": "flavor", "synopsis": "DIAMOND.PARA.SELFCODE.01: the parabolic anchor self-code (external review 2026-07-31, audited and promoted) — the v218 sheet-diamond direction operators U = Q·diag(1,0,0), V = Q·diag(0,1,1) generate the FULL 2|1 parabolic (line-stabiliser) algebra A (dim 7, word determinant −81, multiplicatively closed, mutation-fragile); the anchor a = (1,1,2) is the spectrum of H = I + V(V−I)/2 (dominant Lagrange projector, idempotent, trace 1), and χ_H = x³ − 4x² + 5x − 2 carries the DOUBLE self-code: (4,5,2) = (|μ₄|, g_car, |Z₂|) = (flag dim_R(GL₃/P), Levi dim(A/J) = 2²+1², radical dim J) — the anchor reproduced spectrally through V and categorically through A; the UNIQUENESS THEOREM: x³ − 2mx² + (m²+1)x − m = (x−m)(x²−mx+1), all-positive-integer spectra force m = 2 — a = (1,1,2) is the only member this parabolic family can code; the 81 as a lattice index: the SATURATED integral order Z⟨U,V⟩ has elementary divisors (1,1,1,3,3,3,3) — index 3⁴ = 81 = the v218 determinant-staircase sum (global determinant charge = integral saturation index; mark-local mechanism [O]); the A2 bit carrier: the basic algebra is the A2 path algebra with Ext¹ = 1 — exactly two module classes (split / one nonsplit): the alignment bit gains a canonical algebra carrier (selection stays with RP/geometry); the trace code p_n(a) = 1 + tr(Vⁿ) with 240 and rank 8 as trace readouts (typed re-encoding of AnchorLadder); the CR = 4/3 preregistered test design for CONTRACT.F.01 (universal-progression honesty wired; negative control 28/25; y_F forced fit-free); and the Lorentz/relative-pencil form of the Paper-II rank-3 classification (eigenvalue locking as the named instrument). NO P2 reduction — the 'No Carrier Reconstruction' audit is the named [O] door; the 2..9 table typed as compression (14 checks, ~1 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv566_parabolic_anchor_selfcode.py", "sourceSha256": "655a09f2afc1894b59816dfa4cf631d23d64cf51e1530c5736e95f541c0c738d", "linkedClaimIds": [ "DIAMOND.PARA.SELFCODE.01" ], "sectionIds": [ "section:0360327baf7e82aba7c3", "section:0739148b5a5974d0d662", "section:1234c1fa7fdc0d6d5b35", "section:1bc03b42708092f8463b", "section:22fb298fcb28accfbf39", "section:2678ed3ba0ed508e2d8e", "section:4d29b40dee14dd3fb5c9", "section:51e91159532ef7479ff8", "section:568b5e9acdb7b04367d3", "section:6a93c4dd5fe420e1990e", "section:848c49f799255f4cda92", "section:86289022df2156d0b3e5", "section:8872501633bb702220cd", "section:97886ff8881b257d4648", "section:ab9e7e520130ecc7da7c", "section:ac418863c3194ed2d0cf", "section:c4cf080b9ae6f25f7a71", "section:d90bd5e1e6d8fa41397d", "section:f0ac30137703825661c6", "section:fdf63a1d99769ab37ccb" ], "activeSectionIds": [ "section:1234c1fa7fdc0d6d5b35", "section:1bc03b42708092f8463b", "section:22fb298fcb28accfbf39", "section:51e91159532ef7479ff8", "section:86289022df2156d0b3e5", "section:97886ff8881b257d4648", "section:ab9e7e520130ecc7da7c", "section:ac418863c3194ed2d0cf", "section:fdf63a1d99769ab37ccb" ], "evidenceId": "python_verification:verification/v566_parabolic_anchor_selfcode.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v566_parabolic_anchor_selfcode.py", "pubMirrorHash": "655a09f2afc1894b59816dfa4cf631d23d64cf51e1530c5736e95f541c0c738d", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v566_parabolic_anchor_selfcode.py" }, { "id": "v567_carrier_free_q_reconstruction", "filename": "v567_carrier_free_q_reconstruction.py", "path": "verification/v567_carrier_free_q_reconstruction.py", "cluster": "flavor", "synopsis": "QGEO.QRECON.01: the No-Carrier-Reconstruction audit, Stage A — can Q (hence V and the v566 anchor self-code) be reconstructed WITHOUT carrier/anchor inputs? The circularity located: v11's uniqueness certificate uses row sums (4,5,6), column sums (9,5,1) and chi_Q with its 5 = g_car — all FORBIDDEN here. Allowed: the sheet involution, the winding normalisation Q(I+Σ) = 2N_fam·W, the A3 exponent spectrum {1,2,3}, the sheet-monodromy budget Q₋² = N_fam·P, nonneg integrality, the seam-line demand, and one family invariant (saturation index 81). Results (exact enumeration): 52 admissible → 28 parabolic — and ALL 28 code the SAME anchor (H' = I + Π_dom has char poly x³−4x²+5x−2, spectrum (1,1,2)): THE ANCHOR IS CARRIER-FREE; the 81-pin then selects exactly TWO members — the corpus Q (q32 = 2 = |Z2|) and its q32 = 0 twin — on which every classical carrier-free certificate coincides (anticommutator spectrum (6,−4,−2), commutator charpoly t(t²+12), det 3, saturation 81) while the ONE separating certificate is the carrier column budget (9,5,1) vs (9,3,1): exactly the forbidden input — the residual freedom is ONE binary sheet-block-coupling choice (resonance with the split/nonsplit alignment bit recorded as typed observation). Ablations: dropping the winding input widens 28 → 1376 at bound 3 (real load); bound-stable 6 → 9. Stage A only: the audit RELOCATES to GATE.QGEO.01 (derive the geometric inputs themselves) and to the binary selector; NO P2 reduction, markers untouched (9 checks, ~1 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv567_carrier_free_q_reconstruction.py", "sourceSha256": "1bc6a8f5636ccd7f4077228fed506076dca3ba4519ac36491df94db00922f178", "linkedClaimIds": [ "QGEO.QRECON.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:1234c1fa7fdc0d6d5b35", "section:2678ed3ba0ed508e2d8e", "section:51e91159532ef7479ff8", "section:86289022df2156d0b3e5", "section:8872501633bb702220cd", "section:ab9e7e520130ecc7da7c", "section:abb53343f07d4a85f8f9" ], "activeSectionIds": [ "section:1234c1fa7fdc0d6d5b35", "section:51e91159532ef7479ff8", "section:86289022df2156d0b3e5", "section:ab9e7e520130ecc7da7c", "section:abb53343f07d4a85f8f9" ], "evidenceId": "python_verification:verification/v567_carrier_free_q_reconstruction.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v567_carrier_free_q_reconstruction.py", "pubMirrorHash": "1bc6a8f5636ccd7f4077228fed506076dca3ba4519ac36491df94db00922f178", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v567_carrier_free_q_reconstruction.py" }, { "id": "v568_bit_selector_ladder", "filename": "v568_bit_selector_ladder.py", "path": "verification/v568_bit_selector_ladder.py", "cluster": "flavor", "synopsis": "DIAMOND.BIT.SELECT.01: the residual reconstruction bit located, separated and given a canonical witness — the two 81-twins of the v567 audit (q32 = 2 = |Z2| vs 0) generate DIFFERENT integral orders (equal index 81, different lattices: the bit is integrally visible where every classical invariant coincides); the dominant mode of the sheet direction is v(c) = (1, 2, 2c) identically, and the LADDER SELF-CONSISTENCY — the dominant mode reproduces its own eigenvalue as the geometric ladder (2⁰,2¹,2²) = (1,2,4) — picks c = 2 UNIQUELY on all 28 members of the carrier-free class (no 81-pin, no column budget needed); the witness is prior structure (AnchorLadder steps 2ⁿ, 2 = |Z2|, the v566 trace code), not a found number; the SPLIT geometry sits at q32 = 1 and is EXCLUDED by the demands already imposed (algebra collapses to dim 5 — the v566 A2 Ext arrow is nonzero on the whole class; neither twin splits: the bit toggles WHICH nonsplit order is realised, not split/nonsplit); Priority-2 candidates tested honestly: the mu4-grading fails (order not graded — 81 stays a fingerprint), left V-multiplication induces a canonical F3-action on the cokernel (Z/3)⁴ — computed: charpoly x(x−1)²(x+1) mod 3, eigenvalues {0,1,1,−1}, NOT the regular μ₄ pattern; U acts as zero; twins identical — after two candidates the 81 stays a fingerprint. The physical selection is NOT derived — why the ladder self-consistency should hold is the relocated open question, the same slot as the RP-selection of the alignment bit (11 checks, ~1 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv568_bit_selector_ladder.py", "sourceSha256": "2c4d803060a9f3652f791e007a967281e45f4fca5ff53766443a353ffd986d73", "linkedClaimIds": [ "DIAMOND.BIT.SELECT.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:1234c1fa7fdc0d6d5b35", "section:2678ed3ba0ed508e2d8e", "section:51e91159532ef7479ff8", "section:86289022df2156d0b3e5", "section:8872501633bb702220cd", "section:ab9e7e520130ecc7da7c" ], "activeSectionIds": [ "section:1234c1fa7fdc0d6d5b35", "section:51e91159532ef7479ff8", "section:86289022df2156d0b3e5", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v568_bit_selector_ladder.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v568_bit_selector_ladder.py", "pubMirrorHash": "2c4d803060a9f3652f791e007a967281e45f4fca5ff53766443a353ffd986d73", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v568_bit_selector_ladder.py" }, { "id": "v571_cr_discrete_corners", "filename": "v571_cr_discrete_corners.py", "path": "verification/v571_cr_discrete_corners.py", "cluster": "frontier", "synopsis": "FTR.CRDISC.01: the preregistered cross-ratio check (self-code review Priority 4 / v566 S9), executed on its DISCRETE half — the four solver corners are the in-repo Sheet-Diamond kernels J,K,C,F = M(1,t), t = −2..1 (v224, dets (2,4,14,32)), and the corpus's one canonical declared solver reading, the Koide anchor response ℓ(M) = aᵀM·1 (v183), reads (26, 35, 44, 53) on them: CR = 4/3 EXACTLY, and the fit-free reconstruction forces y_F = 53 from (26,35,44) alone — the Koide numerator is Möbius-determined by the three upstream corners (new exact cross-corner identity); honesty theorem: ℓ is affine on the path (step 9 = N²fam) and every linear functional passes — the check separates linear from nonlinear exports; negative controls with teeth: determinants fail at 28/25 as preregistered, the dominant eigenvalue fails at 1.3222; the DISCRETE half only — the continuous solver states stay open exactly as CONTRACT.F.01 fences them (9 checks, <1 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv571_cr_discrete_corners.py", "sourceSha256": "e54029bfaceaa6687677cbb6ec79436a0ecc2b03aa3c03add69cbdc0a957e502", "linkedClaimIds": [ "FTR.CRDISC.01" ], "sectionIds": [ "section:568b5e9acdb7b04367d3", "section:ab9e7e520130ecc7da7c", "section:f0ac30137703825661c6", "section:fb925495ff0f316b1a06", "section:fdf63a1d99769ab37ccb" ], "activeSectionIds": [ "section:ab9e7e520130ecc7da7c", "section:fb925495ff0f316b1a06", "section:fdf63a1d99769ab37ccb" ], "evidenceId": "python_verification:verification/v571_cr_discrete_corners.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v571_cr_discrete_corners.py", "pubMirrorHash": "e54029bfaceaa6687677cbb6ec79436a0ecc2b03aa3c03add69cbdc0a957e502", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v571_cr_discrete_corners.py" }, { "id": "v572_rp_bit_form", "filename": "v572_rp_bit_form.py", "path": "verification/v572_rp_bit_form.py", "cluster": "flavor", "synopsis": "DIAMOND.BIT.RPFORM.01: the RP form on the 81-twins — spectrally BLIND, integrally ANCHOR-VISIBLE: with the corpus reflection θ(X) = ΣXᵀΣ and the declared states (trace, anchor (1,1,2), ladder (1,2,4), unit), the RP kernel has identical inertia on both twins for every state and is never PSD (no kinematic v534-style positivity selection exists — honest negative, consistent with v567), but the INTEGRAL Smith towers of the anchor-state Gram separate them: (2,2,18,18,18,18,0) vs (2,2,2,18,18,18,0) — one slot, 18 vs 2, a factor 9 = N²fam: the compiler twin carries an extra 3² of divisibility, the ladder state separates identically, anonymous states are blind — the bit is visible to the RP form ONLY through anchor-coupled states; trace discriminant −6561 = −81² on both; q32 = 1 collapses to dim 5 (v568 reproduced); robust under the compiler V-flow (semigroup-deformed kernels keep identical inertia); the Gibbs pencil of the anchor Hamiltonian separates DYNAMICALLY: the compiler twin's kernel degenerates at a finite critical temperature s* = (8−4√19)/15 inside the Gibbs range (det factors with an extra quadratic; constant 81²), the alt twin's never does — a rank-drop marker, not a positivity selection; the critical mode is IDENTIFIED: seam-row supported (the A₂-Ext-carrier row), seam-line fixing, sheet-flow fixed point — the alignment-bit resonance deepens to a shared carrier; the half-sided (Levi/radikal) Restriktionen bleiben ebenfalls blind — the interacting RP construction is the one remaining route, typed open (11 checks, ~1 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv572_rp_bit_form.py", "sourceSha256": "bdac5a854e3e46c04a645c6dfe85d9324f0b9d37c9f3f70f0cc71779cc1281fd", "linkedClaimIds": [ "DIAMOND.BIT.RPFORM.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:1234c1fa7fdc0d6d5b35", "section:1bc03b42708092f8463b", "section:22fb298fcb28accfbf39", "section:2678ed3ba0ed508e2d8e", "section:3e4a71dc12f0870304d4", "section:51e91159532ef7479ff8", "section:6a93c4dd5fe420e1990e", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:ab9e7e520130ecc7da7c", "section:ac418863c3194ed2d0cf", "section:ad7223db244d878602d3", "section:c4cf080b9ae6f25f7a71", "section:d90bd5e1e6d8fa41397d", "section:fad05632a3d0b323783d" ], "activeSectionIds": [ "section:1234c1fa7fdc0d6d5b35", "section:1bc03b42708092f8463b", "section:22fb298fcb28accfbf39", "section:3e4a71dc12f0870304d4", "section:51e91159532ef7479ff8", "section:ab9e7e520130ecc7da7c", "section:ac418863c3194ed2d0cf", "section:ad7223db244d878602d3", "section:fad05632a3d0b323783d" ], "evidenceId": "python_verification:verification/v572_rp_bit_form.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v572_rp_bit_form.py", "pubMirrorHash": "bdac5a854e3e46c04a645c6dfe85d9324f0b9d37c9f3f70f0cc71779cc1281fd", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v572_rp_bit_form.py" }, { "id": "v574_stageb_winding", "filename": "v574_stageb_winding.py", "path": "verification/v574_stageb_winding.py", "cluster": "flavor", "synopsis": "QGEO.WINDING.SELF.01: Stage B of the No-Carrier-Reconstruction audit, first narrowing — the involution TYPE is killed by a rank theorem (any 2-dim-positive involution gives rank-1 V′, char poly x²(x−t) identically: the binary trace code {0,1,2} is unreachable), (E) bounds the winding normalisation (q11 = N must be an A3 exponent — N ≥ 4 empty), the ladder self-consistency selects exactly ONE member for every N ∈ {1,2,3} (28/16/14 → 1/1/1), and the saturation self-consistency sat = N⁴ holds ONLY at N = 3 (32 ≠ 1; 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die Sieben-Wort-Algebra hat Rang 7 und die Simultan-Konjugation g U* g⁻¹ = U_c, g V* g⁻¹ = V_c ist EXAKT gelöst; auf dem saturierten R-Fixgitter (SNF-Zertifikat (1,1,1)) sind die Restriktionen GANZZAHLIG, und die Z-Ordnung der sieben Wörter hat Smith-Elementarteiler (1,1,1,3,3,3,3) — SATURATIONSINDEX 81 = 3⁴, exakt der v566-Selfcode-Index; must-break-Kontrolle besteht; KANONIZITÄT OFFEN (Existenz-Claim); GATE.QGEO bewegt sich nicht (15 checks, ~4 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv600_joint_embedding.py", "sourceSha256": "75a88bf24eeba40b5e9fcb6fde56ef80622dc2a77befa6cc30868a5a4cb5c6fc", "linkedClaimIds": [ "QGEO.EMBED.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:1234c1fa7fdc0d6d5b35", "section:22fb298fcb28accfbf39", "section:25dcbc4eda230593c159", "section:2678ed3ba0ed508e2d8e", "section:38cc1bfba5161e50d0bb", "section:51e91159532ef7479ff8", "section:6a93c4dd5fe420e1990e", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:97886ff8881b257d4648", "section:ab9e7e520130ecc7da7c", "section:ac418863c3194ed2d0cf", "section:c4cf080b9ae6f25f7a71", "section:d90bd5e1e6d8fa41397d" ], "activeSectionIds": [ "section:1234c1fa7fdc0d6d5b35", "section:22fb298fcb28accfbf39", "section:25dcbc4eda230593c159", "section:38cc1bfba5161e50d0bb", "section:51e91159532ef7479ff8", "section:97886ff8881b257d4648", "section:ab9e7e520130ecc7da7c", "section:ac418863c3194ed2d0cf" ], "evidenceId": "python_verification:verification/v600_joint_embedding.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v600_joint_embedding.py", "pubMirrorHash": "75a88bf24eeba40b5e9fcb6fde56ef80622dc2a77befa6cc30868a5a4cb5c6fc", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v600_joint_embedding.py" }, { "id": "v601_equivariant_dual", "filename": "v601_equivariant_dual.py", "path": "verification/v601_equivariant_dual.py", "cluster": "core", "synopsis": "QGEO.CANON.01: die kanonische äquivariante Realisierung — die J-adaptierten Cusp-Projektoren GJₖ = (1−Tₖ)J⁻¹(1−Tₖ)†J sind idempotente Rang-1-Projektoren (char x²(x−1)), rotieren EXAKT unter D₄ (r GJₖ r⁻¹ = GJₖ₊₁; 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V₁^J = exakte Produktumkehr; (U₁,V₁^J) ~ Compiler-Paar, (U₁,V₁) ~ transponiertes Paar); das Wörterbuch schließt in der J-Projektor-Sprache (H = 1+V(V−1)/2 WÖRTLICH die Korpus-Anchor-Formel, char (x−1)²(x−2); Q₊ ~ 2−GJ₁+GJ₂GJ₃; Leiter ~ 2−GJ₁+2GJ₂GJ₃); WEIL-POSITIVITÄT exakt (JC positiv definit, {2√2−2, 2, 2+2√2} = |Spec J| — die Riemann-Bilinearrelationen auf dem ω-Blatt); kanonische Bilinearform B = M†J symmetrisch, det B = 8; ehrlich offen: gᵀg ≠ λB, naive Mark-lokale Abbildung scheitert, Seam-Normale kein Deck-Eigenvektor; Lean-Zertifikat FORM.QGEO.04 (CoverEmbedding.lean, det-freie Smith-Zertifikate, kernel decide) (17 checks, ~8 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv602_duality_forms.py", "sourceSha256": "bfce15fba2ac7fc45591539a2750d72deb236ce66eb6d92a09a8fecec50c7453", "linkedClaimIds": [ "QGEO.DUALFORMS.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:1234c1fa7fdc0d6d5b35", "section:22fb298fcb28accfbf39", "section:25dcbc4eda230593c159", "section:3d2a5b53f3345969fcbc", "section:6a93c4dd5fe420e1990e", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:ab9e7e520130ecc7da7c", "section:ac418863c3194ed2d0cf", "section:c4cf080b9ae6f25f7a71", "section:d90bd5e1e6d8fa41397d" ], "activeSectionIds": [ "section:1234c1fa7fdc0d6d5b35", "section:22fb298fcb28accfbf39", "section:25dcbc4eda230593c159", "section:3d2a5b53f3345969fcbc", "section:ab9e7e520130ecc7da7c", "section:ac418863c3194ed2d0cf" ], "evidenceId": "python_verification:verification/v602_duality_forms.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v602_duality_forms.py", "pubMirrorHash": "bfce15fba2ac7fc45591539a2750d72deb236ce66eb6d92a09a8fecec50c7453", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v602_duality_forms.py" }, { "id": "v603_seam_marks", "filename": "v603_seam_marks.py", "path": "verification/v603_seam_marks.py", "cluster": "core", "synopsis": "QGEO.SEAMMARKS.01: die Seam-und-Marks-Runde — DIE SEAM-LINIE IST REELL: das Linien-Stabilisator-Paar hat eine EINDEUTIGE gemeinsame Eigenlinie v (Uv = 0, Vv = v; explizit (0, (√3−i)/(√3+i), 1)); die reelle Struktur FIXIERT sie (die Seam ist eine reelle Linie des Covers), und S₀ KEHRT sie um — die v590-Seam-Umkehr-Forderung gilt GEOMETRISCH; die ∞-Cusp separiert in der unreduzierten Burau (invariante Spalte (1,1,1,1), Volltwist-Eigenwerte {1, ω×3}); DER ERSTE MARK-LOKALE Z/3-ZEUGE: E₁ restringiert ganzzahlig, liegt in der Wort-Algebra mit Nenner-lcm EXAKT 3 — eine Ordnung-3-Klasse im Kokern (der v566/v597-Mechanismus bekommt seinen ersten exakten Zeugen); ehrlich: E₄ trivial, E₂/E₃ außerhalb (äquivariante per-Mark-Lesart getypt); Übersetzer-Negative quantifiziert (F₂ = gᵀΣg kein Menü-Match, B⁻¹F₂ nicht in der Algebra) (15 checks, ~7 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv603_seam_marks.py", "sourceSha256": "6217d67d9640f37ba43fb8e6c58983713f9ab6d4a508b67b2d730d8d0b03ae00", "linkedClaimIds": [ "QGEO.SEAMMARKS.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:0b80dc1625937c6d13eb", "section:1234c1fa7fdc0d6d5b35", "section:38cc1bfba5161e50d0bb", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:ab9e7e520130ecc7da7c", "section:ac418863c3194ed2d0cf", "section:bec26de23262d380efe5", "section:c4cf080b9ae6f25f7a71" ], "activeSectionIds": [ "section:0b80dc1625937c6d13eb", "section:1234c1fa7fdc0d6d5b35", "section:38cc1bfba5161e50d0bb", "section:ab9e7e520130ecc7da7c", "section:ac418863c3194ed2d0cf", "section:bec26de23262d380efe5" ], "evidenceId": "python_verification:verification/v603_seam_marks.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v603_seam_marks.py", "pubMirrorHash": "6217d67d9640f37ba43fb8e6c58983713f9ab6d4a508b67b2d730d8d0b03ae00", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v603_seam_marks.py" }, { "id": "v604_equivariant_order", "filename": "v604_equivariant_order.py", "path": "verification/v604_equivariant_order.py", "cluster": "core", "synopsis": "QGEO.EQORDER.01: die äquivariante Ordnung und die ∞-Brücke — KORREKTUR: R IST eine Anti-Isometrie der Polarisierung (die richtige Gleichung M†JM = Jᵀ gilt EXAKT; die v599-Diary-Nebenbemerkung testete die falsche); J restringiert zu einer REELLEN SYMMETRISCHEN GANZZAHLIGEN Form J_fix = [[16,2,4],[2,−2,2],[4,2,−2]] mit det 72 = 8·9; die von ALLEN VIER Mark-Frames erzeugte Z-Ordnung hat VOLLEN Rang 18 in M₃(Z[ω]) mit Smith-Teilern (1¹⁵,3,3,3) — Saturationsindex 27 = 3³; DIE 3-TORSION LOKALISIERT BEI ∞: coker(1−T∞) = Z²⊕(Z/3)³ (Torsion 27), alle endlichen Cusp-Twists torsionsfrei — drei Objekte teilen (Z/3)³: ∞-Monodromie, äquivariante Ordnung, det(1−deck); Lesart: 81 = 3⁴ an den endlichen Marks, 27 = 3³ bei ∞; Übersetzer-Negative erweitert (J_fix-Menü + Algebra negativ; ω̄-Blatt benannt) (12 checks, ~4 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv604_equivariant_order.py", "sourceSha256": "92504b83697538d4713d3bf50201e73cd6048f1c45521245938e75f33fba3ced", "linkedClaimIds": [ "QGEO.EQORDER.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:1234c1fa7fdc0d6d5b35", "section:2cfba076381b50ca717c", "section:38cc1bfba5161e50d0bb", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:ab9e7e520130ecc7da7c", "section:ac418863c3194ed2d0cf", "section:c4cf080b9ae6f25f7a71" ], "activeSectionIds": [ "section:1234c1fa7fdc0d6d5b35", "section:2cfba076381b50ca717c", "section:38cc1bfba5161e50d0bb", "section:ab9e7e520130ecc7da7c", "section:ac418863c3194ed2d0cf" ], "evidenceId": "python_verification:verification/v604_equivariant_order.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v604_equivariant_order.py", "pubMirrorHash": "92504b83697538d4713d3bf50201e73cd6048f1c45521245938e75f33fba3ced", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v604_equivariant_order.py" }, { "id": "v605_translator", "filename": "v605_translator.py", "path": "verification/v605_translator.py", "cluster": "core", "synopsis": "QGEO.TRANSLATOR.01: die Übersetzer-Runde — DER RP-ÜBERSETZER EXISTIERT: die Korpus-RP-Anti-Automorphie θ(X) = ΣXᵀΣ, zurückgezogen und mit der J-Adjungierten komponiert, ist ein INNERER Automorphismus φ(A) = cAc⁻¹ (Intertwiner-Raum 1-dim, c invertierbar, exakt) — die RP-Struktur ist vollständig in Kurven-Sprache ausgedrückt (Polarisierung + ein explizites Element); 14c ist Z[ω]-INTEGRAL (Nenner 14 = 2·7); die SEAM ist reine 3-TORSION bei ∞ (freie Koordinaten (0,0), Torsion (2,2,0) mod 3 im ∞-Kokern); DIE 81 ÜBERLEBT das Frame-Joining (Ordnungskette O₁ ⊂ O_joint∩span₁ ⊂ P₁ mit Indizes 3⁵ und 3⁴ = 81); J_fix-Dualität zertifiziert (C_VᵀJ_fix = J_fix·C_Vdual ganzzahlig) + Lean-Nachtrag grün (11 checks, ~11 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv605_translator.py", "sourceSha256": "dbab863bf23797d0ed88c0f2347b77642d4482a5e36865286a4d45c60f4efc17", "linkedClaimIds": [ "QGEO.TRANSLATOR.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:0b80dc1625937c6d13eb", "section:1234c1fa7fdc0d6d5b35", "section:38cc1bfba5161e50d0bb", "section:3d2a5b53f3345969fcbc", "section:66dbe925f5d84de3e49b", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71" ], "activeSectionIds": [ "section:0b80dc1625937c6d13eb", "section:1234c1fa7fdc0d6d5b35", "section:38cc1bfba5161e50d0bb", "section:3d2a5b53f3345969fcbc", "section:66dbe925f5d84de3e49b", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v605_translator.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v605_translator.py", "pubMirrorHash": "dbab863bf23797d0ed88c0f2347b77642d4482a5e36865286a4d45c60f4efc17", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v605_translator.py" }, { "id": "v606_mode_separation", "filename": "v606_mode_separation.py", "path": "verification/v606_mode_separation.py", "cluster": "core", "synopsis": "QGEO.MODESEP.01: die Moden-Separations-Runde — DIE ∞-TORSION TRENNT DIE DREI V-EIGENLINIEN: alle drei Moden (0, 1, 2), auf das unreduzierte integrale Modul geliftet, sind REINE 3-Torsions-Klassen bei ∞ (null freier Anteil), und die drei Klassen sind PAARWEISE VERSCHIEDEN ((2,0,2)/(2,2,0)/(1,2,0) im fixierten Smith-Rahmen; Verschiedenheit rahmen-invariant, keine trivial) — der Selektions-Träger, den die reelle Struktur NICHT liefern konnte (nur die Seam ist R-fix); ehrlich: die kanonische Regel, welche Klasse das „+1“ der v590-Forderung bekommt, bleibt offen; EHRLICHES NEGATIV: der kubische Körper von c (char(7Γ(c)c) = y³+3y²+6y−1) hat Diskriminante −783 = −3³·29, kein Quadrat → Galois S₃, nicht abelsch → keine Kreisteilungs-Identität für c (Kronecker-Weber); die arithmetische Route ist geschlossen (7 checks, ~2 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv606_mode_separation.py", "sourceSha256": "2184b8e3e1f9964ea779733aa0837dfc63004282a1fc3940d386c63fb8af24b8", "linkedClaimIds": [ "QGEO.MODESEP.01" ], "sectionIds": [ "section:0b80dc1625937c6d13eb", "section:38cc1bfba5161e50d0bb", "section:848c49f799255f4cda92", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71" ], "activeSectionIds": [ "section:0b80dc1625937c6d13eb", "section:38cc1bfba5161e50d0bb", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v606_mode_separation.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v606_mode_separation.py", "pubMirrorHash": "2184b8e3e1f9964ea779733aa0837dfc63004282a1fc3940d386c63fb8af24b8", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v606_mode_separation.py" }, { "id": "v607_selection_rule", "filename": "v607_selection_rule.py", "path": "verification/v607_selection_rule.py", "cluster": "core", "synopsis": "QGEO.SELRULE.01: die Selektions-Regel-Runde — DIE KANONISCHE „+1“-REGEL IST GEFUNDEN: die Torsion des ∞-Kokerns ist ein echter F₃-Raum (ω wirkt als Identität), die Deck-Rotation wirkt F₃-linear mit der expliziten Matrix [[0,1,0],[1,0,2],[2,2,2]]; 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Sektor-Upgrade des v519-Schattens); das komprimierte Clock-Spektrum auf dem Fermion-Bereich ist EXAKT {1, √2−1} — multiplizitätsfrei, EINE Generation; MARK-INZIDENZ frei: beide Mark-Algebren PD (4,0,0) mit dim 4 = |μ₄|, Produkte erzeugen die volle 16-dim Basis, und τ₂ IST der Mark-A→Mark-B-Transport (α₂: {4,5}→{6,7}, hermitesch PD) — Kill-Test 7 feuert frei nicht; FIREWALL: nur die freie Scheibe, γ selbst bleibt auf A_hol offen (9 checks, ~1 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv608_gamma_free_slice.py", "sourceSha256": "041230e480442b1c75c0929e45f8fd5303daec3a745a2fb068ef79b06a4fcca2", "linkedClaimIds": [ "WOIT.GAMMA.FREE.01" ], "sectionIds": [ "section:17538bc5f76786fa0bbe", "section:2db6bd35ce5c578613f3", "section:38cc1bfba5161e50d0bb", "section:848c49f799255f4cda92", "section:ab9e7e520130ecc7da7c", "section:b191b0a66e5bacdc1a0e", "section:b4f8dafdea7dae9c5e81", "section:c4cf080b9ae6f25f7a71", "section:d139efd67906ac278dc5" ], "activeSectionIds": [ "section:17538bc5f76786fa0bbe", "section:38cc1bfba5161e50d0bb", "section:ab9e7e520130ecc7da7c", "section:b4f8dafdea7dae9c5e81", "section:d139efd67906ac278dc5" ], "evidenceId": "python_verification:verification/v608_gamma_free_slice.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v608_gamma_free_slice.py", "pubMirrorHash": "041230e480442b1c75c0929e45f8fd5303daec3a745a2fb068ef79b06a4fcca2", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v608_gamma_free_slice.py" }, { "id": "v609_translator_factorization", "filename": "v609_translator_factorization.py", "path": "verification/v609_translator_factorization.py", "cluster": "core", "synopsis": "QGEO.CFACTOR.01: die Übersetzer-Faktorisierung — DIE GEOMETRISCHE IDENTITÄT VON c IST GESCHLOSSEN: der Spiegel-Intertwiner d (dA = Γ(A)d für das realisierte Paar) ist EINDEUTIG (1-dim Lösungsraum), UNIMODULAR (det d = 1), INTEGRAL über Z[ω] und Γ-INVOLUTIV (Γ(d)d = 1 exakt); mit K₁ = J⁻¹·conj(F₂)ᵀ·M⁻¹ faktorisiert das v605-Übersetzer-Element EXAKT: c = λ·K₁·d — θ_corpus = Jadj ∘ inner(K₁) ∘ inner(d): Polarisierung × RP-Metrik × reelle Struktur × kanonischer Spiegel-Intertwiner; der letzte der drei v605-Reste ist aufgelöst (8 checks, ~8 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv609_translator_factorization.py", "sourceSha256": "a9e9828ae3e357cf1e06720a9e8147d1e09f3044491ca66f2b705b0218fd9753", "linkedClaimIds": [ "QGEO.CFACTOR.01" ], "sectionIds": [ "section:0b80dc1625937c6d13eb", "section:38cc1bfba5161e50d0bb", "section:848c49f799255f4cda92", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71" ], "activeSectionIds": [ "section:0b80dc1625937c6d13eb", "section:38cc1bfba5161e50d0bb", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v609_translator_factorization.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v609_translator_factorization.py", "pubMirrorHash": "a9e9828ae3e357cf1e06720a9e8147d1e09f3044491ca66f2b705b0218fd9753", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v609_translator_factorization.py" }, { "id": "v610_curve_landscape", "filename": "v610_curve_landscape.py", "path": "verification/v610_curve_landscape.py", "cluster": "core", "synopsis": "QGEO.LANDSCAPE.01: die Kurven-Landschafts-Runde — WAS DIE KURVE SONST NOCH TRÄGT: die Jacobische ZERFÄLLT (Differential-Charaktere der Ordnungen (12,12,6)) in eine abelsche Fläche mit CM durch Q(ζ₁₂) = Q(i,√3) — den Körper von Deck UND Marks zusammen — und die elliptische Kurve E: y³ = u²−1 mit CM durch Q(ω); PUNKTZÄHLUNGS-BESTÄTIGUNG: a_p(C) = a_p(E) EXAKT für alle 10 getesteten p ≢ 1 mod 12 (die ζ₁₂-Fläche dort supersingulär), Flächen-Spuren nur bei p ≡ 1 mod 12; a_p = 0 für p ≡ 2 mod 3; GANZZAHL-SPEKTREN-CENSUS mit ehrlicher Relativierung: Einzelspektren sind BILLIG (7894 Einträge), die ANCHOR-KLASSE ist die häufigste nichttriviale Familie (286 = Maximum), Nicht-Compiler-Spektren existieren ({1,1,3}: 254) — die Compiler-Auszeichnung ist die GELENK-Struktur (v600), nicht Einzel-Chars; zwei neue kanonische Objekte benannt (Perioden = Beta-Werte) (9 checks, ~1 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv610_curve_landscape.py", "sourceSha256": "95efa38ca807cc95239339e66a6173f14f8c31993c653a9c36528a1e8c2ee54e", "linkedClaimIds": [ "QGEO.LANDSCAPE.01" ], "sectionIds": [ "section:38cc1bfba5161e50d0bb", "section:757aa7c70d8acd2d7063", "section:848c49f799255f4cda92", "section:ab9e7e520130ecc7da7c", "section:afc592079e9bb0b61bda", "section:c4cf080b9ae6f25f7a71" ], "activeSectionIds": [ "section:38cc1bfba5161e50d0bb", "section:757aa7c70d8acd2d7063", "section:ab9e7e520130ecc7da7c", "section:afc592079e9bb0b61bda" ], "evidenceId": "python_verification:verification/v610_curve_landscape.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v610_curve_landscape.py", "pubMirrorHash": "95efa38ca807cc95239339e66a6173f14f8c31993c653a9c36528a1e8c2ee54e", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v610_curve_landscape.py" }, { "id": "v611_periods", "filename": "v611_periods.py", "path": "verification/v611_periods.py", "cluster": "core", "synopsis": "QGEO.PERIODS.01: die Perioden-Runde — DIE ANALYTISCHE SCHICHT DES COVERS IST KLASSISCH: die fünf Basis-Perioden-Integrale sind EXAKT Beta-Werte ((1/4)B((k+1)/4, 1−j/3), symbolisch), und die Gamma-Nenner (Γ(11/12), Γ(7/12), Γ(5/12), Γ(1/12)) liegen ALLE auf dem ζ₁₂-RASTER — die 12 = |μ₄|·|μ₃|-Struktur auch analytisch; die μ₄-Rotation wirkt auf Perioden EXAKT mit den v610-Charakteren (i^(k+1), 40-stellige Zertifikate); Ω_E = B(1/3,1/6)/2 = Γ(1/6)Γ(1/3)/(2√π) exakt (die klassische ω-CM-Periode); Kreuz-Faktor-UNABHÄNGIGKEIT: I_{1,2}/I_{0,2} hat KEINE ganzzahlige Relation vom Grad ≤ 4 (PSLQ) — die zwei CM-Faktoren sind perioden-unabhängig, wie der v610-Zerfall verlangt; das Perioden-Wörterbuch als Hodge/RP-Ressource benannt (6 checks, ~1 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv611_periods.py", "sourceSha256": "ab726ab0b39fc2ee4523cc4485f788cf1a690cc9f2187f52e05a77be26eca026", "linkedClaimIds": [ "QGEO.PERIODS.01" ], "sectionIds": [ "section:38cc1bfba5161e50d0bb", "section:757aa7c70d8acd2d7063", "section:848c49f799255f4cda92", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71" ], "activeSectionIds": [ "section:38cc1bfba5161e50d0bb", "section:757aa7c70d8acd2d7063", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v611_periods.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v611_periods.py", "pubMirrorHash": "ab726ab0b39fc2ee4523cc4485f788cf1a690cc9f2187f52e05a77be26eca026", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v611_periods.py" }, { "id": "v612_polarization_frame", "filename": "v612_polarization_frame.py", "path": "verification/v612_polarization_frame.py", "cluster": "core", "synopsis": "QGEO.POLFRAME.01: die Polarisierungs-Rahmen-Runde — J DIAGONALISIERT EXAKT IN DER ROTATIONS-EIGENBASIS: die Braid-Rotation r hat drei EINFACHE Eigenwerte ζ₁₂·{1,−1,−i} (det r = −1); in der Links-Eigenbasis wird J exakt diagonal, diag((1+√3)/2, (1−√3)/2, −1) (ehrlich: Diagonalität = Standard-Folge der J-Unitarität; der GEHALT sind Werte und Signatur-Verteilung); **DIE HODGE-RICHTUNG IST DER ζ₁₂-EIGENRAUM**: die eindeutige positive Richtung von J (Signatur (1,2)) ist exakt der Eigenraum der PRIMITIVEN 12. Einheitswurzel e^{iπ/6} — analytische Hodge-Struktur und endliche Rotation stimmen überein, wo Positivität wohnt; Produkt der Diagonalwerte = det J/|det W|² = 1/2 exakt; benannter nächster Schritt: die kanonische Perioden-Normierung (Beta-Gewichte) (9 checks, ~2 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv612_polarization_frame.py", "sourceSha256": "bce150221f473b52cde2f78fdd549d8d51e024a03fcfd6e56b4e723a91e2db0f", "linkedClaimIds": [ "QGEO.POLFRAME.01" ], "sectionIds": [ "section:1b7258ac6e85e7a30697", "section:38cc1bfba5161e50d0bb", "section:447deb795673a2406b44", "section:848c49f799255f4cda92", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71" ], "activeSectionIds": [ "section:1b7258ac6e85e7a30697", "section:38cc1bfba5161e50d0bb", "section:447deb795673a2406b44", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v612_polarization_frame.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v612_polarization_frame.py", "pubMirrorHash": "bce150221f473b52cde2f78fdd549d8d51e024a03fcfd6e56b4e723a91e2db0f", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v612_polarization_frame.py" }, { "id": "v613_canonical_periods", "filename": "v613_canonical_periods.py", "path": "verification/v613_canonical_periods.py", "cluster": "core", "synopsis": "QGEO.PERNORM.01: die kanonische Perioden-Normierung — DIE ANALYTISCHE BRÜCKE SCHLIESST: die Viertel-Rotation x→ix wirkt DECK-FREI auf den vier Verzweigungs-Segmenten (alle 12 Wrap-Faktoren exakt 1; Homologie-Relation seg₁+seg₂+seg₃+seg₄ = 0; Must-fail-Kontrolle: rohe Periodenzeilen sind KEINE r-Eigenvektoren); **DAS EXAKTE WÖRTERBUCH r = Deck ∘ Rotation**: char(r) = char(ω·M) exakt — die reduzierte Burau-Rotation bei t = ω ist GL₃-konjugiert zur geometrischen Rotation mal GENAU EINEM Deck-Schritt (erklärt v597s r⁴ = ω strukturell; Deck-Potenz eindeutig unter den vier Skalar-Twists); die Periodenzeilen (hol dx/y², hol x·dx/y², ANTIHOL conj(dx/y)) realisieren den Rotations-Eigenrahmen mit Charakteren (i,−1,−i) und transportiert spec(r); DIE HODGE-GEWICHTE SIND Γ-MONOME: h₀, h₁ = (3√3/16π)Γ(1/3)²Γ(1/6)², h₂ via komplexer Beta-Formel (≤1e−25 verifiziert), Signatur (2,1); **DIE VORZEICHEN-BRÜCKE J = −h PRO CHARAKTER**: Js einzige positive Linie (ζ₁₂) = hs einzige negative Linie (antiholomorph) — Riemann–Hodge-Positivität durch die Kompiler-Polarisierung realisiert (19 checks, ~6 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv613_canonical_periods.py", "sourceSha256": "817740e227e11f119131dca31c85a2812608377ab8e7730533004db49be5b9be", "linkedClaimIds": [ "QGEO.PERNORM.01" ], "sectionIds": [ "section:1b7258ac6e85e7a30697", "section:38cc1bfba5161e50d0bb", "section:4ddc9b76dd9cd0f415e9", "section:848c49f799255f4cda92", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71" ], "activeSectionIds": [ "section:1b7258ac6e85e7a30697", "section:38cc1bfba5161e50d0bb", "section:4ddc9b76dd9cd0f415e9", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v613_canonical_periods.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v613_canonical_periods.py", "pubMirrorHash": "817740e227e11f119131dca31c85a2812608377ab8e7730533004db49be5b9be", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v613_canonical_periods.py" }, { "id": "v614_transport_deck", "filename": "v614_transport_deck.py", "path": "verification/v614_transport_deck.py", "cluster": "core", "synopsis": "QGEO.TRANSPORT.01: die Gauss-Manin-Transport-Runde — **DER DECK-SCHRITT IST DIE RAND-MONODROMIE**: der Transport der Segment-Zyklen entlang der starren Viertel-Rotations-Schleife der vier Verzweigungspunkte lässt die Diskriminante λ(τ) = e^{2πiτ} EINMAL um 0 winden, und die transportierten Perioden faktorisieren EXAKT (I_m(τ) = e^{iπτ(m+1)/2}·e^{−2πiτj/3}·I_m(0)); bei τ = 1 ist der Deck-Faktor ω = t⁴ auf JEDEM Blatt (uniform über alle drei Zeilen; must-fail: t³ ≠ ω, t⁵ ≠ ω — der Exponent 4 = |μ₄| ist durch die Punktezahl erzwungen); **die kanonische Transport-Matrix in der Segment-Basis ist EXAKT ω·M — das v613-Wörterbuch r ~ ω·M ist KANONISCH** (kein Konjugator-Spielraum), (ωM)⁴ = ω·1 leitet v597s r⁴ = ω her; 25-stellige Zertifikate (dps 80, max 5e−28; τ=1 auf 2.7e−81); v613s Rest F1 auf Transport-Ebene geschlossen (12 checks, ~7 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv614_transport_deck.py", "sourceSha256": "fddee120717e4f827639b61ccd7c69882af20384cf4ef37558ed123569dcfe9d", "linkedClaimIds": [ "QGEO.TRANSPORT.01" ], "sectionIds": [ "section:38cc1bfba5161e50d0bb", "section:3d2a5b53f3345969fcbc", "section:4ddc9b76dd9cd0f415e9", "section:848c49f799255f4cda92", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71" ], "activeSectionIds": [ "section:38cc1bfba5161e50d0bb", "section:3d2a5b53f3345969fcbc", "section:4ddc9b76dd9cd0f415e9", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v614_transport_deck.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v614_transport_deck.py", "pubMirrorHash": "fddee120717e4f827639b61ccd7c69882af20384cf4ef37558ed123569dcfe9d", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v614_transport_deck.py" }, { "id": "v615_gamma_toy_interacting", "filename": "v615_gamma_toy_interacting.py", "path": "verification/v615_gamma_toy_interacting.py", "cluster": "core", "synopsis": "WOIT.GAMMA.TOY.01: die wechselwirkende γ-Scheibe auf Toy-Ebene — die γ-Batterie AUF der RP-überlebenden Wechselwirkungsklasse (das Alignment-Bit: δ = π/2, positive Kopplung, v534) des 16-Majorana-FK-Seam-Toys: **DER WECHSELWIRKENDE SPIEGEL-FLIP** — beim erzwungenen Twist η = +i sind die chiralen Grams PD (37,0,0) auf allen vier Cuts (g ∈ {1/32..8}, v534-Regression), und der SPIEGEL-Zustand spaltet sektor-exakt auf JEDEM Cut und JEDEM g: gerade (29,0,0) PD, ungerade (0,8,0) STRIKT NEGATIV DEFINIT (max. Eigenwert ≤ −1.5e−3, vom Nullpunkt weg beschränkt) — **Kill-Test (3) kann auf der überlebenden Klasse nicht feuern** (v608-Upgrade von g = 0 aufs volle Gitter); der Mark-Transport existiert wechselwirkend (α₄: Mark-A → Mark-B exakt 16/16; Gram und Transport-Form hermitesch PD bei jedem g — Kill-Test (7) feuert nicht); das ungerade Transfer-Spektrum ist bei jedem g SIMPEL (8 positive Eigenwerte, min. Abstand 2.3e−5; ehrlich: Beinahe-Verdopplung bei g = 8 ohne Schließen); Kontroll-Mitglied m = 2 indefinit — Bit-Selektion und Chiralität KO-LOKALISIEREN; Kill-Tests (3)/(6)/(7) bleiben formal auf A_hol (11 checks, ~2 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv615_gamma_toy_interacting.py", "sourceSha256": "aece2443349b6d5a35bc02b95b302b6a2a2cde94b01cf8c2ac5abef8630a9c4d", "linkedClaimIds": [ "WOIT.GAMMA.TOY.01" ], "sectionIds": [ "section:17538bc5f76786fa0bbe", "section:2db6bd35ce5c578613f3", "section:38cc1bfba5161e50d0bb", "section:848c49f799255f4cda92", "section:ab9e7e520130ecc7da7c", "section:b191b0a66e5bacdc1a0e", "section:b4f8dafdea7dae9c5e81", "section:c4cf080b9ae6f25f7a71" ], "activeSectionIds": [ "section:17538bc5f76786fa0bbe", "section:38cc1bfba5161e50d0bb", "section:ab9e7e520130ecc7da7c", "section:b4f8dafdea7dae9c5e81" ], "evidenceId": "python_verification:verification/v615_gamma_toy_interacting.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v615_gamma_toy_interacting.py", "pubMirrorHash": "aece2443349b6d5a35bc02b95b302b6a2a2cde94b01cf8c2ac5abef8630a9c4d", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v615_gamma_toy_interacting.py" }, { "id": "v616_su2_internal_kinematic", "filename": "v616_su2_internal_kinematic.py", "path": "verification/v616_su2_internal_kinematic.py", "cluster": "core", "synopsis": "WOIT.SU2.KIN.01: das interne SU(2), kinematische Separation auf Twistor-Ebene — die erste ausgeführte Scheibe des letzten unberührten γ-Kill-Tests (6): auf ℂ⁴ = ℍ² ist **Woits euklidische Struktur wörtlich die interne j-Richtung** (ρ_tw = right-j, v519/v565-Konventionen); das interne su(2) (right-Sp(1)) erhält JEDE Twistor-Faser (trivial auf der Raumzeit S⁴), kommutiert EXAKT mit der gesamten Raumzeit-Quaternionen-Wirkung, Schnitt = {0}: **SEPARATION — der kinematische Zweig von Kill-Test (6) feuert nicht**; **DIE CLOCK FAKTORISIERT: RHO4 = left-u ∘ right-u (u = e^{iπ/4}) EXAKT** — Raumzeit-Halbviertel mal interner Halbviertel-Phase; der ALE-Deck ist rein raumzeit-seitig (DECK4 = left-i), RHO4² = DECK4 ∘ right-i; die komplexe Wahl BRICHT das interne SU(2) auf U(1), und der v519-Mark-Torsor IST die μ₄-Untergruppe des internen U(1) (∘ σ_std); σ_std fixiert die euklidische Struktur und invertiert die interne Ladung; dynamische Hälfte bleibt offen auf A_hol [C] (17 checks, <1 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv616_su2_internal_kinematic.py", "sourceSha256": "1cbbd069535e68c13c50883822014a090dcf0555cc4c365153c7b891d5f36c2f", "linkedClaimIds": [ "WOIT.SU2.KIN.01" ], "sectionIds": [ "section:17538bc5f76786fa0bbe", "section:2db6bd35ce5c578613f3", "section:38cc1bfba5161e50d0bb", "section:848c49f799255f4cda92", "section:ab9e7e520130ecc7da7c", "section:b191b0a66e5bacdc1a0e", "section:c4cf080b9ae6f25f7a71", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:17538bc5f76786fa0bbe", "section:38cc1bfba5161e50d0bb", "section:ab9e7e520130ecc7da7c", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v616_su2_internal_kinematic.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v616_su2_internal_kinematic.py", "pubMirrorHash": "1cbbd069535e68c13c50883822014a090dcf0555cc4c365153c7b891d5f36c2f", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v616_su2_internal_kinematic.py" }, { "id": "v617_seam_cover_forcing", "filename": "v617_seam_cover_forcing.py", "path": "verification/v617_seam_cover_forcing.py", "cluster": "core", "synopsis": "QGEO.SEAMFORCE.01: die Seam-Forcing-Runde — **DIE KONFORMEN SEAM-AXIOME ERZWINGEN DEN μ₃-COVER** (konstruktive Scheibe der Bedrock-Prämisse QGEO.SYM.01): ℤ₄-MÖBIUS-RIGIDITÄT — jede zyklisch ℤ₄-symmetrische 4-Punkt-Konfiguration auf ℙ¹ ist Möbius-äquivalent zu μ₄ (Multiplier ±i erzwungen; Cross-Ratio-Zensus = harmonischer Orbit {2, ½, −1}; must-fail: 4/3 nicht im Orbit); GEWICHTS-ZENSUS — unter allen 81 μ₃-Monodromie-Vektoren sind genau 4 clock-äquivariant, die Mark-Äquivalenz killt das alternierende Paar: **Gewichte UNIFORM erzwungen, j ∈ {1,2} = das konjugierte Blatt-Paar (v613)**; j = 1 gibt EXAKT y³ = x⁴−1, volle ∞-Verzweigung (v603), Riemann–Hurwitz Genus 3 exakt; die Seam-Geometrie passt: Bond-Reflexion z ↦ −iz̄ = das (k,5−k)-Muster von v599s R, Schnittpunkte = die zwei v519-Cut-Punkte; Bedrock-Rest verengt auf (i) die Zyklisch-3-Wahl und (ii) die physisch↔konform-Identifikation [C] (14 checks, <1 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv617_seam_cover_forcing.py", "sourceSha256": "2b19376a7f63e2e2db094760dfa514613695ba15e25965bd0d4b3d02919252e4", "linkedClaimIds": [ "QGEO.SEAMFORCE.01" ], "sectionIds": [ "section:38cc1bfba5161e50d0bb", "section:3d2a5b53f3345969fcbc", "section:848c49f799255f4cda92", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:f1286299e54bfa3f1866" ], "activeSectionIds": [ "section:38cc1bfba5161e50d0bb", "section:3d2a5b53f3345969fcbc", "section:ab9e7e520130ecc7da7c", "section:f1286299e54bfa3f1866" ], "evidenceId": "python_verification:verification/v617_seam_cover_forcing.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v617_seam_cover_forcing.py", "pubMirrorHash": "2b19376a7f63e2e2db094760dfa514613695ba15e25965bd0d4b3d02919252e4", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v617_seam_cover_forcing.py" }, { "id": "v620_cyclic_n_census", "filename": "v620_cyclic_n_census.py", "path": "verification/v620_cyclic_n_census.py", "cluster": "core", "synopsis": "QGEO.NCENSUS.01: der zyklisch-N-Zensus — **DER SEAM LÄSST N ∈ {3,5} ALS PRIMITIVE LORENTZ-ORDNUNGEN ZU, UND DIE COMPILER-KONSTANTEN PINNEN N = 3** (der erste v617-Bedrock-Rest, konditional gemacht): volle ∞-Verzweigung ⟺ gcd(N,4) = 1 ⟺ N ∈ {3,5}; Genus-Tabelle 1,3,3,6,7 (N = 2..6, Riemann–Hurwitz exakt); primitive Blatt-Dimension 3 genau für N ∈ {3,5,6}; **Chevalley–Weil: N = 3 hat BEIDE primitiven Blätter Lorentz ((1,2)/(2,1) — die v599/v613-Signatur), N = 5 ein Lorentz-Paar, N = 6 KEIN primitives Lorentz-Blatt (sein Lorentz-Gehalt = die Ordnung-3-Charaktere: N = 6 REDUZIERT auf N = 3)**; das Pinning: det_ℤ(1−deck) = Φ_N(1)³ = N³ — 27 für N = 3 (EXAKT die maschinell geprüfte v597-Konstante) vs. 125 für N = 5; Saturation 81 = 3⁴ vs. 625 = 5⁴: **N = 3 eindeutig**; der Rest wandert eine Ebene tiefer: warum der Compiler 3-adisch ist = N_fam = 3 (E8-Glue-verankert) (9 checks, <1 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv620_cyclic_n_census.py", "sourceSha256": "8b111c83ff78504b51932689656b708fa69c012ca43bbf5538c6f76a49d5cdd8", "linkedClaimIds": [ "QGEO.NCENSUS.01" ], "sectionIds": [ "section:38cc1bfba5161e50d0bb", "section:848c49f799255f4cda92", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:f1286299e54bfa3f1866" ], "activeSectionIds": [ "section:38cc1bfba5161e50d0bb", "section:ab9e7e520130ecc7da7c", "section:f1286299e54bfa3f1866" ], "evidenceId": "python_verification:verification/v620_cyclic_n_census.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v620_cyclic_n_census.py", "pubMirrorHash": "8b111c83ff78504b51932689656b708fa69c012ca43bbf5538c6f76a49d5cdd8", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v620_cyclic_n_census.py" }, { "id": "v621_interacting_semigroup", "filename": "v621_interacting_semigroup.py", "path": "verification/v621_interacting_semigroup.py", "cluster": "core", "synopsis": "WOIT.GAMMA.SEMI.01: die wechselwirkende Klein–Landau-Halbgruppe — **DIE CLOCK ÜBERLEBT DIE WECHSELWIRKUNG ALS POSITIVER TRANSFER, GENAU AUF DEN μ₄-KOMMENSURABLEN SCHRITTEN**: bei g = 0 reproduziert sich das v524-Muster bei N = 16 exakt (7 Schritte hermitesch, Dimensionen 29,22,16,11,7,4,2; gerade Schritte PD; ungerade k = 1,3,5 indefinit mit EXAKT NULL Einteilchen-Diagonale; k = 7 paritäts-trivial); **bei g > 0 überlebt exakte Hermitizität GENAU auf {4, 6, 7}** und geht auf {1,2,3,5} verloren (dev > 0.1) — die Halbgruppe KONTRAHIERT aufs μ₄-Fenster; **die Clock (k = 4) bleibt hermitesch PD (11,0,0) über das ganze Gitter g ∈ {1/32..8}**; Mechanismus exakt: die Survivor-Wechselwirkung ist α₄-invariant EXAKT und nicht α₁/α₂-invariant (Quartett-Stabilisator {0,4,8,12}); k = 5 zeigt: Quartett-Einbettung allein schützt nicht (gerade Parität UND Alignment nötig); Lesart: die rekonstruierte Rotationsgruppe des wechselwirkenden Toys ist der CLOCK-TURM, nicht der volle Kreis (6 checks, ~2 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv621_interacting_semigroup.py", "sourceSha256": "d77126e6c21265f5ec08cc83e8297d71c35c1c1f8c9abffb9f6cd717dff25b3e", "linkedClaimIds": [ "WOIT.GAMMA.SEMI.01" ], "sectionIds": [ "section:3d2a5b53f3345969fcbc", "section:848c49f799255f4cda92", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:3d2a5b53f3345969fcbc", "section:ab9e7e520130ecc7da7c", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v621_interacting_semigroup.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v621_interacting_semigroup.py", "pubMirrorHash": "d77126e6c21265f5ec08cc83e8297d71c35c1c1f8c9abffb9f6cd717dff25b3e", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v621_interacting_semigroup.py" }, { "id": "v622_seam_identification", "filename": "v622_seam_identification.py", "path": "verification/v622_seam_identification.py", "cluster": "core", "synopsis": "QGEO.SEAMID.01: die Seam-Identifikations-Runde — **DER PHYSISCHE SEAM IST DER KONFORME SEAM** (der zweite v617-Bedrock-Rest, auf Kernel+Wörterbuch-Ebene geschlossen): **DIE KERNEL-IDENTITÄT — der v519-Seam-Kernel c(d) = (2/N)/sin(πd/N) (ungerade d, Null für gerade) ist EXAKT die antiperiodische (NS) chirale Moden-Summe auf dem 16-Punkte-Kreis, für ALLE d = 1..15 inklusive der geraden Nullen: das Flat-Band IST das NS-Spektrum** (geschlossene Form Σ sin((2j+1)x) = sin²(8x)/sin(x) exakt); must-fail: die Ramond-Summe reproduziert den Kernel NICHT (NS erzwungen); die Site-Karte θ_a = (2a+1)π/16 legt die vier Mark-Bond-Mittelpunkte EXAKT auf μ₄ (kein Site trifft eine Mark — v519s Präzision (ii) wörtlich); Gruppen-Wörterbuch exakt (α₁ = Rotation, Clock = z→iz, refl_map(k) = Spiegelung an Achse (k+1)π/16, Cuts ↦ {π/4, π/2, 3π/4, π}); **DAS STRADDLE-GESETZ IST GEOMETRIE: durch-Mark-Achsen = exakt die v534-straddled Cuts {7,15}**; v617s Bond-Reflexion = Cut k = 11 mit dem v599-(k,5−k)-Muster; Kontinuums-Rest benannt: die Covering-Ebene (10 checks, ~1 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv622_seam_identification.py", "sourceSha256": "6617eb3519321ec344d1d9bdf2c359c3c8f8a8c4e92d400a93c48de83430b5de", "linkedClaimIds": [ "QGEO.SEAMID.01" ], "sectionIds": [ "section:003e725a1fda16978fec", "section:3d2a5b53f3345969fcbc", "section:83d94e33024ba3df4db8", "section:848c49f799255f4cda92", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:f1286299e54bfa3f1866" ], "activeSectionIds": [ "section:003e725a1fda16978fec", "section:3d2a5b53f3345969fcbc", "section:83d94e33024ba3df4db8", "section:ab9e7e520130ecc7da7c", "section:f1286299e54bfa3f1866" ], "evidenceId": "python_verification:verification/v622_seam_identification.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v622_seam_identification.py", "pubMirrorHash": "6617eb3519321ec344d1d9bdf2c359c3c8f8a8c4e92d400a93c48de83430b5de", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v622_seam_identification.py" }, { "id": "v623_covered_seam", "filename": "v623_covered_seam.py", "path": "verification/v623_covered_seam.py", "cluster": "core", "synopsis": "QGEO.COVERSEAM.01: die Covered-Seam-Runde — **DAS GITTER-SKELETT DER COVERING-EBENE** (der benannte v622-Rest, erste ausgeführte Scheibe): der auf den μ₃-Cover gehobene Seam ist **EIN 48-Site-NS-Kreis** für die uniformen Gewichte (j = 1, 2) und ZERFÄLLT in 3 Kreise für triviale UND alternierende Gewichte — **ein neuer, unabhängiger Kill des alternierenden Paars (Seam-Konnektivität)**; der explizite Walk schließt nach exakt 48 Schritten (3 Basis-Umläufe, 12 Mark-Kreuzungen); **DIE GEHOBENE CLOCK: L⁴ = Deck und L¹² = id auf ALLEN 48 Punkten mit echter Ordnung 12 — v597s r⁴ = ω und v614s Rand-Monodromie sind GITTER-KOMBINATORIK**; die v622-Kernel-Identität generalisiert wörtlich auf N = 48; **DAS 12-RASTER: die NS-Moden spalten unter dem Deck in drei 16er-Klassen mit Offsets {1/6, 1/2, 5/6}, die 1/2-Klasse = die BASIS-NS-Frequenzen EXAKT** (der ungetwistete Sektor IST der Basis-Seam); der fermionische Deck-Lift erfüllt Deck³ = −1 (Spin-Doppel, (−1)^F-Resonanz), Bilinear-Eigenwert = ω exakt (dort leben die t = ω/ω̄-Blätter); die 12 Mark-Kreuzungen bilden einen einzigen 12-Zyklus unter der Clock; Rest benannt: die wechselwirkende Orbifold-Aussage (9 checks, ~4 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv623_covered_seam.py", "sourceSha256": "956fbf688f39294cf76112691eb1138f2d62b81fdb6f55e67c443cf715588e40", "linkedClaimIds": [ "QGEO.COVERSEAM.01" ], "sectionIds": [ "section:003e725a1fda16978fec", "section:3d2a5b53f3345969fcbc", "section:848c49f799255f4cda92", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:dcbb8ba68bde5b18c375" ], "activeSectionIds": [ "section:003e725a1fda16978fec", "section:3d2a5b53f3345969fcbc", "section:ab9e7e520130ecc7da7c", "section:dcbb8ba68bde5b18c375" ], "evidenceId": "python_verification:verification/v623_covered_seam.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v623_covered_seam.py", "pubMirrorHash": "956fbf688f39294cf76112691eb1138f2d62b81fdb6f55e67c443cf715588e40", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v623_covered_seam.py" }, { "id": "v624_external_lattice_audit", "filename": "v624_external_lattice_audit.py", "path": "verification/v624_external_lattice_audit.py", "cluster": "core", "synopsis": "EXTREV.LATTICE.01: das externe-Review-Gitter-Audit — drei behauptete Ableitungen maschinell geprüft, ein Folgetest ehrlich umgetypt: **(A) DER VIERMARKEN-ABSCHLUSS [E, konditional]: unter der D_{d+1}+A_{d−1}-Glue-Architektur erzwingen DREI unabhängige Selektoren d = 4** (Disc-Gruppen-Zensus mit Negativ-Kontrollen d = 3,5,8; die Norm-Gleichung (d+1)/4+(d−1)/d = 2 mit eindeutiger Lösung; der Pythagoras-Selektor (d−1)²+d² = (d+1)² — das (3,4,5)-Tripel aus Zyklen, Marken, Träger); mit (1,1,2) als einziger 3-Teil-Partition von 4 und c₃ = 1/(8π): **die Zwei-Eingaben-Darstellung reduziert auf EINEN Grenzgrad d = 4 plus π** (ehrlich: konditional auf die Architektur); (B) DER ANCHOR-BYTECODE [E]: χ = (t−1)²(t−2), Rekursion p_{n+2} = 3p_{n+1}−2p_n, Newton, 240+8 = 248; **(C) DIE LORENTZ-KONGRUENZ [E]: PᵀJ_det P = J_fix EXAKT (det P = −6)** — Primzahl-Determinantenform und Cover-Polarisierungsgitter sind DIESELBE rationale quadratische Form (Index 6; 36 = 6²; 6 = p₂(a)); der Review-Folgetest zu B = M†J ist SCHLECHT GESTELLT (B komplex-symmetrisch, det 8 — must-fail ehrlich); Suzuki arXiv 2606.09096 + 2607.24830 web-verifiziert für den PRIME.WEIL.OPERATOR-Vertrag (14 checks, <1 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv624_external_lattice_audit.py", "sourceSha256": "71d0e6fbabad7f3d2187d708638371a2df5722f5a9d5eb80d851e205e577cc9b", "linkedClaimIds": [ "EXTREV.LATTICE.01" ], "sectionIds": [ "section:3d2a5b53f3345969fcbc", "section:81a6dc002dc46cf7b6c5", "section:848c49f799255f4cda92", "section:93b8868beb643874af75", "section:ab9e7e520130ecc7da7c", "section:aeb16d254373e2e88a13", "section:c4cf080b9ae6f25f7a71", "section:c86ec693b903bfd2aa01", "section:c9d9fdab1f8620914792", "section:daecafc150c9651ad391", "section:eb00caf29086b02d5bf5", "section:f5274c8105ff62e99dcd" ], "activeSectionIds": [ "section:3d2a5b53f3345969fcbc", "section:81a6dc002dc46cf7b6c5", "section:ab9e7e520130ecc7da7c", "section:aeb16d254373e2e88a13", "section:c86ec693b903bfd2aa01", "section:f5274c8105ff62e99dcd" ], "evidenceId": "python_verification:verification/v624_external_lattice_audit.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v624_external_lattice_audit.py", "pubMirrorHash": "71d0e6fbabad7f3d2187d708638371a2df5722f5a9d5eb80d851e205e577cc9b", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v624_external_lattice_audit.py" }, { "id": "v626_e8_code", "filename": "v626_e8_code.py", "path": "verification/v626_e8_code.py", "cluster": "core", "synopsis": "E8.CODE.01: die E8-Code-Runde — **E8 IST EIN FEHLERKORRIGIERENDER CODE** (Theorem, nicht Metapher). [E] Der erweiterte Hamming-Code [8,4,4]: 16 Codewörter, Gewichte {0:1, 4:14, 8:1}, selbst-dual; Construction A liefert ein gerades unimodulares Rang-8-Gitter = E8 (Eindeutigkeit); Schalen 240/2160 = v625-Theta; Einzelbit-Fehler exhaustiv korrigierbar (16×8 Fälle, eindeutige nächste Codewörter). [C] Compiler-Bezüge getypt: 8 = Rang, 4 = d = |μ₄|, 16 = Halbspinor, 14 = 2×7 (Parabolik-Dimension) (7 checks, ~2 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv626_e8_code.py", "sourceSha256": "dc0571adef1702ecf0c2ec8f4578ca6e291678d1cf5f504434290c3ac933dd97", "linkedClaimIds": [ "E8.CODE.01" ], "sectionIds": [ "section:3d2a5b53f3345969fcbc", "section:848c49f799255f4cda92", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:df8999b098e725de7d02", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:3d2a5b53f3345969fcbc", "section:ab9e7e520130ecc7da7c", "section:df8999b098e725de7d02", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v626_e8_code.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v626_e8_code.py", "pubMirrorHash": "dc0571adef1702ecf0c2ec8f4578ca6e291678d1cf5f504434290c3ac933dd97", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v626_e8_code.py" }, { "id": "v628_orbifold_casimir", "filename": "v628_orbifold_casimir.py", "path": "verification/v628_orbifold_casimir.py", "cluster": "core", "synopsis": "QGEO.ORBCAS.01: die Orbifold-Casimir-Runde — **DIE DREI DECK-MODENKLASSEN DER GEDECKTEN NAHT TRAGEN EXAKT DIE ℤ₃-TWIST-CASIMIR-DATEN** (erste quantitative Scheibe des v623-Orbifold-Rests). [E, exakt] Geschlossene Form E₀(ν,N) = −cos(π(2ν−1)/2N)/(2 sin(π/2N)); 1/N-Koeffizient exakt π(6ν²−6ν+1)/12; Sektor-Tabelle (1/72, −1/24, 1/72) für ν = (1/6, 1/2, 5/6): Twisted-Paar entartet, Verhältnis −1/3, Twist-Gap 1/18 exakt. [C] Der verbleibende Rest ist die WECHSELWIRKENDE Aussage (Twist-Feld-OPE, Crossing, RP) (5 checks, ~1 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv628_orbifold_casimir.py", "sourceSha256": "96632e8f809733d5fe9447df19265e73309133beb727b82d8a8d1f852f7bb28d", "linkedClaimIds": [ "QGEO.ORBCAS.01" ], "sectionIds": [ "section:3d2a5b53f3345969fcbc", "section:83d94e33024ba3df4db8", "section:848c49f799255f4cda92", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:3d2a5b53f3345969fcbc", "section:83d94e33024ba3df4db8", "section:ab9e7e520130ecc7da7c", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v628_orbifold_casimir.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v628_orbifold_casimir.py", "pubMirrorHash": "96632e8f809733d5fe9447df19265e73309133beb727b82d8a8d1f852f7bb28d", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v628_orbifold_casimir.py" }, { "id": "v629_root_incidence", "filename": "v629_root_incidence.py", "path": "verification/v629_root_incidence.py", "cluster": "core", "synopsis": "E8.INCIDENCE.01: der Wurzel-Inzidenz-Zensus — **DIE NAIVE 48×5-INZIDENZ AUF DIE 240 E8-WURZELN IST GEKILLT, DER POSITIV-REST IST SCHARF** (der Kill-Test des Reviews, erste Hürde ausgeführt). [E, KILL] Das compiler-kanonische Ordnung-12-Element (μ₄-Clock × Familien-3-Zyklus) wirkt NICHT frei: Orbits 19×12 + 3×4 statt 20 freier ζ₁₂-Orbits. [E, positiv] Die μ₄-Clock allein wirkt FREI mit EXAKT 60 Orbits — 60 = D_start als freier Orbit-Zählwert auf den Wurzeln; der 3-Zyklus fixiert exakt 12 Wurzeln (= gehobene Marks, v623) (6 checks, ~1 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv629_root_incidence.py", "sourceSha256": "a483a61f791b5eeaf90198d3c546ed07da22ec6afdc1e5d999de2ad91a56820b", "linkedClaimIds": [ "E8.INCIDENCE.01" ], "sectionIds": [ "section:3d2a5b53f3345969fcbc", "section:848c49f799255f4cda92", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:3d2a5b53f3345969fcbc", "section:ab9e7e520130ecc7da7c", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v629_root_incidence.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v629_root_incidence.py", "pubMirrorHash": "a483a61f791b5eeaf90198d3c546ed07da22ec6afdc1e5d999de2ad91a56820b", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v629_root_incidence.py" }, { "id": "v632_ftransfer_pgl2", "filename": "v632_ftransfer_pgl2.py", "path": "verification/v632_ftransfer_pgl2.py", "cluster": "core", "synopsis": "FTR.PGL2.01: die F_transfer-PGL₂-Runde — **DIE VIER EXTERNEN TRANSFER-SOLVER TEILEN EINE GEMEINSAME MÖBIUS-AKTION AUF DER DISKRIMINANTE-−7-NORMLINIE, WO SIE ÜBERHAUPT WIRKEN — DAS KILL-KRITERIUM ‚VIER INKOMPATIBLE ARITHMETISCHE AKTIONEN‘ IST NICHT ERFÜLLT** (die v533-Präregistrierung in wörtlicher Gruppenform ausgeführt). [E] Diskrete Hälfte: die v183-Koide-Lesart induziert die Schritt-Aktion +9 = N_fam² (parabolisch, exakt mit der Basis-Translation T verflochten, Φ∘T = g∘Φ); CR = 4/3 exakt; Möbius-Transport erzwingt die F-Ecke 53 fit-frei. [E] Kontinuierliche Hälfte: g_pole hyperbolisch (2/3)⁶, g_Boltzmann = g_pole identisch (v425-Single-Flow), g_QCD parabolisch und EXAKT zu T konjugiert (Translation +7/(2π) in 1/α), g_relic = Identität; Uniflow-Degeneration (v575) und Own-Clock-Äquivalenz (v578) reproduziert; 5 Must-fail-Kontrollen (25 checks, ~1 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv632_ftransfer_pgl2.py", "sourceSha256": "d7795cf409e6bfc979e017468cb2e47f378021a09a23497d620aad1c943d62bc", "linkedClaimIds": [ "FTR.PGL2.01" ], "sectionIds": [ "section:0aa531691d44e875db34", "section:3d2a5b53f3345969fcbc", "section:568b5e9acdb7b04367d3", "section:7ee581db787f8ddbcb4a", "section:83d94e33024ba3df4db8", "section:848c49f799255f4cda92", "section:8d1e955857da6655fadd", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:c519f45910c30ff3c0ae", "section:f091de1c3533bab48372", "section:f0ac30137703825661c6", "section:fdf63a1d99769ab37ccb" ], "activeSectionIds": [ "section:3d2a5b53f3345969fcbc", "section:83d94e33024ba3df4db8", "section:8d1e955857da6655fadd", "section:ab9e7e520130ecc7da7c", "section:f091de1c3533bab48372", "section:fdf63a1d99769ab37ccb" ], "evidenceId": "python_verification:verification/v632_ftransfer_pgl2.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v632_ftransfer_pgl2.py", "pubMirrorHash": "d7795cf409e6bfc979e017468cb2e47f378021a09a23497d620aad1c943d62bc", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v632_ftransfer_pgl2.py" }, { "id": "v633_orbit60_quotient", "filename": "v633_orbit60_quotient.py", "path": "verification/v633_orbit60_quotient.py", "cluster": "core", "synopsis": "E8.ZIQUOTIENT.01: die μ₄-Quotienten-Runde — **DER QUOTIENT DER 240 E8-WURZELN NACH DER FREIEN μ₄-CLOCK IST DAS HERMITESCH-UNIMODULARE ℤ[i]-E8 MIT DEM 60-HYPEREBENEN-SYSTEM VON ST31; DIE 60→6-KASKADEN-ROUTE AUF DEM QUOTIENTEN IST GEKILLT**. [E] H(v,v) = 2 auf allen 60 Repräsentanten; ℤ[i]-Spann = volles E8 (Covolumen 256), hermitesch-unimodulare Basis unter den Reps (det Gram = 1); σ auf den 60 Linien: 19×3 + 3 fix (= die J-Orbits der 12 σ-fixen Wurzeln); alle 60 Ordnung-2-Reflexionen erhalten die Wurzeln, Linien-Gruppe der Ordnung 11520 = 46080/4 (ST31-Fingerprint; ST32 durch 40 Hyperebenen gekillt). [E, KILL] Kaskaden-Harttest: Gram-Rang 4, beide Quotienten-Graphen regulär, keine kanonische Paar-Regel — getyptes Negativ (17 checks, ~3 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv633_orbit60_quotient.py", "sourceSha256": "5a1dbfaa1331b39874faaaa575f40b60692f3fb03764c761154666c51fed9ed6", "linkedClaimIds": [ "E8.ZIQUOTIENT.01" ], "sectionIds": [ "section:3d2a5b53f3345969fcbc", "section:848c49f799255f4cda92", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:3d2a5b53f3345969fcbc", "section:ab9e7e520130ecc7da7c", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v633_orbit60_quotient.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v633_orbit60_quotient.py", "pubMirrorHash": "5a1dbfaa1331b39874faaaa575f40b60692f3fb03764c761154666c51fed9ed6", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v633_orbit60_quotient.py" }, { "id": "v634_st31_structure", "filename": "v634_st31_structure.py", "path": "verification/v634_st31_structure.py", "cluster": "core", "synopsis": "E8.ST31.01: die ST31-Struktur-Runde — **G31 IST DER VOLLE UNITÄRE STABILISATOR (EXAKT GEZÄHLT: 46080), DIE GRADE (8,12,20,24) SIND MOLIEN-EINDEUTIG, σ = c⁴ UND J = c⁹ EXAKT — UND DIE NUMEROLOGIE |G31| = |W(D5)|·|W(A3)| TRÄGT KEINE STRUKTUR: DREIFACH GEKILLT** (keine Isomorphie: Zentren 4 vs 1; kein (semi)direktes Produkt: die Vereinigung aller kleinen Normalabschlüsse hat Ordnung 64; W(D5) bettet in KEINE Rang-4-Gruppe ein — minimale treue Dimension 5 > 4; W(A3) = S4 bettet ein). Echte Struktur BERECHNET: G31 = (Z4∘2^{1+4})·Sp₄(2); Wurzel-Stabilisator = G(4,2,3) (Steinberg), Linien-Stabilisator = Z4 × G(4,2,3); EHRLICH: die v629-Uhr c ist NICHT das Springer-reguläre 12-Element (Zensus 19×12+3×4, |C(c)| = 72 ≠ 288) — der freie 20er-Kamm gehört der regulären 12-Uhr, einer anderen Konjugationsklasse; Lean-Anker: die Ordnungs-Identitäten in G31Orders.lean maschinell bewiesen (56 checks, ~10 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv634_st31_structure.py", "sourceSha256": "5ff53ed031ca03103187ac22edf723aabce88bee3df1085c52486ecb0044d37c", "linkedClaimIds": [ "E8.ST31.01" ], "sectionIds": [ "section:3d2a5b53f3345969fcbc", "section:636458c5f2b1b281e60a", "section:848c49f799255f4cda92", "section:ab9e7e520130ecc7da7c", "section:bc80e633fbb98ca8173d", "section:c4cf080b9ae6f25f7a71", "section:df8999b098e725de7d02", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:3d2a5b53f3345969fcbc", "section:636458c5f2b1b281e60a", "section:ab9e7e520130ecc7da7c", "section:bc80e633fbb98ca8173d", "section:df8999b098e725de7d02", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v634_st31_structure.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v634_st31_structure.py", "pubMirrorHash": "5ff53ed031ca03103187ac22edf723aabce88bee3df1085c52486ecb0044d37c", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v634_st31_structure.py" }, { "id": "v638_code_semantics", "filename": "v638_code_semantics.py", "path": "verification/v638_code_semantics.py", "cluster": "core", "synopsis": "E8.CODESEM.01: die Code-Semantik-Runden (Kill + Stufe 2) — **DIE EINDEUTIGE ÄQUIVARIANTE HAMMING-PLATZIERUNG C* IST REED–MULLER RM(1,3) AUF AG(3,2) UND TRÄGT EIN EXAKTES WÖRTERBUCH**: Informationsbits = 1 pro μ₄-Paar (3 Familien + 1 Anker; das eindeutige minimale Z6-Orbit der Informationsmengen), Syndrom = In-Paar-Bit + Paar-Zeiger mit σ-3-Zyklus (Anker = Summe der Familien), Decode = Projektion wörtlich auf der ganzen Einzel-Fehler-Klasse (3840/3840, exakte Fraction-Arithmetik) — **und ALLES stirbt für jede nicht-äquivariante Platzierung** (nur 2/30 tragen die Struktur; naive v626-Platzierung tot für πσ; Kill-Kontrolle feuert) (27 checks, ~3 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv638_code_semantics.py", "sourceSha256": "156908004bcde25cce065c20bd07f4184da35b19bd2ec1c5d557f733e6b115c7", "linkedClaimIds": [ "E8.CODESEM.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:1234c1fa7fdc0d6d5b35", "section:2678ed3ba0ed508e2d8e", "section:3d2a5b53f3345969fcbc", "section:51e91159532ef7479ff8", "section:83d94e33024ba3df4db8", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:dcbb8ba68bde5b18c375", "section:df8999b098e725de7d02", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:1234c1fa7fdc0d6d5b35", "section:3d2a5b53f3345969fcbc", "section:51e91159532ef7479ff8", "section:83d94e33024ba3df4db8", "section:ab9e7e520130ecc7da7c", "section:dcbb8ba68bde5b18c375", "section:df8999b098e725de7d02", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v638_code_semantics.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v638_code_semantics.py", "pubMirrorHash": "156908004bcde25cce065c20bd07f4184da35b19bd2ec1c5d557f733e6b115c7", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v638_code_semantics.py" }, { "id": "v639_twist_ope", "filename": "v639_twist_ope.py", "path": "verification/v639_twist_ope.py", "cluster": "core", "synopsis": "QGEO.TWISTOPE.01: die Twist-Feld/OPE-Runde — **DIE WECHSELWIRKENDE SCHEIBE DER ℤ₃-ORBIFOLD-AUSSAGE STEHT AUF DEM ABELSCHEN VERTEX-NIVEAU**: h_σ = 1/36 aus DREI exakten Routen (Konventionen versöhnt, η(1−η)/2-Falle exakt aufgelöst), Gitter-Zweipunkt 2Δ = 2/9 auf 0.05–0.11%, Crossing EXAKT symmetrie-geschützt (1.4e−14), geschlossene Vierpunkt-Form [w(1−w)]^{−2Δ} < 0.1% nach N^{−2/3}-Extrapolation, OPE c₁ = 2/9 modellgebunden 0.19% (modellfrei ±15%-Band offen, getypt); **RP differenziert: ℤ₂-Klasse exakt PSD (Maschinerie validiert), naive ℤ₃-Paarung N-stabil verletzt (−4.5e−3) → der parafermionische Klein-Twist ist das benannte Offen-Item**; GATE.QGEO bewegt sich nicht (25 checks, ~1 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv639_twist_ope.py", "sourceSha256": "1fcb4446d1f7b71b7f67e4587303458f19a3d4315f4171ed9030fb5a030e4cb8", "linkedClaimIds": [ "QGEO.TWISTOPE.01" ], "sectionIds": [ "section:3d2a5b53f3345969fcbc", "section:83d94e33024ba3df4db8", "section:848c49f799255f4cda92", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:3d2a5b53f3345969fcbc", "section:83d94e33024ba3df4db8", "section:ab9e7e520130ecc7da7c", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v639_twist_ope.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v639_twist_ope.py", "pubMirrorHash": "1fcb4446d1f7b71b7f67e4587303458f19a3d4315f4171ed9030fb5a030e4cb8", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v639_twist_ope.py" }, { "id": "v645_klein_rp", "filename": "v645_klein_rp.py", "path": "verification/v645_klein_rp.py", "cluster": "core", "synopsis": "QGEO.KLEINRP.01: der parafermionische Klein-Twist — **DER ℤ₃-TWIST-SEKTOR IST REFLEXIONSPOSITIV auf dem Naht-Doppel-Gitter unter der Klein-Paarung (Spiegelung ∘ LADUNGSKONJUGATION, ω^{k·q}-Nullmoden-Phasen, η = (1,1) EINDEUTIG aus 36)** — das benannte Offen-Item von QGEO.TWISTOPE.01 ist auf Gitter-OS-Ebene GELÖST: alle geladenen Klein-Blöcke exakt reell-symmetrisch UND PSD (worst 2.9e−12), N-stabil 48…384, beide Achsen, **volle gemischte OS-Gram {1, σ₁, σ₂, Dipole} ohne Sektor-Projektion PSD**; die naive Paarung reproduziert ihre N-stabile Verletzung (−4.5e−3, must-fail); Kontinuums-OS/Modularität getypt offen; GATE.QGEO bewegt sich nicht (17 checks, ~30 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv645_klein_rp.py", "sourceSha256": "a7974da59e2d3aca79cbe6c266bba1d00dfe4bbdcbdd99e3095699f372203a3d", "linkedClaimIds": [ "QGEO.KLEINRP.01" ], "sectionIds": [ "section:3d2a5b53f3345969fcbc", "section:83d94e33024ba3df4db8", "section:848c49f799255f4cda92", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:3d2a5b53f3345969fcbc", "section:83d94e33024ba3df4db8", "section:ab9e7e520130ecc7da7c", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v645_klein_rp.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v645_klein_rp.py", "pubMirrorHash": "a7974da59e2d3aca79cbe6c266bba1d00dfe4bbdcbdd99e3095699f372203a3d", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v645_klein_rp.py" }, { "id": "v646_rm13_reverse", "filename": "v646_rm13_reverse.py", "path": "verification/v646_rm13_reverse.py", "cluster": "core", "synopsis": "E8.RM13REV.01: die RM(1,3)-Rückwärts-Lesung — sind Compiler-Zahlen CODE-Operationen? **EHRLICH ZWEIGETEILT: die σ-fixierten Syndrome tragen EXAKT die Anker-Zerlegung (Leader-Gewichte (0,1,1,2), Norm 6, Anker = Familiensumme P3 = P0+P1+P2 — die AUSWAHL ist äquivarianz-spezifisch, die Gewichte selbst generisch für jede [8,4,4]-Platzierung), aber die Bytecode-Folge p_n = 2+2ⁿ hat KEINE Code-Lesart (0/11 Familien; 18/27/81 ohne Treffer — das Bingo ist beerdigt)**; Kill-Kontrolle feuert SELEKTIV (naive Platzierung verliert q-Universalität + σ-Aktion, behält generische Gewichte und sogar den Zähler 12 — ehrlich umgetypt) (20 checks, ~1 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv646_rm13_reverse.py", "sourceSha256": "0aa92c90459979b9ff9cd707f322f949a5e9b7803f895f939b14cf5ea9adb1df", "linkedClaimIds": [ "E8.RM13REV.01" ], "sectionIds": [ "section:3d2a5b53f3345969fcbc", "section:83d94e33024ba3df4db8", "section:848c49f799255f4cda92", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:3d2a5b53f3345969fcbc", "section:83d94e33024ba3df4db8", "section:ab9e7e520130ecc7da7c", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v646_rm13_reverse.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v646_rm13_reverse.py", "pubMirrorHash": "0aa92c90459979b9ff9cd707f322f949a5e9b7803f895f939b14cf5ea9adb1df", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v646_rm13_reverse.py" }, { "id": "v647_st31_degree24", "filename": "v647_st31_degree24.py", "path": "verification/v647_st31_degree24.py", "cluster": "core", "synopsis": "E8.ST31DEG.01: die ST31-Grad-24/-20-Runde — **DAS μ₄-ZENTRUM IST EINE POTENZ BEIDER REGULÄRER UHREN (w⁶ = ±J mit χ_w = x⁴+ix²−1 exakt, primitive ζ₂₄; u⁵ = ±J zentral), UND DIE UHR-FRAGE c = w² IST PER PARITÄTSSATZ GETÖTET** — die 12-Zyklen eines Quadrats entstehen PAARWEISE aus 24-Zyklen, census(c) = 19×12 + 3×4 hat UNGERADE Zahlen: unmöglich selbst in S₂₄₀ (beweisfest); u⁴ wirkt frei mit Zensus {5:48}, 48 = 240/5 exakt, Linien {5:12}; die Gleichheit 48 = Naht-Sites bleibt getypte BEOBACHTUNG (25 checks, ~4 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv647_st31_degree24.py", "sourceSha256": "e95935664064ee526a8aba1f6bae7b9e796370d982f9cb5b41b2470ef6bb771b", "linkedClaimIds": [ "E8.ST31DEG.01" ], "sectionIds": [ "section:83d94e33024ba3df4db8", "section:848c49f799255f4cda92", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:83d94e33024ba3df4db8", "section:ab9e7e520130ecc7da7c", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v647_st31_degree24.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v647_st31_degree24.py", "pubMirrorHash": "e95935664064ee526a8aba1f6bae7b9e796370d982f9cb5b41b2470ef6bb771b", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v647_st31_degree24.py" }, { "id": "v649_discipline_audit", "filename": "v649_discipline_audit.py", "path": "verification/v649_discipline_audit.py", "cluster": "frontier", "synopsis": "META.DISCIPLINE.01: das Disziplin-Audit — die Suite parst SICH SELBST und zertifiziert ihre Prozess-Disziplin als eingefrorene Mindestwerte: **214 Ledger-Zeilen dokumentieren Kills/ehrliche Negative/Retypes, 1469 Must-fail/Kill/Scramble-Vorkommen in 233 von 643 Modulen, 47 Contract-Rows (29 mit benannten Kill-Kriterien; ausgeführt: FTR.PGL2 v533→v632, W1-Kette →v643), deterministisches Replay 12/12 (deklarierte Stichprobe v55–v648, zwei frische Läufe), 5 Klassik-Anker gegen die Literatur nachgerechnet (Jacobi r₄, Construction A → 240 Minimalvektoren, ST31-Grade, Suzuki-Konstanten 25+ Stellen, ξ-Funktionalgleichung), 54 committete Lean-Beweismodule**; ehrliche Grenze [C]: Prozess-Disziplin, nicht Wahrheit der Physik — die offenen Gates bleiben offen (278 Klasse-O-Rows) (17 checks, ~200 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv649_discipline_audit.py", "sourceSha256": "ba5351438f993e9ed985d5b7f0e782ac95025246daf9d5129322d54236978ea0", "linkedClaimIds": [ "META.DISCIPLINE.01" ], "sectionIds": [ "section:83d94e33024ba3df4db8", "section:848c49f799255f4cda92", "section:a25026597f4b790eb050", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71" ], "activeSectionIds": [ "section:83d94e33024ba3df4db8", "section:a25026597f4b790eb050", "section:ab9e7e520130ecc7da7c" ], "evidenceId": "python_verification:verification/v649_discipline_audit.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v649_discipline_audit.py", "pubMirrorHash": "ba5351438f993e9ed985d5b7f0e782ac95025246daf9d5129322d54236978ea0", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v649_discipline_audit.py" }, { "id": "v650_orbifold_modular", "filename": "v650_orbifold_modular.py", "path": "verification/v650_orbifold_modular.py", "cluster": "core", "synopsis": "QGEO.ORBMOD.01: die Modular-Daten des ℤ₃-Orbifolds der Naht auf dem Gitter — **ALLE NEUN Z[g,h] TREFFEN |θ[g/3,h/3]/η|² AUF < 1 %, DIE MODULARE S-KOVARIANZ IST GEMESSEN MIT SAUBERER N⁻⁴-RATE (das N⁻²-Gitterartefakt ist selbst S-kovariant und KÜRZT SICH), T IST DER EXAKTE ℤ₆-DEHN-TWIST (g,h) → (g, g+h) × (−1)^F auf Maschinenpräzision** — die getwisteten Charaktere tragen h_σ = 1/36 (rel 5.6e−4) mit dem parafermionischen 1/6-Gap, die v628-Casimir-Tafel reproduziert pro Deck-Klasse, und **deck³ = (−1)^F schließt EXAKT als ℤ₆-Spur-Arithmetik** (inkl. 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**C3s Odd-Sektor-Vorhersagen 85/18 und 81/18 verfehlen die Messung um Faktor 85.0 und 9.0** (der Defekt-String ist exakt ladungsneutral: C3 exzidiert Zustände, die auf der Gitter-Naht mit positiver Klein-Norm existieren); der v639-2/9-Read allein ist B-vs-C3-BLIND (beide stimmen auf geraden Sektoren exakt überein) — das neue τ-Datum: OPE-Exponent 1/18 (rel 2.9e−3); Bond-Defekt-Prämisse → v653 (15 checks, ~30 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv652_orbifold_arf.py", "sourceSha256": "e95916a9e911908aa2ee66eaf05e6d447b6324c56a45f85f94605df08183b782", "linkedClaimIds": [ "QGEO.ORBARF.01" ], "sectionIds": [ "section:83d94e33024ba3df4db8", "section:848c49f799255f4cda92", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:edc607bc9be0dce5ac62" ], "activeSectionIds": [ "section:83d94e33024ba3df4db8", "section:ab9e7e520130ecc7da7c", "section:edc607bc9be0dce5ac62" ], "evidenceId": "python_verification:verification/v652_orbifold_arf.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v652_orbifold_arf.py", "pubMirrorHash": "e95916a9e911908aa2ee66eaf05e6d447b6324c56a45f85f94605df08183b782", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v652_orbifold_arf.py" }, { "id": "v653_bond_defect", "filename": "v653_bond_defect.py", "path": "verification/v653_bond_defect.py", "cluster": "core", "synopsis": "QGEO.BONDDEF.01: die Bond-Defekt-Prämisse wird ein GITTER-SATZ — **TWIST-SEKTOR = DECK-RANDBEDINGUNG = BOND-DEFEKT, KANONISCH UND EXAKT (unitäre Äquivalenz A_r = √3·R·P_r auf allen Moden, in ℚ(ζ₆) exakt, bei 16/48 UND 48/144), MIT D_can = L⁴ UND D_can³ = −1 ALS OPERATOR-IDENTITÄTEN** (die Viertel-Uhr FIXIERT den kanonischen Sektions-Lift); die Defekt-Position ist REINE EICHUNG (symbolischer Teleskop-Satz in allen 16 freien Bond-Phasen) mit geometrisch gepinnter Eichklasse (Blatt-Reduktion = eine uniforme Twist-Einheit pro Mark; Kozykel-Träger = Mark-Menge); **Alternativen-Zensus vollständig: die Basiskette hat KEIN anderes ℤ₃, Traces/Holonomie/v628-Casimir töten alles außerhalb — inkl. der EHRLICHEN isospektralen NN-Kette (existiert auf 7.8e−16! rein spektral nicht ausschließbar, aber keine ℤ₃-Twist-Realisierung, und die gemessenen String-Daten diskriminieren sie)**; Kontinuums-CFT + Naht-Identifikation bleiben [C] (18 checks, ~40 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv653_bond_defect.py", "sourceSha256": "56528ce9d67262d3e9d4d4dc8a569fe31c89a6954ae5411452f61767e8344c14", "linkedClaimIds": [ "QGEO.BONDDEF.01" ], "sectionIds": [ "section:83d94e33024ba3df4db8", "section:848c49f799255f4cda92", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:83d94e33024ba3df4db8", "section:ab9e7e520130ecc7da7c", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v653_bond_defect.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v653_bond_defect.py", "pubMirrorHash": "56528ce9d67262d3e9d4d4dc8a569fe31c89a6954ae5411452f61767e8344c14", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v653_bond_defect.py" }, { "id": "v654_st31_degree8", "filename": "v654_st31_degree8.py", "path": "verification/v654_st31_degree8.py", "cluster": "core", "synopsis": "E8.ST31D8.01: die ST31-Grad-8-Runde + der vereinheitlichte d/4-SATZ — **JEDE Springer-reguläre d-Uhr von G31 erfüllt x^{d/4} = ±i·Id, einen ERZEUGER von μ₄ (nie ±1; eine Formel aus der Exponenten-Systematik: alle Exponenten ≡ 3 mod 4); DIE UMKEHRUNG IST EXAKT BEI d ∈ {8, 20, 24}, UND DIE EINZIGE AUSNAHME BEI d = 12 IST DIE COMPILER-UHR-KLASSE** (1280 Extra-Elemente = Klasse von c und Galois-Zwilling; χ_c = (x−i)²(x²+ix−1) = die HALBE reguläre 12er-Springer-Box, alle Eigenwerte λ³ = −i — exakt darum ist c³ = J³ zentral: die Compiler-Uhr-Klassen sind die EINZIGEN nicht-regulären Uhren in ganz G31, deren d/4-Potenz das Zentrum erzeugt); **Ordnung-8-Landschaft komplett (10560 Elemente, 480 regulär = 2 Galois-Klassen, χ = (x²+i)² exakt) und der ehrliche KILL: „frei ⇒ regulär“ ist FALSCH** (4320 freie 8er nichtzentral; schon bei Ordnung 4: 510, keins regulär); Grade = freie Ordnungen mit 4 | d, d > 4 (30 checks, ~10 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv654_st31_degree8.py", "sourceSha256": "3985927e55fa122dbafff7a12d9c35e530ce1c8ef7fb5b36b22bd76e02205205", "linkedClaimIds": [ "E8.ST31D8.01" ], "sectionIds": [ "section:83d94e33024ba3df4db8", "section:848c49f799255f4cda92", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:83d94e33024ba3df4db8", "section:ab9e7e520130ecc7da7c", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v654_st31_degree8.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v654_st31_degree8.py", "pubMirrorHash": "3985927e55fa122dbafff7a12d9c35e530ce1c8ef7fb5b36b22bd76e02205205", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v654_st31_degree8.py" }, { "id": "v664_look_elsewhere", "filename": "v664_look_elsewhere.py", "path": "verification/v664_look_elsewhere.py", "cluster": "frontier", "synopsis": "META.LOOKELSEWHERE.01: das Look-Elsewhere-Audit — das Bingo-Budget der getypten [C]-Koinzidenzen, quantifiziert — **N = 42 STRUKTUR-SLOTS, K = 19 TREFFER, 6 KILLS ALS 0-TREFFER-TRIALS IM BUDGET; GLOBAL p = 5.08e−3 IM KONSERVATIVSTEN VON DREI NULL-MODELLEN (das Ensemble überlebt die ehrliche Korrektur), PSEUDO-THEORIE-KONTROLLE: nur 0.2 %/0.3 % von 2000 größengematchten Listen erreichen Trefferzahl/p — ABER KEINE EINZELBEOBACHTUNG IST FÜR SICH SIGNIFIKANT**: suggestiv (0.01…0.1) nur 60 = D_start, 12 = Marks, G31-Grade, 48 = Ω_adm; unauffällig (p > 0.1): 6 = p₂(a) (p = 0.169) und die CODESEM-Zahlen-Batterie (p = 0.593 — der v646-Befund quantifiziert); 14/16 FORCED (ihr Wert ist das Theorem, nicht die Zahl); **Re-Typisierungen als datierte Ledger-Notes AUSGEFÜHRT (EXTREV.LATTICE.01, E8.CODESEM.01, E8.CODE.01)**; Seed 20260802, 100k MC, exakte Poisson-Binomial-Tails (14 checks, ~2 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv664_look_elsewhere.py", "sourceSha256": "764de991da3a69ab0c67f9a7b6f5beed531e933e306337d28257571f5cb52735", "linkedClaimIds": [ "META.LOOKELSEWHERE.01" ], "sectionIds": [ "section:83d94e33024ba3df4db8", "section:848c49f799255f4cda92", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:83d94e33024ba3df4db8", "section:ab9e7e520130ecc7da7c", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v664_look_elsewhere.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v664_look_elsewhere.py", "pubMirrorHash": "764de991da3a69ab0c67f9a7b6f5beed531e933e306337d28257571f5cb52735", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v664_look_elsewhere.py" }, { "id": "v679_orbifold_continuum_os", "filename": "v679_orbifold_continuum_os.py", "path": "verification/v679_orbifold_continuum_os.py", "cluster": "core", "synopsis": "QGEO.ORBOS.01: die erste Kontinuums-OS-Scheibe des Naht-Orbifolds B — **KORRELATOR-KONVERGENZ MIT VERSTANDENEN RATEN: alle sechs σ-Kanal-Observablen teilen die uniforme Roh-Rate 0.659 = die vorhergesagte Fisher-Hartwig-2/3-Branche, der τ-Kanal-Kontrast misst 1.298 vs 4/3 (Kanal-Gesetz ρ = 2(1−β)² − 2β²: die Raten sind VERSTANDEN, nicht gefittet); nach EINEM FH-Term liegen die Limites < 0.05% an den CFT-Werten; RP ÜBERLEBT DEN LIMES: λ_min-Extrapolationen weg von Null (σ 1.36e−3, Marge 7×; τ 2.80e−4, Marge 358×; gemischter OS-Gram 1.34e−3, Marge 31×; must-fail η = −1 kippt)**; Cluster in Raum UND euklidischer Zeit exakt (2Δ = 0.222220 vs 2/9 auf 8e−6, Zylinder-/cosh-Formen punktgenau, Zeit-Gap = ε-Level 0.99933 vs 1); Charaktere 1/36, 1/9, 5/18, 4/9 auf 1e−12 mit gemessener N⁻²-Rate 2.000; **getypt: E0/E2/E3/E4 auf Konvergenz-Ebene GEMESSEN, E1 nur diskret exakt; der formale Limes-Rest ist benannt (uniforme Schranken, GNS-Limes-Hilbertraum, Operator-Konvergenz, R-Sektoren, B-Assembly) — GATE.QGEO bewegt sich NICHT** (19 checks, ~3 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv679_orbifold_continuum_os.py", "sourceSha256": "0a0515e24197cea6060f011cc820cbded88033e902c1ca4736ea990074aaa32e", "linkedClaimIds": [ "QGEO.ORBOS.01" ], "sectionIds": [ "section:83d94e33024ba3df4db8", "section:848c49f799255f4cda92", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:83d94e33024ba3df4db8", "section:ab9e7e520130ecc7da7c", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v679_orbifold_continuum_os.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v679_orbifold_continuum_os.py", "pubMirrorHash": "0a0515e24197cea6060f011cc820cbded88033e902c1ca4736ea990074aaa32e", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v679_orbifold_continuum_os.py" }, { "id": "v689_gaussian_code_bridge", "filename": "v689_gaussian_code_bridge.py", "path": "verification/v689_gaussian_code_bridge.py", "cluster": "core", "synopsis": "E8.GAUSSCODE.01: die Gauß-Codebrücke (Review-Vertrag E8.GAUSSIAN.CODE.01) — **E8(Z[i])/(1+i) ≅ F₂⁴ EXAKT (Smith-Normalform; 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(ii) σ-Struktur TOT (Orbitgrößen {3,1}, keine 2-Blöcke); (iii) INVOLUTIONS-ZEUGE EXISTIERT NICHT: der volle Involutions-Census der Liniengruppe LG (Ordnung 11520; 375 Involutionen, 21 Klassen) zeigt KEIN Element vom Zykeltyp 2²⁷1⁶ (Fixlinien-Census {0:120, 4:180, 12:15, 16:60}); (iv) W(E8)-Coxeter steigt nicht ab; (v) MUST-FAIL-Numerologie-Kontrolle feuert: regelfreies lexikographisches Paar-Entfernen reproduziert 60−2n in exakt 27 Schritten, > 10⁷⁰ gleich-erfolgreiche Sequenzen — die Zählung trägt keine Struktur**; A5-Einzeiler: Ordnung-5-Elemente existieren (2304), aber keine sichtbare natürliche A5-Aktion (⟨σ, Ordnung-5⟩ hat Ordnung 960); GEPARKT per Review-Protokoll; deterministisch (18 Checks, ~1 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv700_orbit60_census.py", "sourceSha256": "18e2e1a9641244a24d0fc315b24d3f8ecf5358fa60a02415ffff5bfdd4ae42f1", "linkedClaimIds": [ "E8.ORBIT60.01" ], "sectionIds": [ "section:83d94e33024ba3df4db8", "section:848c49f799255f4cda92", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:83d94e33024ba3df4db8", "section:ab9e7e520130ecc7da7c", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v700_orbit60_census.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v700_orbit60_census.py", "pubMirrorHash": "18e2e1a9641244a24d0fc315b24d3f8ecf5358fa60a02415ffff5bfdd4ae42f1", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v700_orbit60_census.py" }, { "id": "v705_chain_deck_sector", "filename": "v705_chain_deck_sector.py", "path": "verification/v705_chain_deck_sector.py", "cluster": "core", "synopsis": "Original v705 D1 physical NS circle: 48-site antiperiodic shift, order-12 clock, projective deck cube -1 and three 16-mode deck sectors.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv705_chain_deck_sector.py", "sourceSha256": "43383b9e43bb882bc88265b588a2c0aca7c300d5c3748a1d2480c2f8d58dd7ce", "linkedClaimIds": [ "QGEO.DECKSECTOR.01" ], "sectionIds": [ "section:848c49f799255f4cda92", "section:93b8868beb643874af75", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:e7e7f78a69bea2986c9f", "section:eb00caf29086b02d5bf5", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:ab9e7e520130ecc7da7c", "section:e7e7f78a69bea2986c9f", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v705_chain_deck_sector.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v705_chain_deck_sector.py", "pubMirrorHash": "43383b9e43bb882bc88265b588a2c0aca7c300d5c3748a1d2480c2f8d58dd7ce", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v705_chain_deck_sector.py" }, { "id": "v715_qgeo_car_continuum", "filename": "v715_qgeo_car_continuum.py", "path": "verification/v715_qgeo_car_continuum.py", "cluster": "core", "synopsis": "QGEO.CARLIMIT.01: QGEO-CAR — die quasifreie CAR-Route zum formalen Orbifold-Kontinuumslimes (GATE.QGEO), erste Scheibe — **QGEO-CAR-RATES-SUMMABLE: alle 6+1 Deck/Twist-Kanäle sind Schatten-Norm-Cauchy auf ε-separierten Konfigurationen (N bis 3072/6144) mit geometrisch summierbaren Raten; 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die Sonde verweigert ehrlich den NEEDS-LINDBLAD-Ausweg (v238-GKSL ebenfalls all-loxodromisch); mit v723 sind BEIDE Thermal-Time-Routen geschlossen: der externe Uhren-Vertrag steht (12 mechanische Checks, ~1 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv724_phys_t3b_modular_flows.py", "sourceSha256": "19ee886bab409be09034da299a7d7d8f57099e035f115b9f056823a4987cb6d0", "linkedClaimIds": [ "FTRANSFER.COCYCLE.01" ], "sectionIds": [ "section:00b05ea692eac25e3d3e", "section:01c88746fb95cc0958d7", "section:0aa531691d44e875db34", "section:2805350687457d7649bf", "section:354f7e98a6c16208d1a4", "section:568b5e9acdb7b04367d3", "section:5c7b501c80f2e5816761", "section:83d94e33024ba3df4db8", "section:848c49f799255f4cda92", "section:98cf6dab6e992992d2c9", "section:a3401d23c565056512c5", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:f0ac30137703825661c6", "section:fdf63a1d99769ab37ccb" ], "activeSectionIds": [ "section:00b05ea692eac25e3d3e", "section:01c88746fb95cc0958d7", "section:2805350687457d7649bf", "section:83d94e33024ba3df4db8", "section:a3401d23c565056512c5", "section:ab9e7e520130ecc7da7c", "section:fdf63a1d99769ab37ccb" ], "evidenceId": "python_verification:verification/v724_phys_t3b_modular_flows.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v724_phys_t3b_modular_flows.py", "pubMirrorHash": "19ee886bab409be09034da299a7d7d8f57099e035f115b9f056823a4987cb6d0", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v724_phys_t3b_modular_flows.py" }, { "id": "v725_phys_vgeo_torsor_audit", "filename": "v725_phys_vgeo_torsor_audit.py", "path": "verification/v725_phys_vgeo_torsor_audit.py", "cluster": "core", "synopsis": "VGEO.TORSOR.01: T1-SCHLUSS — der Kalibrations-/Skalen-Torsor-Audit der v_geo-Schnittstelle — **TORSOR-SCHLIESSUNG: die v_geo-Schnittstelle ist als R₊-Skalen-Torsor STRUKTURELL GESCHLOSSEN — (1) vollständige Export-Tabelle O_i = r_i·v_geo^{d_i}, (2) Dimensionsmatrix Rang 1 (konditional [A] auf dem Flavor-Block, benannt), (3) alle Konsistenz-Bedingungen λ-homogen (Maschinenform des No-Unit-Satzes v153), (4) Zwei-Anker leave-one-out kompatibel (G vs ρ_Λ: 0.11%), (5) Kalibrations-Satz in Torsor-Sprache formuliert**; FENCE: Struktur-Schließung, KEINE Skalen-Ableitung (per No-Unit unmöglich); Moonshot BENANNT, nicht ausgeführt: H_EW = ln(M̄/v_EW) = 37.1776 (21 Checks, ~1 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv725_phys_vgeo_torsor_audit.py", "sourceSha256": "13f14036812be4e37459ecab39180ae111c253f477a8b191a5bac7cfddac0afa", "linkedClaimIds": [ "VGEO.TORSOR.01" ], "sectionIds": [ "section:10eb7a1a008b9b2bbd4b", "section:2805350687457d7649bf", "section:39807bac57329dd11bcf", "section:51b5da5a67a36e5155ae", "section:697c671889813baf24f5", "section:6c9d1c3b370b8f366d55", "section:81a6dc002dc46cf7b6c5", "section:848c49f799255f4cda92", "section:93b8868beb643874af75", "section:970b604e67143eb148a6", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:c8d53f7c2e20223e312d", "section:dcbb8ba68bde5b18c375", "section:ea84c12b5f6b31caebb5", "section:eb00caf29086b02d5bf5" ], "activeSectionIds": [ "section:2805350687457d7649bf", "section:697c671889813baf24f5", "section:6c9d1c3b370b8f366d55", "section:81a6dc002dc46cf7b6c5", "section:970b604e67143eb148a6", "section:ab9e7e520130ecc7da7c", "section:c8d53f7c2e20223e312d", "section:dcbb8ba68bde5b18c375", "section:ea84c12b5f6b31caebb5" ], "evidenceId": "python_verification:verification/v725_phys_vgeo_torsor_audit.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v725_phys_vgeo_torsor_audit.py", "pubMirrorHash": "13f14036812be4e37459ecab39180ae111c253f477a8b191a5bac7cfddac0afa", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v725_phys_vgeo_torsor_audit.py" }, { "id": "v726_phys_car_pp_index", "filename": "v726_phys_car_pp_index.py", "path": "verification/v726_phys_car_pp_index.py", "cluster": "core", "synopsis": "GNET.PPINDEX.01: PHYS-T2-Hauptscheibe — Pimsner-Popa/Watatani-Index 4 auf der CAR-Leiter, mit HERGELEITETER μ₄-Wirkung und Ramond-Nullmoden-Test — **T2-SLICE-GO: die optimale PP-Konstante ist EXAKT ¼ (expliziter Rang-1-Minimierer + Pinching-Satz) und der Watatani-Index EXAKT 4 via expliziter Quasi-Basis (Σvv* == 4·1, Gewichte ERZWUNGEN — uniforme Gewichte brechen die Skalarität, Z₂-Mittel gibt Index 2); 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der Watatani-Index der lokalen Fixpunkt-Inklusion ist LOKAL EXAKT 4 für jedes Intervall ℓ ≥ 2 — die [D,A]-Index-Aussage ist intervall-lokal, nicht nur global; Ramond = Halblinien-/Bond-Defekt (solitonisch; lokaler Footprint, Leckage √(2/N))**; 4 Must-Fail-Kontrollen feuern; fehlende Kontinuums-Sätze BENANNT, nicht behauptet (GNS-Limes-Netz, Index-Kontinuität Pimsner–Popa/Longo, Longo-Q-System-Identifikation zu GATE.METRIC.11, getwistete DHR/Longo–Roberts-Sektoren, Haag-Dualität/Split) (16 Checks, ~2 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv746_phys_gnet_local_functor.py", "sourceSha256": "464d00726d312d88e9cfd07b8edaff2e38104fbbd9f0788be5cd4f26309753d7", "linkedClaimIds": [ "GNET.LOCALNET.01" ], "sectionIds": [ "section:848c49f799255f4cda92", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:cbcb5b486b59ced607c8", "section:dcbb8ba68bde5b18c375", "section:e8967e47143a0fba6b23", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:ab9e7e520130ecc7da7c", "section:cbcb5b486b59ced607c8", "section:dcbb8ba68bde5b18c375", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v746_phys_gnet_local_functor.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v746_phys_gnet_local_functor.py", "pubMirrorHash": "464d00726d312d88e9cfd07b8edaff2e38104fbbd9f0788be5cd4f26309753d7", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v746_phys_gnet_local_functor.py" }, { "id": "v752_projective_hamming_incidence", "filename": "v752_projective_hamming_incidence.py", "path": "verification/v752_projective_hamming_incidence.py", "cluster": "core", "synopsis": "E8.PROJHAMMING.01: das projektive Hamming-Inzidenzlemma auf V = L/(1+i)L — der symplektische F2^4 des unimodularen hermiteschen E8-Gitters, und die v737-Auflösung — **PROJ-HAMMING-EXACT: h = H/4 ist Z[i]-wertig mit hermitescher Gram-Determinante 1 (Z[i]-UNIMODULAR); h̄ alternierend (doubly-even), nicht-entartet ⇒ (V, h̄) symplektisch mit expliziter Darboux-Basis; |H_y| = 7, Paarschnitte 3; B Bᵀ = 4I + 3J EXAKT, char. Polynom (x−7)(x−2)⁹(x+2)⁵ — die Multiplizitäten (1, 9, 5) sind die SYMPLEKTIK-Signatur; K² = (4/49) I + (45/49) Π₀ exakt (K selbst ehrlich nicht psd); NS/R-χ = h̄(·, y0) für den EINDEUTIGEN σ-fixen Punkt y0 = FSUM (das Anker-Bit), 112 + 128 = 240, +8 Cartan: 248 = 120 + 128; DIE v737-AUFLÖSUNG: Verteilung 0:96/1:64/2:64/3:16 exakt abgeleitet (16 × 3×5-Label-Tafel) UND die 5×48-Koordinatisierung existiert via genau EINEN ū-invarianten Spread (Kill erklärt, nicht revidiert)**; zwei ehrliche Korrekturen an der Review-Herleitung dokumentiert; Lean-Begleitmodul ProjectiveHamming.lean (32 Theoreme) (36 Checks, ~5 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv752_projective_hamming_incidence.py", "sourceSha256": "9d3b20e18493937546bf69c37978b0df327b2d2b2a4d6985c387224acd4a61d2", "linkedClaimIds": [ "E8.PROJHAMMING.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:1234c1fa7fdc0d6d5b35", "section:2678ed3ba0ed508e2d8e", "section:51e91159532ef7479ff8", "section:6c4044608163b007c4c2", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:93b8868beb643874af75", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:dcbb8ba68bde5b18c375", "section:eb00caf29086b02d5bf5", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:1234c1fa7fdc0d6d5b35", "section:51e91159532ef7479ff8", "section:6c4044608163b007c4c2", "section:ab9e7e520130ecc7da7c", "section:dcbb8ba68bde5b18c375", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v752_projective_hamming_incidence.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v752_projective_hamming_incidence.py", "pubMirrorHash": "9d3b20e18493937546bf69c37978b0df327b2d2b2a4d6985c387224acd4a61d2", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v752_projective_hamming_incidence.py" }, { "id": "v757_fano_disc7_bridge", "filename": "v757_fano_disc7_bridge.py", "path": "verification/v757_fano_disc7_bridge.py", "cluster": "core", "synopsis": "QGEO.FANODISC7.01: die preregistrierte Fano→Diskriminante(−7)-Brücke — die Dreizyklus-Hälfte real, die Paritäts-Hälfte stirbt arithmetisch — **FANO-DISC7-DECORATIVE (Bruch exakt bei Bedingung 2): das NS/R-Paritäts-Bit hat KEINEN arithmetischen Träger in O_{−7} — 2 SPALTET in Q(√−7) (−7 ≡ 1 mod 8, O ⊗ Z₂ = Z₂ × Z₂), jeder 2-adische Idealquotient hat 2-Rang ≤ 2 < 3 (vollständiger Zensus aller Norm-8/16-Ideale): die Code-F₂-Strukturen sind arithmetisch UNREALISIERBAR; DIE REALE HÄLFTE (COND1, exakt): äquivariante Lifts existieren für beide kanonischen Differenzmengen-Fano-Modelle, die kanonische Ordnung-3-Wirkung ist x → 2x (der Differenzmengen-Multiplikator, 2 = der Transfer-Schritt), jeder Lift schickt den eindeutigen σ̄-Fixpunkt auf 0 = red(α₀) = die C-Ecke (Norm 14 = dim G2)**; die Sieben-Korrelation dauerhaft als DEKORATIV getypt; Kontrollen feuern; der eine [FAIL] = der preregistrierte COND2-Bruch (26 Checks, ~1 s)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv757_fano_disc7_bridge.py", "sourceSha256": "9363d7966a2d1bdc41e86e86f62a7d511eee2e19df5a641ed7778b0fcb458735", "linkedClaimIds": [ "QGEO.FANODISC7.01" ], "sectionIds": [ "section:848c49f799255f4cda92", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:dcbb8ba68bde5b18c375", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:ab9e7e520130ecc7da7c", "section:dcbb8ba68bde5b18c375", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v757_fano_disc7_bridge.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v757_fano_disc7_bridge.py", "pubMirrorHash": "9363d7966a2d1bdc41e86e86f62a7d511eee2e19df5a641ed7778b0fcb458735", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v757_fano_disc7_bridge.py" }, { "id": "v774_arf_spinor_compiler", "filename": "v774_arf_spinor_compiler.py", "path": "verification/v774_arf_spinor_compiler.py", "cluster": "core", "synopsis": "ARF.SPINORCOMPILER.01: der Arf/Spinor-Compiler auf V = L/(1+i)L = F2^4 (Priorität 1 des Arf-Programms) — **ARF-SPINOR-EXACT (46/46, ~2 s, null Kills, beide Must-fail-Kontrollen feuern): der Paritäts-Lift iota: V ≅ C_even(5) trägt beta = hbar EXAKT in allen 256 Zellen (Crosslink 1); Brute force über alle 2^16 Funktionen: GENAU 16 quadratische Verfeinerungen; Arf-Zensus 6 + 10 mit |Sp(4,2)| = 720 (voller 65536-Matrix-Zensus) und treuer+surjektiver S6-Wirkung; der eingefrorene Selektor (sigma-Invarianz 4 -> q(A) = 1: 2 -> q(F_Sigma) = 0: 1) wählt ein EINDEUTIGES q*, und die Gewichtsform q_wt IST q* (Offset 0; alle 16 Verfeinerungen = q* + hbar(., c) bijektiv); Stab(q*) ≅ S5 liefert 16 = 1 + 5bar + 10 auf Verfeinerungen UND Worten; das K6-Duaden-Modell ist eine Sp/sigma-äquivariante Bijektion auf E(K6) (Split 5 + 10); B = I + A_KG(6,2) in allen 225 Zellen, Charpoly (x-7)(x-2)^9(x+2)^5, Ovoid-Eigenvektor EXAKT (die 6 Indikatoren spannen den (-2)-Raum); alle 6 voll-isotropen Spreads tragen q*-Signatur (1, 2); die Hyperladungs-Tafel X = (-2,-2,-2,3,3) reproduziert das v310/v14-Wörterbuch (Werte UND Multiplizitäten); Code-Polynom-Momente (16, 0, 120, 0) mit der Kette 40/41/240/248 (v2-Master-Moment 120 = 5!); Pati–Salam 8 + 8 mit B-L = 1 - 2 n_c/3 exakt; chi_NSR = das Anker-Bit a. SEMANTIK-TRENNUNG: A3^Fam (Familienzyklus) != A3^PS (3+2-Slot-Split) — dasselbe sigma, zwei Register. ZAUN: die Code->Materie-Lesart ist NICHT beansprucht — v775 tötet sie auf Wurzel-Niveau. Lean-Begleitmodul ArfSpinorCompiler.lean (23 Kernel-Theoreme, lake build grün)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv774_arf_spinor_compiler.py", "sourceSha256": "3ef92c17d9f0de62212bab940ac2c017be866645d8a5b276bdcf2d92128bae8c", "linkedClaimIds": [ "ARF.SPINORCOMPILER.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:10e10da547a5ac9014b8", "section:1234c1fa7fdc0d6d5b35", "section:2678ed3ba0ed508e2d8e", "section:51e91159532ef7479ff8", "section:5cd560246f81af39b2ac", "section:6c4044608163b007c4c2", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:93b8868beb643874af75", "section:ab9e7e520130ecc7da7c", "section:bc80e633fbb98ca8173d", "section:c4cf080b9ae6f25f7a71", "section:dcbb8ba68bde5b18c375", "section:eb00caf29086b02d5bf5", "section:eb5830602d5801bd979a", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:10e10da547a5ac9014b8", "section:1234c1fa7fdc0d6d5b35", "section:51e91159532ef7479ff8", "section:6c4044608163b007c4c2", "section:ab9e7e520130ecc7da7c", "section:bc80e633fbb98ca8173d", "section:dcbb8ba68bde5b18c375", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v774_arf_spinor_compiler.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v774_arf_spinor_compiler.py", "pubMirrorHash": "3ef92c17d9f0de62212bab940ac2c017be866645d8a5b276bdcf2d92128bae8c", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v774_arf_spinor_compiler.py" }, { "id": "v775_gaussian_class_d5_purity", "filename": "v775_gaussian_class_d5_purity.py", "path": "verification/v775_gaussian_class_d5_purity.py", "cluster": "core", "synopsis": "ARF.ROOTCLASS.01: der GEFEUERTE physikalische Kill des Arf-Compiler-Programms — **ROOTCLASS-MIXED (18/18, alle 3 Kontrollen feuern; FROZEN_SPEC SHA-256 58d9be9b… gehasht VOR allen Wurzeldaten): KEINE D5⊕A3/SU(5)-Konvention macht auch nur EINEN vollen Satz von 15 Gauß-Klassen rein — die einbettungs-UNABHÄNGIGE Zählschranke (jede Einbettung hat genau 128 Spinor-Wurzeln, 240 > 128) erzwingt >= 7 Adjoint-seitige Klassen für JEDE D5⊕A3-Einbettung; der erschöpfende Konventions-Scan (56 Splits x 240 Zuordnungen x 2 Chiralitäten) findet NULL reine Konventionen; alle 8 Spinor-Klassen mischen je 8 verschiedene 16-Gewichts-Paare (bestes Match des eingefrorenen linearen Wörterbuchs 8/128; X-Purity sekundär 0/15). KONSEQUENZ (Zaun, bindend): die Code->Materie-Lesart darf in KEINEN Hauptclaim — einschließlich der 'leerer-Briefkasten = rechtshändiges Neutrino'-Lesart; die Arf-Mathematik von v774 bleibt unberührt. Kontrollen: falsche Ladungsvektoren, LCG-Scramble, falsche symplektische Form (alle feuern)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv775_gaussian_class_d5_purity.py", "sourceSha256": "f6d503b943d202465e69cd40606572d42eedde7c06af4201db65be539817d2f6", "linkedClaimIds": [ "ARF.ROOTCLASS.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:1234c1fa7fdc0d6d5b35", "section:2678ed3ba0ed508e2d8e", "section:51e91159532ef7479ff8", "section:6bcd4464dbd4c8f8f003", "section:6c4044608163b007c4c2", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:dcbb8ba68bde5b18c375", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:1234c1fa7fdc0d6d5b35", "section:51e91159532ef7479ff8", "section:6bcd4464dbd4c8f8f003", "section:6c4044608163b007c4c2", "section:ab9e7e520130ecc7da7c", "section:dcbb8ba68bde5b18c375", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v775_gaussian_class_d5_purity.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v775_gaussian_class_d5_purity.py", "pubMirrorHash": "f6d503b943d202465e69cd40606572d42eedde7c06af4201db65be539817d2f6", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v775_gaussian_class_d5_purity.py" }, { "id": "v776_boundary_hamming_uniqueness", "filename": "v776_boundary_hamming_uniqueness.py", "path": "verification/v776_boundary_hamming_uniqueness.py", "cluster": "core", "synopsis": "ARF.BOUNDARY.CODE.01: Rand-Code-Eindeutigkeit — **BOUNDARY-CODE-UNIQUE (31/31): die nicht-zirkuläre Kette Rand -> Code -> E8 -> F2^4 -> 5 Slots SCHLIESST mit g_car = 5 als OUTPUT — Zensus 135 -> 30 -> 14 -> 2 -> 1 ohne Hamming/E8-Input; das Flag-Datum ist EIN deck-invariantes Z2 (Produkt der vier Seiten-Orientierungen; alle drei vordeklarierten Formalisierungen wählen denselben Code, alle 16 Flag-Zuordnungen entscheiden nur über sum(s) mod 2); die Rand-Eichgruppe (Zentralisator, Ordnung 12) macht das flaglose Zweifach pure Eichung; Construction A -> E8 EXAKT (240/2160-Theta, Cartan det 1, Arme 1-2-4; Post-Selektions-Check: Gewicht-4-Träger == die deployte v638-C*-Liste); q* eindeutig mit der rand-kanonischen Anker-Benennung; Pakete 1 + 4 -> g_car = 5. EHRLICHE RESIDUEN: R1 die Universums-Prämisse (doppelt-gerade Selbstdualität — die Zirkularität ist VERLAGERT und GESCHRUMPFT, nicht entfernt), R2 Deck-Platzierungs-Blindheit (SEMANTISCH, getypt — die Wrong-Deck-Kontrolle feuert nicht), R3 Anker-Benennung (bbar(F_Sigma, A) = 1). KEIN P2-Entfernungs-Claim; die neue Vertragsform (Evenness/Selbstdualität aus den Naht-Axiomen ableiten) als ARF.BOUNDARY.CODE.01 [O] registriert", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv776_boundary_hamming_uniqueness.py", "sourceSha256": "2d1624a3ab822b96d69fd5ca8848a54f8ee092fdff1e5c3e6d71a50fafb641e4", "linkedClaimIds": [ "ARF.BOUNDARY.CODE.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:1234c1fa7fdc0d6d5b35", "section:2678ed3ba0ed508e2d8e", "section:51e91159532ef7479ff8", "section:6bcd4464dbd4c8f8f003", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:93b8868beb643874af75", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:dcbb8ba68bde5b18c375", "section:eb00caf29086b02d5bf5", "section:f091de1c3533bab48372", "section:f22c82858ff073c133d4" ], "activeSectionIds": [ "section:1234c1fa7fdc0d6d5b35", "section:51e91159532ef7479ff8", "section:6bcd4464dbd4c8f8f003", "section:ab9e7e520130ecc7da7c", "section:dcbb8ba68bde5b18c375", "section:f091de1c3533bab48372", "section:f22c82858ff073c133d4" ], "evidenceId": "python_verification:verification/v776_boundary_hamming_uniqueness.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v776_boundary_hamming_uniqueness.py", "pubMirrorHash": "2d1624a3ab822b96d69fd5ca8848a54f8ee092fdff1e5c3e6d71a50fafb641e4", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v776_boundary_hamming_uniqueness.py" }, { "id": "v777_ftransfer_clock_jets", "filename": "v777_ftransfer_clock_jets.py", "path": "verification/v777_ftransfer_clock_jets.py", "cluster": "core", "synopsis": "FTRANSFER.CLOCKS.01 AUSGEFÜHRT + die gefaserte Verfeinerung von CONTRACT.F.01, EIN Modul aus zwei Probes — **NO-COMMON-CONNECTION + FTRANSFER-FIBERED-CARRIES (24 + 14 Checks, 0 Fails): der präregistrierte K1-Kill EXAKT wie der eingefrorene Prior erwartet (Prereg-YAML 880224f7… byte-verifiziert; Datentabellen VOR dem ersten Lauf kuratiert + eingefroren: Saikawa–Shirai g_*s 8ae2a4fe…, PDG-2024 alpha_s 2ca6332d…); alle vier Wörterbücher konstruktions-valide (Koide-Schema-Check 571x, Washout-Drift 1.15e-4, QCD-Overlay 0.83%, Relikt-Steigung 0.0602); der Kill sympy-exakt {-Δ²/2, -Δ²/2, 0} — ein Pass bräuchte GENAU den verbotenen nicht-affinen Möbius-Clock (K1-Duty exhibiert). Die diskrete Schicht koinzidiert EXAKT (CR = 4/3 symbolisch, Deck-Einheit |Δσ| = 1, unit-parabolische Klasse — v632 gitter-explizit); die Obstruktion ist der KONSTANTE Naht-Kozykel mit Werten exakt {0, ±Δ²/2} (Antisymmetrie + Kozykel-Identität exakt, d/dσ ≡ 0 auf 50 Digits); Klassifikation = der vordeklarierte Thermal-vs-RG-Marker; Relikt degeneriert unklassifiziert; alle Kontrollen inkl. Möbius-Transplantat feuern; das float64-Artefakt des ersten Groupoid-Laufs offengelegt, Schranke unberührt. Die Jet-Route von CONTRACT.F.01 schließt auf Physik-Clock-Ebene; nächster benannter proof-grade Schritt: die Coset-Zuordnung aus KMS/modularer Clock-Typisierung ableiten", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv777_ftransfer_clock_jets.py", "sourceSha256": "af2e26cb676946b868807b5ba1dbbf367ae1805c3c8ca5177f4d52d81da80dde", "linkedClaimIds": [ "FTRANSFER.CLOCKS.01" ], "sectionIds": [ "section:01c88746fb95cc0958d7", "section:568b5e9acdb7b04367d3", "section:5c7b501c80f2e5816761", "section:848c49f799255f4cda92", "section:98cf6dab6e992992d2c9", "section:a3401d23c565056512c5", "section:ab9e7e520130ecc7da7c", "section:c160f54e23592ab7f2ef", "section:c4cf080b9ae6f25f7a71", "section:dcbb8ba68bde5b18c375", "section:f0ac30137703825661c6", "section:fbc55d19f88e095d54eb", "section:fdf63a1d99769ab37ccb" ], "activeSectionIds": [ "section:01c88746fb95cc0958d7", "section:a3401d23c565056512c5", "section:ab9e7e520130ecc7da7c", "section:dcbb8ba68bde5b18c375", "section:fbc55d19f88e095d54eb", "section:fdf63a1d99769ab37ccb" ], "evidenceId": "python_verification:verification/v777_ftransfer_clock_jets.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v777_ftransfer_clock_jets.py", "pubMirrorHash": "af2e26cb676946b868807b5ba1dbbf367ae1805c3c8ca5177f4d52d81da80dde", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v777_ftransfer_clock_jets.py" }, { "id": "v778_qgeo_gridsup_logsum", "filename": "v778_qgeo_gridsup_logsum.py", "path": "verification/v778_qgeo_gridsup_logsum.py", "cluster": "core", "synopsis": "QGEO.GRIDSUP.01: Rest (a) des (L1)-Majoranten-Lemmas VOLL geschlossen in der korrigierten (1 + ln M)-Form, EIN Modul aus zwei Probes — **GRIDSUP-SPLIT-CLOSED-LOG-LAW + FOURIER-LOGSUM-CLOSED (19/19 + 19/19): der v745-Rest (a) spaltet vierfach — (a1) das Kontinuums-Supremum GESCHLOSSEN (Taylor 5/8 symbolisch + Hüllkurven symbolisch; ~1.26e6 Zensus-Ungleichungen, 0 Verletzungen), (a2) Konfigurations-S1 GESCHLOSSEN mit explizitem B_conf(ε) (Packung + Nachbar-Leiter + ζ(2)/ζ(3)), (a3) der Verfeinerungs-Rest GESCHLOSSEN mit RHO(ε) via exakten csc³-Integralen (uniform über ALLE M <= N/2), (a4) der führende Teil ist ehrlich LOG-divergent (sprung-getrieben, Taper-kontrolliert) — die wörtliche v715-Klausel 'ein B(ε) für ALLE Gitter-Verfeinerungen' ist bei r1 = 1 FALSCH und wird zu (1 + ln M) repariert; die überlebende Ungleichung auf THEOREM-Niveau zertifiziert: exakte ν-getwistete Zirkulanten-Diagonalisierung + zwei exakte zyklische Summationen-nach-Teilen + harmonischer Vergleich: ||F_q^(M)(ε)||₁ <= c0(q,ε) + (J(ε)/4) ln(M+3), a fortiori (J/π) ln M, J = 2|f_q'(ε)|, alle Konstanten exakte csc-Integrale/Hüllkurven; 162-Fälle-Zensus bis M = 6144 mit 0 Verletzungen in allen sieben Klauseln; die reparierte (L1)-Klausel ||D_N^(M)||₁ <= [B0 + (J/2) ln(M+3)]/N auf allen 252 Transfer-Fällen verifiziert; Araki/Powers-Størmer-Summierbarkeit in expliziter geschlossener Form. EHRLICH: die gemessene Steigung ist J/π² (Spike-Interferenz) — die Schranke ist valide, NICHT scharf. Residuen (b) L2 / (c) L3 unberührt und offen; GATE.QGEO bewegt sich NICHT", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv778_qgeo_gridsup_logsum.py", "sourceSha256": "c560f66ee97b509c2e3ec4a0506842d2cf5a148a3a8a7468c7b9fc8243582bf7", "linkedClaimIds": [ "QGEO.GRIDSUP.01" ], "sectionIds": [ "section:83d94e33024ba3df4db8", "section:848c49f799255f4cda92", "section:93b8868beb643874af75", "section:9a6aaf6fc60f9b74b301", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:dcbb8ba68bde5b18c375", "section:eb00caf29086b02d5bf5", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:83d94e33024ba3df4db8", "section:9a6aaf6fc60f9b74b301", "section:ab9e7e520130ecc7da7c", "section:dcbb8ba68bde5b18c375", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v778_qgeo_gridsup_logsum.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v778_qgeo_gridsup_logsum.py", "pubMirrorHash": "c560f66ee97b509c2e3ec4a0506842d2cf5a148a3a8a7468c7b9fc8243582bf7", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v778_qgeo_gridsup_logsum.py" }, { "id": "v779_gnet_gns_arf", "filename": "v779_gnet_gns_arf.py", "path": "verification/v779_gnet_gns_arf.py", "cluster": "core", "synopsis": "GNET.GNSLIMIT.01: der G_net-Kontinuums-Strang, EIN Modul aus zwei Probes — **GNS-PRECURSORS-COHERENT + GNET-ARF-NO-CORRESPONDENCE (27/27 + 27/27): die Haar-Skalierungs-Isometrie intertwinet EXAKT (<= 2.2e-16), die kommutierenden Index-4-Erwartungs-Quadrate sind exakt (<= 1.5e-14), der kanonische Zustand ist Cauchy geometrisch ~1/4 pro Verdopplung, der Index-Zensus ist maschinen-exakt auf JEDER Stufe ohne Degradation, der getwistete Haag-Dualitäts-Defekt = 0 mit dim B'/dim A' = 4 = Watatani-Index (l = 1: 3); 10-Abschnitts-Kontinuums-Paper-Skelett. Das EXAKTE Dimensions-Gesetz d_c(l) = 4^(l-1) + 2^(l-1) cos(πc/2) macht die C[Z4]-Quasi-Basis-Obstruktion exakt 2^-l (asymptotisch restauriert — der endliche Vorläufer der GATE.METRIC.08/11-Identifikation) und ERKLÄRT die l = 1-Anomalie (d_2(1) = 0); explizite 185-Element-Quasi-Basis bei l = 2 (sum v v* = 4·1 exakt); sektor-aufgelöste uniforme Split-Schranken entlang des Turms. DAS EHRLICHE NEGATIV, erschöpfend: das 16 = 1 + 5 + 10-Zähl-Echo ist REAL und exakt, aber NICHT geometrisch (F2-Rang-Zertifikat 3 vs 4, GL(4,2)-Zensus 0/20160, kein nichttrivialer interner Ordnung-3-Träger); K_matter regiert den Turm-Gewichts-Transport NICHT (x5 = (0.414, 0.586) vs (1/3, 2/3)); die zwei Vieren (Index 4 = |mu4| vs Kanal 4/49) bleiben in ihren Registern. Alle fünf Kontrollen feuern", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv779_gnet_gns_arf.py", "sourceSha256": "54f31b454b0cd1ed8fe327d42cadc5ba2a08e582b1529773d33a478af1d20256", "linkedClaimIds": [ "GNET.GNSLIMIT.01" ], "sectionIds": [ "section:848c49f799255f4cda92", "section:93b8868beb643874af75", "section:9a6aaf6fc60f9b74b301", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:cb1bdab881371b610e8f", "section:cbcb5b486b59ced607c8", "section:d0d4a62b7872b9bb3a1c", "section:d3f2b7d7ec6acb95794a", "section:dcbb8ba68bde5b18c375", "section:e8967e47143a0fba6b23", "section:eb00caf29086b02d5bf5", "section:eea2436d67f35ca41c00", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:9a6aaf6fc60f9b74b301", "section:ab9e7e520130ecc7da7c", "section:cbcb5b486b59ced607c8", "section:d0d4a62b7872b9bb3a1c", "section:dcbb8ba68bde5b18c375", "section:eea2436d67f35ca41c00", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v779_gnet_gns_arf.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v779_gnet_gns_arf.py", "pubMirrorHash": "54f31b454b0cd1ed8fe327d42cadc5ba2a08e582b1529773d33a478af1d20256", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v779_gnet_gns_arf.py" }, { "id": "v781_one_object_clock_census", "filename": "v781_one_object_clock_census.py", "path": "verification/v781_one_object_clock_census.py", "cluster": "core", "synopsis": "E8.ONEOBJECT.01: der d = 4-Forcing-Zensus + der 60-Linien-Uhren-Kill, EIN Modul aus zwei Probes — **ONE-OBJECT-PARTIAL + CLOCK-FIBER-DEAD (21/21 + 23/23): das TFPT-Glue-Muster (zyklische isotrope Verklebung, Geradheit q = 0 mod 2Z, Unimodularität |H|² = 4d) lässt eine gerade unimodulare DIAGONALE Verklebung von A_{d−1} ⊕ D_{d+1} GENAU für d = 4 zu (Zensus d = 2..12, exakte Brüche; bei d = 4 exakt die zwei v92-Lagrangians k -> k und k -> 3k; explizites E8-Zertifikat mit 240 Norm-2-Vektoren; d = 9 stirbt an der Isotropie; beide Relaxations-Kontrollen feuern) — Korollare am erzwungenen d: g_car = d+1 = 5, N_fam = d−1 = 3, Rang 2d = 8, Index 4 = d = |mu4|; EHRLICHKEITS-GATE: c3 = 1/(2πd)|_{d=4} = 1/(8π) ist eine korpus-legitime UMSCHREIBUNG (v23-Anker), KEINE neue P1-Ableitung. DER UHREN-KILL: die Faserprodukt-Wirkung Z12 ×_{Z6} Z30 auf den 60 Gauß-Linien ist auf DREI Ebenen tot — die Coxeter-Uhr erhält die Linien-Partition nicht; die VOLLE linien-kompatible Gruppe hat Ordnung 23040 mit maximaler Elementordnung 12 (Ordnungen 15/30/60 fehlen für JEDE Realisierung); das Faserprodukt selbst ist zyklisch Z60 (exakte SNF-Arithmetik); alle drei Kontrollen feuern (CC2-Sampler-Korrektur offengelegt)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv781_one_object_clock_census.py", "sourceSha256": "97e046cf4d06d09e8ac7dafd8ec592f7a34e7164a7e75774c46ff9c671e8cdfa", "linkedClaimIds": [ "E8.ONEOBJECT.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:10e10da547a5ac9014b8", "section:6c4044608163b007c4c2", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:dcbb8ba68bde5b18c375", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:10e10da547a5ac9014b8", "section:6c4044608163b007c4c2", "section:ab9e7e520130ecc7da7c", "section:dcbb8ba68bde5b18c375", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v781_one_object_clock_census.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v781_one_object_clock_census.py", "pubMirrorHash": "97e046cf4d06d09e8ac7dafd8ec592f7a34e7164a7e75774c46ff9c671e8cdfa", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v781_one_object_clock_census.py" }, { "id": "v782_e8_transition_bus", "filename": "v782_e8_transition_bus.py", "path": "verification/v782_e8_transition_bus.py", "cluster": "core", "synopsis": "E8.TRANSITIONBUS.01: der Transition-Bus-Struktursatz — **TRANSITION-BUS-TORSOR (35/35): die 240 Wurzeln des unimodularen hermiteschen Gauß-E8 sind 15 disjunkte Koordinaten-8-Rahmen über der Klassenabbildung V = L/(1+i)L; auf L/2L sind die 120 Wurzel-PAARE exakt die 120 q = 1-Punkte des Plus-Typ-Quadratraums, und die 8 Paar-Bilder jeder Klasse bilden einen kanonischen TORSOR unter v_perp (affiner F2³ ohne ausgezeichneten Ursprung); das Deck J wirkt als Translation um v; der OBSTRUKTIONS-Zensus ist beweisfest: KEINE deck-äquivariante Wurzel-Etikettierung R(E8) = V × (V∖0) existiert (−1 frei auf Wurzeln, trivial auf Paaren; J ist 4-Zyklus, Torsor-Translationen Ordnung ≤ 2); das eingefrorene symplektische Prädikat reproduziert ALLE 57600 geordneten Skalarprodukte inkl. Vorzeichengesetz und h-Verfeinerung; Spread-Schicht 240 = 5 × 3 × 16 mit dem q*-Selektor; der A15-Vergleich quantifiziert (A15 ist ein strikter Bus MIT kanonischem Startzustand, E8 beweisbar OHNE; Nicht-Orthogonalität exakt verdoppelt 26880 vs 13440); Kontrollen C1–C3 feuern (C3-Kontroll-Design-Korrektur offengelegt)", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv782_e8_transition_bus.py", "sourceSha256": "86a98edd4ae409a24a75be9d75edef19ea164c06eb24773830dbd4baeb67c407", "linkedClaimIds": [ "E8.TRANSITIONBUS.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:10e10da547a5ac9014b8", "section:6c4044608163b007c4c2", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:93b8868beb643874af75", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:eb00caf29086b02d5bf5", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:10e10da547a5ac9014b8", "section:6c4044608163b007c4c2", "section:ab9e7e520130ecc7da7c", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v782_e8_transition_bus.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v782_e8_transition_bus.py", "pubMirrorHash": "86a98edd4ae409a24a75be9d75edef19ea164c06eb24773830dbd4baeb67c407", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v782_e8_transition_bus.py" }, { "id": "v783_two_qubit_clifford", "filename": "v783_two_qubit_clifford.py", "path": "verification/v783_two_qubit_clifford.py", "cluster": "core", "synopsis": "E8.CLIFFORD2Q.01: die Zwei-Qubit-Stabilizer-Identifikation des Compiler-Trägers — **CLIFFORD-PARTIAL(H4) (32/32): unter der EINEN vordeklarierten Karte U (Koordinaten-Klassen-Rahmen -> Rechenbasis, z_k = r_{2k} + i r_{2k+1}) SIND die 60 Gauß-E8-Linien die 60 reinen Zwei-Qubit-Stabilizer-Strahlen, eintrags-exakt über Z[i] (60/60; Träger-Zensus 4 + 24 + 32 beidseits); U G31 U^{-1} ist Index-2-Untergruppe der Zwei-Qubit-Clifford-Matrixgruppe (|C2| = 92160 = 2 × 46080, Nebenklasse zeta8 G31; projektiv gleich, beide 11520); 46080 = 4 × 16 × 720 = mu4 × Pauli16 × Sp(4,2) mit den 15 Klassen = 15 Pauli-Kontexten (W(3,2) = GQ(2,2)-Identifikation, alle 105 Paare), die 6 Spreads = MUB-Pentaden (|⟨psi|phi⟩|² = 1/4 exakt); H4 FÄLLT WIE VORDEKLARIERT: das Index-Bit konjugiert WEDER J noch mu4 — es ist das Galois-sqrt2/Hadamard-Bit Gal(Q(zeta8)/Q(i)) (tauscht die zwei mu8-Lift-Klassen), das J <-> −J-Bit ist die separate antiunitäre äußere Z2; alle vier Kontrollen feuern (T-Gate-Twist EXAKT die vordeklarierten 16/60); Stabilizer-Mathematik über den Träger — ROOTCLASS-MIXED (v775) unberührt, keine Materie-Lesart", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv783_two_qubit_clifford.py", "sourceSha256": "8f4851634b83f61671b04f3a6211059c40758d21caaf1f779302c799e1e9d6c4", "linkedClaimIds": [ "E8.CLIFFORD2Q.01" ], "sectionIds": [ "section:0360327baf7e82aba7c3", "section:0739148b5a5974d0d662", "section:0ee9c6150b29e6e55585", "section:10e10da547a5ac9014b8", "section:4d29b40dee14dd3fb5c9", "section:5cd560246f81af39b2ac", "section:6c4044608163b007c4c2", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:93b8868beb643874af75", "section:ab9e7e520130ecc7da7c", "section:bc80e633fbb98ca8173d", "section:c4cf080b9ae6f25f7a71", "section:cbcb5b486b59ced607c8", "section:e8967e47143a0fba6b23", "section:eb00caf29086b02d5bf5", "section:eb5830602d5801bd979a", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:0ee9c6150b29e6e55585", "section:10e10da547a5ac9014b8", "section:6c4044608163b007c4c2", "section:ab9e7e520130ecc7da7c", "section:bc80e633fbb98ca8173d", "section:cbcb5b486b59ced607c8", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v783_two_qubit_clifford.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v783_two_qubit_clifford.py", "pubMirrorHash": "8f4851634b83f61671b04f3a6211059c40758d21caaf1f779302c799e1e9d6c4", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v783_two_qubit_clifford.py" }, { "id": "v784_curve_code_2torsion", "filename": "v784_curve_code_2torsion.py", "path": "verification/v784_curve_code_2torsion.py", "cluster": "core", "synopsis": "CURVE.CODE.2TORSION.01: der Kurven/Code-2-Torsions-Entscheider — **CURVE-CODE-PARTIAL (33/33): die eingefrorene CM-Modell-Route durch die Naht-Kurve y³ = x⁴ − 1 (exakte Differentialcharaktere zeta^11, zeta^7 = v610; JEDE Generator-Periode als ganzzahlige O = Z[zeta_12]-Erkennung zertifiziert, dps 120, Residuen < 1e−35, HNF-Index 1; A[2] = O/2O = F2⁴ ab dort EXAKT; tau = Mult. mit zeta⁴ als einzige Ordnung-3-Klasse ABGELEITET; minimale UNGERADE tau-invariante Polarisation Typ (1,3) — keine Hauptform im tau-invarianten Kegel, Einheiten-Vorzeichen-Obstruktion; q_Theta = die eindeutige tau-fixe Verfeinerung): die Korrespondenz STIRBT an zwei exakten Schichten — (1) SIGMA: tau wirkt FREI auf A[2] (Zykeltyp [3,3] auf den 6 ungeraden Theta-Charakteristiken, Synthem-Seite), der Code-sigma-bar fixiert eine 2-Ebene ([3,1,1,1], Duaden-Seite) — nur die ÄUSSERE S6-Automorphie tauscht die Klassen, äquivarianter Zensus 0; (2) VERFEINERUNG: q_Theta ist GERADE (Arf 0, 1+6+9), der Code-Selektor q* UNGERADE (Arf 1, 1+5+10) — Arf ist Transport-Invariante, Zensus 0; Gesamt-Zensus 0 mit Positiv-Kontrolle 6; alle Muss-Kontrollen feuern", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv784_curve_code_2torsion.py", "sourceSha256": "7633435fe362aad85b0af60f877f26db07ad411fe60259be1ee687b8939d5baf", "linkedClaimIds": [ "CURVE.CODE.2TORSION.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:10e10da547a5ac9014b8", "section:6c4044608163b007c4c2", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:93b8868beb643874af75", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:eb00caf29086b02d5bf5", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:10e10da547a5ac9014b8", "section:6c4044608163b007c4c2", "section:ab9e7e520130ecc7da7c", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v784_curve_code_2torsion.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v784_curve_code_2torsion.py", "pubMirrorHash": "7633435fe362aad85b0af60f877f26db07ad411fe60259be1ee687b8939d5baf", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v784_curve_code_2torsion.py" }, { "id": "v792_ftransfer_kms_coset", "filename": "v792_ftransfer_kms_coset.py", "path": "verification/v792_ftransfer_kms_coset.py", "cluster": "core", "synopsis": "FTRANSFER.KMSCOSET.01: die Coset-Zuweisung des gefaserten Uhren-Funktors ist ein THEOREM aus KMS/modularem Typing — **KMS-COSET-THEOREM (18/18): S = −(ln λ)²/2 mit λ = dem PGL2-Multiplikator der Zeit-1-Holonomie pro Uhren-e-Fold; 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der äußere Zeuge exakt ([3,1,1,1] ↔ [3,3] uniform); q_Θ zieht sich KONSTANT auf q_even* zurück mit q* = q_even* + h̄(·, A) — der Anker-Shift löst den v784-Arf-Konflikt kanonisch; 5̄/10 und 3+2 transportieren exakt auf die S*-Linien-Geometrie; t_A ↦ ρ = J auf jeder Brücke; chi_NSR ein ehrlicher exakter ZWEI-Varianten-Torsor (durch die v752-NS/R-Parität gepinnt); Kontrollen: innere Zensus 0/0, ungerader Arf-Rückzug 0, gestörtes σ 0; die INNERE Identifikation bleibt tot (v784); keine Materie-Semantik", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv796_duad_syntheme_bridge.py", "sourceSha256": "06c40f938d5c69a8349c76fd408c68fdb7a49f263ca6f8a7511fff744b85d6d0", "linkedClaimIds": [ "CURVE.CODE.OUTERSPIN.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:10e10da547a5ac9014b8", "section:6c4044608163b007c4c2", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:93b8868beb643874af75", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:eb00caf29086b02d5bf5", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:10e10da547a5ac9014b8", "section:6c4044608163b007c4c2", "section:ab9e7e520130ecc7da7c", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v796_duad_syntheme_bridge.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v796_duad_syntheme_bridge.py", "pubMirrorHash": "06c40f938d5c69a8349c76fd408c68fdb7a49f263ca6f8a7511fff744b85d6d0", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v796_duad_syntheme_bridge.py" }, { "id": "v798_seam_clifford_modular_s", "filename": "v798_seam_clifford_modular_s.py", "path": "verification/v798_seam_clifford_modular_s.py", "cluster": "core", "synopsis": "SEAM.CLIFFORD.MODULAR_S.01: das fehlende Clifford-Bit als metaplektischer Lift des modularen S bei τ = i — **MODULAR-S-PARTIAL (27/27): COSET POSITIV — der Pro-Binärfaktor-Hadamard K1 = H ⊗ I IST der Weil-Lift von S bei τ = i und landet exakt in der fehlenden Nebenklasse ζ₈ G31 (exakte Relationen S² = I, T² = Pauli-Parität, (TK)³ = ζ₈ I); der TOTALE Fourier H ⊗ H liegt IN G31 mit metaplektischer Anomalie (T3 K3)³ = i I = J — das Deck IST die Anomalie des totalen modularen Lifts (R2 platziert); ζ₈ = (1+J)/√2 das reelle Halb-Deck, das das Naht-Paar {L, ζ₈L} tauscht; F4 als Nicht-Trägersymmetrie ausgetypt; OS-Reflexions-Gate exakt. DER STRIKTE EINDEUTIGKEITS-ZENSUS IST LEER (0/46080): kein Θ-reelles metaplektisches Element der Nebenklasse fixiert q* — der Arf-Defekt ist unvermeidlich; retypter Zensus: 32 Überlebende = EINE G31-Konjugationsklasse; R3 BENANNT, nicht fixiert: die σ-Orbit-Defekte sind exakt {A + F_Σ + F_i} mit XOR = der Anker A selbst; Kontrollen: CZ in G31, falsche Phase bricht S², Selektivität 480 → 96 → 32", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv798_seam_clifford_modular_s.py", "sourceSha256": "957dc3e396b3b3ea47acf366b22c70c3237d80313826b3b5646b8387d2061e3b", "linkedClaimIds": [ "SEAM.CLIFFORD.MODULAR_S.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:0ee9c6150b29e6e55585", "section:10e10da547a5ac9014b8", "section:2678ed3ba0ed508e2d8e", "section:51e91159532ef7479ff8", "section:6c4044608163b007c4c2", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:93b8868beb643874af75", "section:ab9e7e520130ecc7da7c", "section:bc80e633fbb98ca8173d", "section:c4cf080b9ae6f25f7a71", "section:cbcb5b486b59ced607c8", "section:dcbb8ba68bde5b18c375", "section:e8967e47143a0fba6b23", "section:eb00caf29086b02d5bf5", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:0ee9c6150b29e6e55585", "section:10e10da547a5ac9014b8", "section:51e91159532ef7479ff8", "section:6c4044608163b007c4c2", "section:ab9e7e520130ecc7da7c", "section:bc80e633fbb98ca8173d", "section:cbcb5b486b59ced607c8", "section:dcbb8ba68bde5b18c375", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v798_seam_clifford_modular_s.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v798_seam_clifford_modular_s.py", "pubMirrorHash": "957dc3e396b3b3ea47acf366b22c70c3237d80313826b3b5646b8387d2061e3b", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v798_seam_clifford_modular_s.py" }, { "id": "v799_seam_code_typeii", "filename": "v799_seam_code_typeii.py", "path": "verification/v799_seam_code_typeii.py", "cluster": "core", "synopsis": "SEAM.CODE.TYPEII.01: Typ II aus drei physikalischen Naht-Axiomen ERZWUNGEN — der direkte Angriff auf Residual R1 von ARF.BOUNDARY.CODE.01 — **TYPEII-FORCED (19/19): erschöpfend über ALLE 308.993 Unterräume von F2⁸ (dim 0..4, Gauß-Binomiale; dim > 4 per Rang-Nullität): gegenseitige Lokalität der Construction-A-Vertex-Wörter ⇔ selbst-orthogonal (135 bei dim 4; Lift-Shift-Braiding-Identität erschöpfend); ganzzahliger konformer Spin ⇔ doppelt-gerade (30); Holomorphie/Index eins (|disc| = 1, exakte Fraction-Gram-Determinanten) ⇔ selbstdual — die Überlebenden sind EXAKT die 30 ê₈-Kopien; kein rand-legaler Nicht-Typ-II-Code existiert; jeder nicht-selbstduale doppelt-gerade Code hat einen Diskriminanten-Sektor gebrochenen Gewichts ([8,3]-Zeuge mit exakten Coset-Thetas). 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Iso eindeutig, der falsche Split-Ring F2×F2 scheitert an allen 24 Bijektionen); W = L/2L FREI vom Rang 4 über den dualen Zahlen (explizite Z[i]-Basis via Hermite-Reduktion, Kovolumen-zertifiziert); 0 → eps W → W → V → 0 exakte SELBST-Erweiterung mit ker(eps) = im(eps); das Deck IST die Jet-Einheit J = 1 + eps und reproduziert den v782-Torsor auf allen 240 Wurzeln; NULL μ₄-äquivariante Splittings unter allen 65536 linearen Schnitten — die Kein-Ursprung-Obstruktion IST die Nicht-Spaltbarkeit; die 120 Wurzelpaare = die q = 1-Einheitsschale (Plus-Typ, 240 = 15 × 8 × 2: Wurzel = (Adresse, Fehler-Jet, Orientierung)). TEIL 2: V \\ {0} = 7 NS + affiner 8-Punkt-Torsor; 112 D8-Wurzeln (NS) + 128 Ramond-Spinor (R), 248 = (112+8)+128; Stab(χ_NSR) = AGL(3,2) Ordnung 1344 = Aut(H8) mit DERSELBEN natürlichen 8-Punkt-Wirkung (Brute-Force 40320); affine Funktionen auf dem Torsor rekonstruieren RM(1,3) = H8 mit exakt 1344 Äquivalenzen; Sp(4,2)-Stabilisator (Ordnung 48) wirkt INNERHALB von AGL(3,2). 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TEIL 2: die symbolische Identität Σ(x_i+x_j)² − 3Σx² = (Σx)² liefert Tr_{S+}X² = 4|X|² = 4·h(E8) = 120 in einer Zeile; Charpoly (t+2)³(t−3)² exakt, 72 nur-Audit; die 210 = C(10,4)-Karte DEKORATIV — äquivariante Bijektionen durch die Fixpunkt-Obstruktion GETÖTET (beide Gruppen, beide Indizierungen, erschöpfend), keine der sechs eingefrorenen Gewichtsfamilien hält; nur die partielle 80 → 5×16-Miss-Slot-Karte und der Newton-Tie überleben als Audit", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv810_cutcode_moment.py", "sourceSha256": "8dcf729eb9be10b4d51ecdc61f41624f8cf87a991cd5a2c72eaeb2269212afae", "linkedClaimIds": [ "CARRIER.CUTCODE.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:10e10da547a5ac9014b8", "section:173b55d885e94fe4bfb5", "section:38538ebfe54ea1f0dd1c", "section:6c4044608163b007c4c2", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:93683d7c3fd300bd9861", "section:93b8868beb643874af75", "section:ab9e7e520130ecc7da7c", "section:aed67380a36c30ec03d3", "section:c4cf080b9ae6f25f7a71", "section:dba90b4fc50977b45cff", "section:e2ac56d63dc5b474ddb4", "section:eb00caf29086b02d5bf5", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:10e10da547a5ac9014b8", "section:6c4044608163b007c4c2", "section:ab9e7e520130ecc7da7c", "section:dba90b4fc50977b45cff", "section:e2ac56d63dc5b474ddb4", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v810_cutcode_moment.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v810_cutcode_moment.py", "pubMirrorHash": "8dcf729eb9be10b4d51ecdc61f41624f8cf87a991cd5a2c72eaeb2269212afae", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v810_cutcode_moment.py" }, { "id": "v812_flavor_graph_filtration", "filename": "v812_flavor_graph_filtration.py", "path": "verification/v812_flavor_graph_filtration.py", "cluster": "core", "synopsis": "FLAVOR.GRAPH.FILTRATION.01: die Flavor-Matrix-Filtration Q → K → L als Inzidenz-Compiler-Fingerabdruck — **FILTRATION-FINGERPRINT-ONLY (16/16): die Zeilen-Budgets sind EXAKTE, ordnungs-exakte Zählungen der K_{3,2}/Prisma/K5/H8-Inzidenzkette — Q (4,5,6), K (6,9,10) (Liniengraph ≅ Dreiecksprisma ≅ C6(2,3)), L (10,14,16) — mit der stufenweisen Additivität (4,5,6) + (6,9,10) = (10,14,16), die das deployte L = K + Q spiegelt (Matrizen lokalisiert: v11/v12/v37/v4; 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bipartites Vorzeichen −2/3; falscher Raum ×9) — der deployete Sechser ist der UHR-EXPONENT (v124 λ_n = (1−n/3)⁶, v486-Hand, festes Eigensystem); SECHSTPOTENZ-BLINDHEIT [E neu]: C6 und 2K3 haben identische sechste Potenzen — nur Schritt-Daten unterscheiden Walk von Uhr; KORREKTUR (datierte Notiz auf der v808-Zeile): T_v221 (exakte Spektralsumme des v221-Transfers (1−w)⁶) == B⁶ BIT-EXAKT — das SIXTHROOT-Verdikt wird BITEXACT-vs-v221; der kanonische Vorschlag T10 = P10⁶ in der Λ²-Basis (v774-Wörterbuch) besteht ALLE Gates: Spektrum {1, (1/3)⁶×5, (2/3)⁶×4} (Multiplizitäten (5,4) = (g_car, |μ₄|)), äquitable v774-Partition, Quotient == (Q_Pet/3)⁶ bit-exakt — promotionsreifer VORSCHLAG, kein Deploy-Anspruch; Kontrollen feuern; kein Marker-Move, KEIN RH-Anspruch", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv814_k5_sixstep_transport.py", "sourceSha256": "6d457a4e1d3192fe95a10bcb03159c4ea7fe21c3fbe64e2c4dc50b6e6a85af53", "linkedClaimIds": [ "K5.SIXSTEP.TRANSPORT.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:10e10da547a5ac9014b8", "section:4048b27ddae15185c715", "section:6c4044608163b007c4c2", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:93b8868beb643874af75", "section:a9e4936094020237f825", "section:ab9e7e520130ecc7da7c", "section:bc80e633fbb98ca8173d", "section:c4cf080b9ae6f25f7a71", "section:d84c8a8b6b42a871e6ef", "section:e9ee831b73445d2d858c", "section:eb00caf29086b02d5bf5", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:10e10da547a5ac9014b8", "section:6c4044608163b007c4c2", "section:ab9e7e520130ecc7da7c", "section:bc80e633fbb98ca8173d", "section:d84c8a8b6b42a871e6ef", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v814_k5_sixstep_transport.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v814_k5_sixstep_transport.py", "pubMirrorHash": "6d457a4e1d3192fe95a10bcb03159c4ea7fe21c3fbe64e2c4dc50b6e6a85af53", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v814_k5_sixstep_transport.py" }, { "id": "v817_positive_descent_master", "filename": "v817_positive_descent_master.py", "path": "verification/v817_positive_descent_master.py", "cluster": "core", "synopsis": "Abstract positive-descent theorem and G_net finite hypothesis checks; the prime packet instance is maintained by Prime Front.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv817_positive_descent_master.py", "sourceSha256": "6aa67e224fe448c150f23036e1416bff877c8e9003cf9ee8dfc4dec997b3915f", "linkedClaimIds": [ "TFPT.POSITIVE_DESCENT.MASTER.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:93b8868beb643874af75", "section:ab9e7e520130ecc7da7c", "section:bc80e633fbb98ca8173d", "section:c4cf080b9ae6f25f7a71", "section:eb00caf29086b02d5bf5", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:ab9e7e520130ecc7da7c", "section:bc80e633fbb98ca8173d", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v817_positive_descent_master.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v817_positive_descent_master.py", "pubMirrorHash": "6aa67e224fe448c150f23036e1416bff877c8e9003cf9ee8dfc4dec997b3915f", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v817_positive_descent_master.py" }, { "id": "v832_anchor_flavor_checksum", "filename": "v832_anchor_flavor_checksum.py", "path": "verification/v832_anchor_flavor_checksum.py", "cluster": "core", "synopsis": "ANCHOR.AFFINE.01 + FLAVOR.BIDIR.01: die affine Anker-Normalform und die bidirektionale Flavor-Prüfsumme — zwei exakte Korpus-Kompressionen — **ANCHOR-AFFINE-EXACT + FLAVOR-BIDIR-CHECKSUM (selektiv) (18/18 + 15/15): der Anker a = (1,1,2) hat Potenzsummen p_n = 2 + 2^n mit der affinen Rekursion p_{n+1} = 2p_n − 2 identisch in n (sympy); T(x) = 2x − 2 hat den EINDEUTIGEN Fixpunkt 2 = |Z₂| (das Blatt), und der T-Orbit von 4 ist exakt das Compiler-Quintett (4, 6, 10, 18, 34) = (|μ₄|, |R⁺(A₃)|, A_L, N_fam·|R⁺(A₃)|, Z₆-Lift), mit p₀ = 3 = N_fam vorangestellt; das GESAMTE Budget aus EINER Rekursion: |R(E8)| = p₁p₂p₃ = 240, dim E8 = 240 + q₃ = 248 (Leiter-Identität p₄ − p₃ = p₃ − 2 = 8 = h(D5) = rank E8), h(E8) = p₂p₃/2 = 30, |R(D5)| = p₁p₃ = 40, Ω_adm = 2p₁p₂ = 48, (e₁,e₂,e₃) = (4,5,2), 10b₁ = 41. Teil B: R = [[1,3,0],[1,5,2],[2,5,3]] dekodiert DENSELBEN Anker beidseitig — Ra = (4, 10, 13) = (p₁, p₃, N(3+2i)), Rᵀa = (6, 18, 8) = (p₂, p₄, p₃−2); der Geschwister-Kill: von 12 Kandidaten besteht GENAU EINER — die akzeptierte (1,5,2) — den vollen Identitätssatz, und die Anker-Kontraktion (Ra)₂ = 10 = p₃ tötet beide Geschwister (11 und 12). Kontrollen feuern (falsche Karte, falscher Anker, Geschwister (1,4,3) reproduziert tfpt_2s Fehlerzahlen WÖRTLICH). Exakt sympy/Integer; keine Floats, kein RNG, kein Fit.**", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv832_anchor_flavor_checksum.py", "sourceSha256": "cda54a8c508ac90f300b1a1090faea9a04ef3966eb4eb7499b27cd9cb7ea0ba1", "linkedClaimIds": [ "ANCHOR.AFFINE.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:10e10da547a5ac9014b8", "section:1234c1fa7fdc0d6d5b35", "section:5d8f619883df80c56b36", "section:649c3b4e330a4dfc876d", "section:6ff4670b89c8b83d4b0f", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:ab9e7e520130ecc7da7c", "section:b76309fbfced7aff0c43", "section:bc80e633fbb98ca8173d", "section:c4cf080b9ae6f25f7a71", "section:ef3ac63aa9e6dcddf33d", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:10e10da547a5ac9014b8", "section:1234c1fa7fdc0d6d5b35", "section:5d8f619883df80c56b36", "section:649c3b4e330a4dfc876d", "section:ab9e7e520130ecc7da7c", "section:bc80e633fbb98ca8173d", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v832_anchor_flavor_checksum.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v832_anchor_flavor_checksum.py", "pubMirrorHash": "cda54a8c508ac90f300b1a1090faea9a04ef3966eb4eb7499b27cd9cb7ea0ba1", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v832_anchor_flavor_checksum.py" }, { "id": "v833_gaussian_ramification_ladder", "filename": "v833_gaussian_ramification_ladder.py", "path": "verification/v833_gaussian_ramification_ladder.py", "cluster": "core", "synopsis": "GAUSSIAN.RAMLADDER.01: die (1+i)-Verzweigungsleiter — die vier dokumentierten Rollen des verzweigten Gaußschen Primelements π₂ = 1+i sind EIN maschinell geprüftes Objekt mit vier Sprossen, jede von Grund auf re-zertifiziert — **RAMIFICATION-LADDER-EXACT (33/33): SPROSSE 1 (Norm-Verdopplung): N(π₂) = 2, (π₂²) = (2); auf dem Gaußschen E8-Gitter (1+J)ᵀ(1+J) = 2I₈ EXAKT; min L = 4 per Zensus, die Nullklasse von L/(1+i)L trägt KEINE Wurzel (0/240), 240 = 15 × 16, Elementarteiler (1,1,1,1,2,2,2,2), Index 16 = N(π₂)⁴; SPROSSE 2: L/(1+i)L ≅ F₂⁴ mit dem Deck J TRIVIAL wirkend — der 4-Bit-Adressraum; SPROSSE 3 (der nicht-spaltende Jet): Z[i]/(2) ≅ F₂[ε]/(ε²) (Ring-Iso EINDEUTIG unter allen 24 Bijektionen), W = L/2L frei vom Rang 4 über den dualen Zahlen, Deck = JET-EINHEIT 1 + ε, und von ALLEN 65536 linearen Schnitten sind EXAKT 0 deck-äquivariant — die Kein-kanonischer-Ursprung-Obstruktion IST Nicht-Spaltung (v803); Plus-Typ-Form 136/120, die 120 Wurzelpaare SIND die q = 1-Schale; SPROSSE 4 (der metaplektische Lift): ζ₈ = (1+i)/√2, (1+J)² = 2J, (SH)³ = ζ₈I, (T₃K₃)³ = iI = DAS DECK (v798); exakter Z[ζ₈]-BFS-Zensus: |C₂/μ₈| = 11520 = 16 × 720, NULL Galois-gemischte Klassen, C₂ = K ∪ ζ₈K (v783 [E]); Zeugen-Paritäten χ(H⊗I) = 1 (das RM-CSS-ζ₈-Phasenbit), χ(H⊗H) = χ(CZ) = 0. Kontrollen feuern (der SPALT-Ring F₂×F₂: 0 Isos; die spaltende Selbsterweiterung: 65536/65536 Schnitte). Exakt Integer/sympy; keine Floats, kein RNG.**", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv833_gaussian_ramification_ladder.py", "sourceSha256": "1f3834004f892a8db720750f55711b2974097c5227eaf271498a6778f36b6b87", "linkedClaimIds": [ "GAUSSIAN.RAMLADDER.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:10e10da547a5ac9014b8", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:ab9e7e520130ecc7da7c", "section:bc80e633fbb98ca8173d", "section:c4cf080b9ae6f25f7a71", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:10e10da547a5ac9014b8", "section:ab9e7e520130ecc7da7c", "section:bc80e633fbb98ca8173d", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v833_gaussian_ramification_ladder.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v833_gaussian_ramification_ladder.py", "pubMirrorHash": "1f3834004f892a8db720750f55711b2974097c5227eaf271498a6778f36b6b87", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v833_gaussian_ramification_ladder.py" }, { "id": "v834_pg32_flag_completion", "filename": "v834_pg32_flag_completion.py", "path": "verification/v834_pg32_flag_completion.py", "cluster": "core", "synopsis": "PG32.FLAGS.01: die PG(3,2)-Flaggen-Normalform für die 105 + 35-Vakuum-Vervollständigung, mit dem Inzidenz-Kill-Test als Split typisiert — **PG32-FLAGS-EXACT + INCIDENCE-SPLIT (26/26): die Zähl-Normalform [4 über 2]₂ = 35, 140 affine 2-Flats = 35 durch den Ursprung + 105 nicht; PG(3,2): 15 Punkte, 35 Geraden, 105 = 35 × 3 Flaggen ≅ C(15,2) Paare; RM-Schicht (v819/v821/v822 neu aufgebaut): [15,10,4]-Enumerator EXAKT, die 105 Gewicht-4-Wörter SIND die Flats ohne 0, Grams 22I+6J / 6I+J / 28I+7J; Vakuum-Lesart: die Vakuum-Koordinate ist URSPRUNGS-RESTAURATION (EIN Ursprungsplan entkürzt dim 10 → 11); DER INZIDENZ-SPLIT (der typisierte Kill): 105 = 45 + 60 ist die Sp(4,2)-ORBIT-Zerlegung auf BEIDEN Seiten (|Sp(4,2)| = 720 brute force); auf den 60 NICHT-ISOTROPEN Sprossen ist die Polaritätskarte Φ: (U,t) → ((t+U) ∩ U^ω, U^ω) wohldefiniert, bijektiv, Sp(4,2)-ÄQUIVARIANT (60 × 720) und INZIDENZ-ERHALTEND; auf den 45 DOILY-Sprossen ist die Obstruktion typisiert: U^ω = U und (t+U) ∩ U = LEER für 45/45 — und das Flaggen-Gram 18I+3J ≠ 22I+6J. TYPISIERTE FOLGERUNG: '105 Checks = 105 Flaggen' ist exakt als deck-äquivariante BIJEKTION, NICHT als Inzidenz-Isomorphismus — die Obstruktion sitzt exakt auf dem Doily (der typisierte Grund, warum v822s Kontinuums-Dilatation starb). Die Nullklasse trägt keine Wurzel (0/240, v689 [E]). Kontrollen feuern. Exakt Integer; keine Floats, kein RNG.**", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv834_pg32_flag_completion.py", "sourceSha256": "3c07a7e6c02acf39021499e5ee0648e56d768b9432bc5bad4660ddc23ae037a4", "linkedClaimIds": [ "PG32.FLAGS.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:10e10da547a5ac9014b8", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:ab9e7e520130ecc7da7c", "section:bc80e633fbb98ca8173d", "section:c4cf080b9ae6f25f7a71", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:10e10da547a5ac9014b8", "section:ab9e7e520130ecc7da7c", "section:bc80e633fbb98ca8173d", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v834_pg32_flag_completion.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v834_pg32_flag_completion.py", "pubMirrorHash": "3c07a7e6c02acf39021499e5ee0648e56d768b9432bc5bad4660ddc23ae037a4", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v834_pg32_flag_completion.py" }, { "id": "v844_message_doily_rank", "filename": "v844_message_doily_rank.py", "path": "verification/v844_message_doily_rank.py", "cluster": "core", "synopsis": "MESSAGE.LADDER.01 + DOILY.PASCAL.RANK.01: die E8-Adressformel und das Doily-Pascal-Rangtheorem — zwei exakte Korpus-Kompressionen, EIN Modul aus zwei Probes — **MESSAGE-LADDER-EXACT + DOILY-PASCAL-RANK-EXACT (23/23 + 16/16): TEIL A: M_n = 15·Δp_n = 15·2^n gegen die TATSÄCHLICH neu aufgebauten Objekte zertifiziert, eine BENANNTE Struktur pro Sprosse: M_0 = 15 = Adressraum (Klassen von V = L/(1+i)L); M_1 = 30 = h(E8), HIER aus dem neu aufgebauten Wurzelsystem hergeleitet, nicht zitiert (8 einfache Wurzeln, zusammenhängende einfach geschnürte Cartan-Matrix mit det 1 und E8-Gradfolge, höchste Wurzel EINDEUTIG bei Höhe 29 mit Marken {2,2,3,3,4,4,5,6}, h = 1 + 29 = 30 = |R|/Rang); M_2 = 60 Gaußsche Wurzellinien (μ4-Orbits, alle Größe 4, genau 4 pro Klasse); M_3 = 120 = |R+| = Vorzeichenpaare; M_4 = 240 = |R(E8)| mit Zensus 240 = 15×16 (Nullklasse LEER); Coda 248 = 15·16 + 8 gegen Zensus und HNF-Rang; die strukturelle Verdopplung 60 → 120 → 240 typisiert. Kontrollen feuern (falscher Anker (1,2,2) → (45,105,225,465); falsche Multiplikatoren 14/16 verfehlen alle Ziele und brechen die Coda). TEIL B: die Duaden-Synthemen-Inzidenz N des Cremona-Richmond-Doilys (15×15, 3-regulär beidseitig) und die symplektische Punkt-Inzidenz B auf PG(3,2) (B·B^T = 4I + 3J zellweise, charpoly (x−7)(x−2)^9(x+2)^5 exakt) sind EIN Objekt: über das K6-Duaden-Modell trägt die Bijektion N·N^T auf B + 2I ZELLWEISE (alle 225 Zellen) — Duaden-Kollinearität = symplektische Orthogonalität. DAS RANGTHEOREM (exakt): charpoly(N·N^T) = (x−9)(x−4)^9·x^5 — Rang N = 10 = A_Λ (Dekupel-Sektor), Kern = 5 = g_car (Fünf-Slot-Träger), Multiplizität 9 = N_fam², Top-Singulärwert 3 = N_fam; die SECHS Ovoid-Indikatoren SPANNEN den Kern — die P2-Ganzzahlen sind die Singulärwert-Daten der Doily-Inzidenz. Recovery-Wert sing(N/3) = {1, 2/3 ×9, 0 ×5} exakt, 2/3 = (N_fam−1)/N_fam (v327); Exponentiationsidentität: der Sechs-Schritt hat exakt (2/3)^6 = 64/729 als λ_2 (v330/v486); TYPISIERTE Lücke erneut bestätigt, KEIN Upgrade: 1/729 ist KEINE Wurzel — der deployte (1/3)^6-Modus bleibt auf der Uhr-Seite (v814). Kontrollen feuern (zirkulante und LCG-3-reguläre Paarungen: Rang 13 ≠ 10, falsches charpoly). Exakte Integer/Fraction/sympy-Arithmetik.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv844_message_doily_rank.py", "sourceSha256": "413cd148b4243858e935417a4de7f43d1842dbec3dd56a2ade94f40fc71b7c65", "linkedClaimIds": [ "MESSAGE.LADDER.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:10e10da547a5ac9014b8", "section:6bcd4464dbd4c8f8f003", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:93b8868beb643874af75", "section:ab9e7e520130ecc7da7c", "section:bc80e633fbb98ca8173d", "section:c4cf080b9ae6f25f7a71", "section:d0d4a62b7872b9bb3a1c", "section:eb00caf29086b02d5bf5", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:10e10da547a5ac9014b8", "section:6bcd4464dbd4c8f8f003", "section:ab9e7e520130ecc7da7c", "section:bc80e633fbb98ca8173d", "section:d0d4a62b7872b9bb3a1c", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v844_message_doily_rank.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v844_message_doily_rank.py", "pubMirrorHash": "413cd148b4243858e935417a4de7f43d1842dbec3dd56a2ade94f40fc71b7c65", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v844_message_doily_rank.py" }, { "id": "v845_cfin_normal_form", "filename": "v845_cfin_normal_form.py", "path": "verification/v845_cfin_normal_form.py", "cluster": "core", "synopsis": "NORMALFORM.CFIN.01: der endliche Compiler als EIN Objekt C_fin = (V, ħ, q*, σ, ι), vom Gaußschen Quotienten ABGELESEN (nicht postuliert), mit dem Code-zu-Materie-Kill als eingebautem NEGATIV und der verbleibenden P2-Brücke typisiert — **NORMAL-FORM-ASSEMBLED (28/28, SPEC v2): V = L/(1+i)L (Zensus 240 = 15×16, Nullklasse LEER); ħ = die Bit-Form (GEFUNDENE Familien/Anker-Basis (F1,F2,F3,A) mit Gram J − I, auf allen 256 Paaren); σ = der abgestiegene Ordnung-3-Deck (σ³ = id, symplektisch, genau 3 Fixklassen {A, F_Σ, F_Σ+A}, 4 freie 3-Orbits — der Familienzyklus); q* = die EINDEUTIGE Verfeinerung (genau 16 per Brute-Force über 2^16, Arf-Zensus 6 + 10; Selektor σ-invariant: 4 → q(A)=1: 2 → q(F_Σ)=0: 1, Arf-Typ 1, σ-erhalten); ι = der Paritäts-Lift bijektiv auf C_even(5) (β == ħ in allen 256 Zellen, q_wt == q*, σ wirkt auf den FÜNF Träger-Slots als 3+2-Split — Nachrichten- und Trägerregister verschränkt). ABGELEITET aus dem EINEN Objekt: |Sp(4,2)| = 720 (voller 65536-Matrizen-Zensus), Stab(q*) = 120 TREU als S5 auf den Fünf, Orbits [1, 5, 10]; 16 = 1+5+10, 15 = 5+10; PASCAL-Lesart (1, 10, 5) = (C(5,0), C(5,2), C(5,4)); PROJEKTIVE Lesart: PG(3,2) mit 15 Punkten, 35 Geraden, 15 isotrop (das Doily), die 5̄ ist ein OVOID (trifft jede isotrope Gerade genau einmal); Budget gegen die echten Gitterobjekte: 240 = 16·15, 60 Linien = 4·15, 30 = 2·15 = h(E8), Rang 8, 248 = 16·15 + 8. EINGEBAUTES NEGATIV (v775 neu verankert): die exakte 128-Spinor-Zählschranke — höchstens 8 rein-spinorale Klassen, ≥ 7 der 15 Klassen tragen IMMER Adjoint-Seiten-Wurzeln (konkreter Zensus SATURIERT beide Schranken: 8 + 7, NULL Mischklassen — der J-Quotient respektiert die D8-Graduierung); Gewichts-Kill am kanonischen Split: jede Spinor-Klasse = 8 verschiedene Halbspinor-Gewichtspaare, NIE 1 — v775 ROOTCLASS-MIXED bestätigt, NICHT umgestoßen. P2 TYPISIERT (kein Upgrade): alle 30 Platzierungen sind Typ-II-[8,4]-Codes (v799-Echo); C_fin leitet A1–A3, die OPE-Linearitäts-Notiz und die v776-Auswahl NICHT her — P2 (g_car = 5 = ι-Slot-Zahl) auf v799s Residuum R1′ ([C]) VERENGT, nicht eliminiert. Kontrollen feuern (Dot-Form: 0 Verfeinerungen; trivialer Deck: q* nicht eindeutig; falscher Lift bricht β == ħ).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv845_cfin_normal_form.py", "sourceSha256": "4cc5ae4faf7daa2e23a1dfdeedbf0b49690c1b26ec7726254587701b6a0cbf91", "linkedClaimIds": [ "NORMALFORM.CFIN.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:6bcd4464dbd4c8f8f003", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:93b8868beb643874af75", "section:ab9e7e520130ecc7da7c", "section:bc80e633fbb98ca8173d", "section:c4cf080b9ae6f25f7a71", "section:d0d4a62b7872b9bb3a1c", "section:eb00caf29086b02d5bf5", "section:f091de1c3533bab48372", "section:f22c82858ff073c133d4" ], "activeSectionIds": [ "section:6bcd4464dbd4c8f8f003", "section:ab9e7e520130ecc7da7c", "section:bc80e633fbb98ca8173d", "section:d0d4a62b7872b9bb3a1c", "section:f091de1c3533bab48372", "section:f22c82858ff073c133d4" ], "evidenceId": "python_verification:verification/v845_cfin_normal_form.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v845_cfin_normal_form.py", "pubMirrorHash": "4cc5ae4faf7daa2e23a1dfdeedbf0b49690c1b26ec7726254587701b6a0cbf91", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v845_cfin_normal_form.py" }, { "id": "v849_cfin_unique_cofinal_lean", "filename": "v849_cfin_unique_cofinal_lean.py", "path": "verification/v849_cfin_unique_cofinal_lean.py", "cluster": "core", "synopsis": "CFIN.UNIQUE.01: finite compiler uniqueness, one orbit and C6 automorphisms; cofinal Weil mirror moved to Prime Front.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv849_cfin_unique_cofinal_lean.py", "sourceSha256": "4cd1127dced960e9a72cafed0c77c57d866f714b4898a5c74a5f9ecbd40588a5", "linkedClaimIds": [ "CFIN.UNIQUE.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:6bcd4464dbd4c8f8f003", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:93b8868beb643874af75", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:eb00caf29086b02d5bf5", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:6bcd4464dbd4c8f8f003", "section:ab9e7e520130ecc7da7c", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v849_cfin_unique_cofinal_lean.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v849_cfin_unique_cofinal_lean.py", "pubMirrorHash": "4cd1127dced960e9a72cafed0c77c57d866f714b4898a5c74a5f9ecbd40588a5", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v849_cfin_unique_cofinal_lean.py" }, { "id": "v852_arf_vacuum_ovoid", "filename": "v852_arf_vacuum_ovoid.py", "path": "verification/v852_arf_vacuum_ovoid.py", "cluster": "core", "synopsis": "ARF.VACUUM.SYNDROME.01 + OVOID.DECODER.01: **ARF-VACUUM-SYNDROME-EXACT (24/24) + OVOID-DECODER-EXACT (23/23)** — der Arf-Bit-Satz: a(t+U) = h̄(u,v) für ALLE 140 affinen Flats (positions-unabhängig; alle 4 Nebenklassen stimmen überein); die Zwei-Bit-Syndromtafel (s_vac, s_Arf) zerlegt die 140 Flats EXAKT in 15/20/45/60 (die v821- und v834-Zählungen als Zeilen EINER Tafel auf dem Hamming-Code); der LOKALE Hecke-Satz an ALLEN 15 Punkten (12+16 = 28 = σ₃(3), 12−16 = −4 = a₃, mit den isotropen Richtungen in Bijektion zu den Punkten von x^⊥/⟨x⟩); der Code-Bleistift H = [15,11,3] ⊃ {D = [15,10,4], C_iso, C_non = [15,10,3]} ⊃ K = [15,9,4] (Gewicht-3/4-Wörter = die 35 Geraden / 105 Off-Origin-Flats als MENGEN-Gleichheiten; das Kanonizitäts-Lemma: alle 16 Verfeinerungen differieren um Simplex-Wörter und induzieren EIN Arf-Funktional auf H); der Vakuum-Bit IST das Paritätsbit, das RM(2,4) restauriert (Punktierung → H, Verkürzung → D, Bijektion exakt). DER DECODER: NᵀV = 0 aus perfekten Matchings, Gram VᵀV = 36I−6J, SNF(N) = diag(1¹⁰,0⁵) TORSIONSFREI über ℤ (det-±1-Minor exhibiert), Moore-Penrose N⁺ = Nᵀ/4 − J/36 (alle vier Penrose-Axiome exakt in ℚ), der Träger-Projektor P₅ = I/2 − B/4 + J/12 mit tr = 5 = g_car, der geschlossene Decoder m̂ = (I−P₅)m EXAKT auf dem vordeklarierten Testsatz (Kernmoden unsichtbar, im(N) voll sichtbar), ker Nᵀ = die S₆-STANDARD-Darstellung (11/11 Klassen-Charaktere = fix−1), und der Mod-2-Schatten v_a mod 2 = q_a: DREI RINGE (ℝ-Ovoid-Spann / ℤ-torsionsfrei Rang 5 / F₂-Code A_q = [15,5,6]), EIN Kern — der Doily-Erholungskanal hat jetzt eine explizite integrale Inverse, nicht nur ein Spektrum. Exakte Algebra durchgehend; Kontrollen feuern; KEINE Marker-Bewegung. KEIN RH-Anspruch.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv852_arf_vacuum_ovoid.py", "sourceSha256": "29cd8df66ca1934f25cae194745529da3d0b3f3f6625bc19a7440ac936694cbd", "linkedClaimIds": [ "ARF.VACUUM.SYNDROME.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:10e10da547a5ac9014b8", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:93b8868beb643874af75", "section:ab9e7e520130ecc7da7c", "section:bc80e633fbb98ca8173d", "section:c4cf080b9ae6f25f7a71", "section:eb00caf29086b02d5bf5", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:10e10da547a5ac9014b8", "section:ab9e7e520130ecc7da7c", "section:bc80e633fbb98ca8173d", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v852_arf_vacuum_ovoid.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v852_arf_vacuum_ovoid.py", "pubMirrorHash": "29cd8df66ca1934f25cae194745529da3d0b3f3f6625bc19a7440ac936694cbd", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v852_arf_vacuum_ovoid.py" }, { "id": "v853_bent_css_mangoldt", "filename": "v853_bent_css_mangoldt.py", "path": "verification/v853_bent_css_mangoldt.py", "cluster": "core", "synopsis": "ARF.BENT.CSS.01: exact bent phase and CSS code identities; Mangoldt incidence experiment moved to Prime Front.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv853_bent_css_mangoldt.py", "sourceSha256": "531221fbf98e164b984d2cc80917498b6b008ee32bae5d2a642fd3503606065f", "linkedClaimIds": [ "ARF.BENT.CSS.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:10e10da547a5ac9014b8", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:93b8868beb643874af75", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:eb00caf29086b02d5bf5", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:10e10da547a5ac9014b8", "section:ab9e7e520130ecc7da7c", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v853_bent_css_mangoldt.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v853_bent_css_mangoldt.py", "pubMirrorHash": "531221fbf98e164b984d2cc80917498b6b008ee32bae5d2a642fd3503606065f", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v853_bent_css_mangoldt.py" }, { "id": "v857_simplex_fourier_winding", "filename": "v857_simplex_fourier_winding.py", "path": "verification/v857_simplex_fourier_winding.py", "cluster": "core", "synopsis": "E8.SIMPLEX.FOURIER.01 + FLAVOR.WINDING.QUADRATIC.01: **SIMPLEX-FOURIER-EXACT + INTERTWINER-IDENTIFIED (26/26) + WINDING-QUADRATIC-EXACT (20/20)** — die E8-Audits I: der Gauß-Zensus IST ein Fourier-Gesetz — r̂ = (240, −16¹⁵), Kanal P = (J−I)/15 mit Spektrum {1, (−1/15)¹⁵} und Zwei-Schritt-Kontraktion 1/225 (exakt in Brüchen); Ramifikation Θ₀(ungerade) = 0 mit Ein-Zeilen-Beweis; Äquidistribution auf JEDEM Level ≤ 16; der Paket-Zähler (Th0−Th1+Th2−Th3)(n) == die Code-Walsh-Transformierte auf JEDEM Level ≤ 16 (beide Leitern [−16, 112, −448, 1136, …]; Eisenstein-Normalform 15Θ_D8 = 7Θ_L + 8Θ₀); der WERT-SATZ: mh₂(n) = −1/15 für JEDES ungerade n ≤ 16500 (Ganzzahl-Identität, alle 1911 ungeraden Primzahlen abgedeckt) — v817s Pro-Primzahl-Messung ist die Primzahl-Restriktion eines CHARAKTER-SATZES des Codes; ehrlich typisiert: SPEKTRAL (die Paket-Gradierung (52,60,128) und die Code-Gradierung 15×16 verfeinern einander NICHT); 3 Kontrollen feuern, 2 Invarianzen halten (24 explizite Isometrien; die andere invariante Platzierung C**). Die Windungs-Quadratik (tfpt_2 I.5): χ_{R_s} − χ_R = −s·q_wind mit q_wind = e₁ᵀ adj(tI−R) 1 = t² − g_car·t + |Z2| EXAKT (Adjugat-Lemma; irreduzibel über Q, disc 17); die Keybox-Koeffizienten (9+s, 10+5s, 8+2s), das det-Inkrement 2 = |Z2| und das Minor-Gesetz (5, 3(s+1), 2(s+1)) sind Auslesungen der EINEN Quadratik; Dreifach-Lock s = 6 (Spur/Determinante/Coxeter-Lift, Schnitt {6} = {|R+(A3)|}); Δ(6) = 39200 = 2·140² > 0 (KEIN Kollisionspunkt; der EINZIGE 2×Quadrat-Treffer im Fenster −2…12); Realitäts-Schwelle s* ≈ 2.8250 = die einzige Δ-Wurzel in (2,3) (deployt ≈ 2.83); 4 Kontrollen feuern (Geschwister-Richtungen brechen Lock UND Quadratik). Exakte Korpus-Kompressionen deployter Ansprüche (v817/v833/v844, v4/v94) — kein neuer physikalischer Anspruch, keine Marker-Bewegung.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv857_simplex_fourier_winding.py", "sourceSha256": "e812ff8e539e2cc4894194b135f4bdd260d270b621a2598d2ddf800cf90e07c6", "linkedClaimIds": [ "E8.SIMPLEX.FOURIER.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:10e10da547a5ac9014b8", "section:2678ed3ba0ed508e2d8e", "section:51e91159532ef7479ff8", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:93b8868beb643874af75", "section:ab9e7e520130ecc7da7c", "section:bc80e633fbb98ca8173d", "section:c4cf080b9ae6f25f7a71", "section:d0d4a62b7872b9bb3a1c", "section:eb00caf29086b02d5bf5", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:10e10da547a5ac9014b8", "section:51e91159532ef7479ff8", "section:ab9e7e520130ecc7da7c", "section:bc80e633fbb98ca8173d", "section:d0d4a62b7872b9bb3a1c", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v857_simplex_fourier_winding.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v857_simplex_fourier_winding.py", "pubMirrorHash": "e812ff8e539e2cc4894194b135f4bdd260d270b621a2598d2ddf800cf90e07c6", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v857_simplex_fourier_winding.py" }, { "id": "v858_g31_clock_alphabet", "filename": "v858_g31_clock_alphabet.py", "path": "verification/v858_g31_clock_alphabet.py", "cluster": "core", "synopsis": "E8.G31.CLOCK_ALPHABET.01: **CLOCK-ALPHABET-SELECTIVE (19/19)** — Deg(G31)/4 = {2, 3, 5, 6} = {|Z2|, N_fam, g_car, |R+(A3)|} = das Compiler-Uhren-Alphabet als NORMALFORM: gcd = 4 = |μ4|, lcm = 120 = |R+(E8)|, lcm/gcd = 30 = h(E8), Audit-Identität (Σd/4)(Σ(d−1)/4) = 16 × 15 = 240 = |R(E8)| auf den Wurzeln REALISIERT (die 60 Spiegelungen = die 60 Gauß-Linien, 4 pro Klasse — dieselbe 15×16-Zählung wie die Code-Seite); der Rebuild gewardet (BFS-Abschluss |G| = 46080 = ∏Deg; EXAKTER Spiegelungs-Zensus: 60 Elemente mit rank(M−I) = 2, NULL Quasi-Spiegelungen — v634 reproduziert); der arithmetische Pin: (8,12,20,24) das EINZIGE Ganzzahl-Quadrupel mit Produkt 46080 und Summe 64 (gemessen); der Kill-Scan über ALLE 607 Rang-4-Shephard-Todd-Gruppen (Katalog-Integrität: ∏(Grade) = |G| für jeden Eintrag): G31 der EINZIGE Voll-Batterie-Passer — Schwach-Tripel-Impostoren G(20,10,4)/G(20,20,4)/G29 und Roh-Summe-64-Koinzidenzen G(8,2,4)/G(10,10,4)/W(H4) typisiert; Familien-Grenze G(m,p,4) bis m = 120 leer (typisiertes Argument); EHRLICHKEITS-LINIE: Grad-Audits können G31 vom reduziblen Torus Z8×Z12×Z20×Z24 nicht trennen — eingefrorener Geltungsbereich = die irreduzible Rang-4-Liste; X1/X2-Kontrollen feuern. Der W(D5)×W(A3)-Zaun mit BERECHNETEM Ein-Zahl-Invariant erneut getötet: |Z(G31)| = 4 = ⟨J⟩ = μ4 vs |Z(W(D5)×W(A3))| = 1 — NICHT isomorph, KEINE Zerlegung (v634 T1.3–T1.5 zitiert). Normalform + scharfe Kill-Regel für ein deploytes Objekt (v634/v654) — kein neuer Anspruch.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv858_g31_clock_alphabet.py", "sourceSha256": "c21a68f253ead39c4b770ff88b2e62d876eee69f2cb9ce5430f18e6c69291384", "linkedClaimIds": [ "E8.G31.CLOCK_ALPHABET.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:10e10da547a5ac9014b8", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:93b8868beb643874af75", "section:ab9e7e520130ecc7da7c", "section:bc80e633fbb98ca8173d", "section:c4cf080b9ae6f25f7a71", "section:d0d4a62b7872b9bb3a1c", "section:eb00caf29086b02d5bf5", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:10e10da547a5ac9014b8", "section:ab9e7e520130ecc7da7c", "section:bc80e633fbb98ca8173d", "section:d0d4a62b7872b9bb3a1c", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v858_g31_clock_alphabet.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v858_g31_clock_alphabet.py", "pubMirrorHash": "c21a68f253ead39c4b770ff88b2e62d876eee69f2cb9ce5430f18e6c69291384", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v858_g31_clock_alphabet.py" }, { "id": "v874_feedback_decoder_lean", "filename": "v874_feedback_decoder_lean.py", "path": "verification/v874_feedback_decoder_lean.py", "cluster": "core", "synopsis": "FLAVOR.FEEDBACK.NORMALFORM.01 + E8.WINDING.DECODER.01: **FEEDBACK-NORMALFORM-EXACT + WINDING-DECODER-EXACT (14/14 + 11/11, + Lean-Spiegel)** — zwei exakte Compiler-Theoreme: EINE ganzzahlige Basis P = [2·𝟙 | e₃ | R e₃] (det −4, SNF diag(1,2,2)) konjugiert die GESAMTE Windungslinie R_s = R + s 𝟙 e₁ᵀ exakt (symbolisch in s) in die Gain-plus-Companion-Normalform [[s+4,0,3],[0,0,−2],[4,1,5]]: Gain-Kanal s+|μ₄|, Companion-Block des Windungsquadrats q_wind = t²−g_car t+|Z₂|, Kopplungspaar (3,4) mit Schleifenprodukt N_fam·|μ₄| = 12 = dim g_SM — also χ_{R_s} = (t−s−|μ₄|)·q_wind − 12t, und bei s = 6 sind (15,40,20) die drei Gain-10-Ablesungen; die ehrliche Typisierung ist tragend: der Quotient ℤ³/Pℤ³ = ℤ₂² hat KARDINALITÄT 4 = |μ₄|, aber EXPONENT 2 — NICHT μ₄, keine Identifikation behauptet. Der Decoder: q_wind bildet das G31-Uhr-Alphabet {2,3,5,6} auf (−|μ₄|,−|μ₄|,|Z₂|,h(D5)) ab (q(2)=q(3) von der Palindrom-Achse g_car/2 erzwungen); D(y) = (y+4)²(y−2)(y−8) trägt die Budget-Koeffizienten (|Z₂|, Ω_adm=48, 2^g_car=32, 2^rk(E8)=256); und |μ₄|·q(|Z₂|)/|R(E8)| = −1/15 ist EXAKT der Walsh-Eigenwert des Gauß-Zensus — typisiert als AUDIT-Theorem, kein physikalischer Funktor. Lean-Spiegel: TfptCarrier/FlavorFeedback.lean (11 Theoreme, Standard-Axiome, kein sorry).", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv874_feedback_decoder_lean.py", "sourceSha256": "acf8f3143a743806aa020c012d493c2f69d076548249fd44dc6a93f0fa9530b8", "linkedClaimIds": [ "FLAVOR.FEEDBACK.NORMALFORM.01", "E8.WINDING.DECODER.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:2678ed3ba0ed508e2d8e", "section:51e91159532ef7479ff8", "section:6bcd4464dbd4c8f8f003", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:93b8868beb643874af75", "section:ab9e7e520130ecc7da7c", "section:bc80e633fbb98ca8173d", "section:c4cf080b9ae6f25f7a71", "section:d0d4a62b7872b9bb3a1c", "section:eb00caf29086b02d5bf5", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:51e91159532ef7479ff8", "section:6bcd4464dbd4c8f8f003", "section:ab9e7e520130ecc7da7c", "section:bc80e633fbb98ca8173d", "section:d0d4a62b7872b9bb3a1c", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v874_feedback_decoder_lean.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v874_feedback_decoder_lean.py", "pubMirrorHash": "acf8f3143a743806aa020c012d493c2f69d076548249fd44dc6a93f0fa9530b8", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v874_feedback_decoder_lean.py" }, { "id": "v875_shell_global_lean", "filename": "v875_shell_global_lean.py", "path": "verification/v875_shell_global_lean.py", "cluster": "core", "synopsis": "E8.SHELL.GLOBAL.01: **SHELL-GLOBAL-THEOREM (15/15, + Lean-Skelett)** — das Zensus→Theorem-Upgrade: Θ̂ᵤ/Θ_L = −1/15 auf ALLEN ungeraden Schalen (nicht mehr nur n ≤ 16500). Die drei Inputs, jeder gewardet: (i) die G31-Klassenwirkung = die 60 symplektischen Transvektionen erzeugen Sp(4,2) (Ordnung 720), TRANSITIV auf den 15 Nichtnull-Klassen und IDENTISCH mit der Schalenmodul-Wirkung; (ii) Normverdopplung durch (1+i): Θ₀(2m) = Θ_L(m), Θ₀(ungerade) = 0; (iii) Θ_L = 240σ₃ (klassisch, Eisenstein E₄). Kontrollen: eine nicht-transitive Untergruppe liefert einen invarianten NICHT-uniformen Zensus (das Gesetz bricht — Transitivität ist tragend); die Gerade-Schalen-Formel weicht korrekt ab (7/135 bei n = 2). Lean-Skelett: TfptCarrier/GaussianShells.lean prüft die KONSEQUENZKETTE im Kern (7 Theoreme aus dem benannten Hypothesenbündel ShellSystem; jede Aussage eine exakte Ganzzahl-Identität, keine Division), die drei Inputs bleiben BENANNTE Hypothesen mit typisierter Provenienz — die Haus-Disziplin: das globale Statement kann keine Lücke verstecken.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv875_shell_global_lean.py", "sourceSha256": "65beb96eb31c770dd1ead1347e4cb3bd5a303278dba1d0c4aefeae081f3e28b8", "linkedClaimIds": [ "E8.SHELL.GLOBAL.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:6bcd4464dbd4c8f8f003", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:93b8868beb643874af75", "section:ab9e7e520130ecc7da7c", "section:bc80e633fbb98ca8173d", "section:c4cf080b9ae6f25f7a71", "section:d0d4a62b7872b9bb3a1c", "section:eb00caf29086b02d5bf5", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:6bcd4464dbd4c8f8f003", "section:ab9e7e520130ecc7da7c", "section:bc80e633fbb98ca8173d", "section:d0d4a62b7872b9bb3a1c", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v875_shell_global_lean.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v875_shell_global_lean.py", "pubMirrorHash": "65beb96eb31c770dd1ead1347e4cb3bd5a303278dba1d0c4aefeae081f3e28b8", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v875_shell_global_lean.py" }, { "id": "v878_ledger_integrity", "filename": "v878_ledger_integrity.py", "path": "verification/v878_ledger_integrity.py", "cluster": "registry", "synopsis": "", "publicationNotes": [ "Non-scientific synopsis omitted." ], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv878_ledger_integrity.py", "sourceSha256": "b68425c19bc486e5886c5f41712d0cea3c921aa0b5e371fa33a88ae1d447d908", "linkedClaimIds": [ "GATE.LEDGER.01" ], "sectionIds": [ "section:848c49f799255f4cda92", "section:93b8868beb643874af75", "section:ab9e7e520130ecc7da7c", "section:bc80e633fbb98ca8173d", "section:c4cf080b9ae6f25f7a71", "section:d0d4a62b7872b9bb3a1c", "section:eb00caf29086b02d5bf5", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:ab9e7e520130ecc7da7c", "section:bc80e633fbb98ca8173d", "section:d0d4a62b7872b9bb3a1c", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v878_ledger_integrity.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v878_ledger_integrity.py", "pubMirrorHash": "b68425c19bc486e5886c5f41712d0cea3c921aa0b5e371fa33a88ae1d447d908", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v878_ledger_integrity.py" }, { "id": "v880_finite_anchor_theorems", "filename": "v880_finite_anchor_theorems.py", "path": "verification/v880_finite_anchor_theorems.py", "cluster": "core", "synopsis": "CFIN.QSTAR.NORMALFORM.01 + DOILY.ANCHOR.CLASSIFY.01 + DOILY.HODGE.FACTOR.01 + P2.QUADRATIC.EXHAUSTION.01: **die vier endlichen Anker-Sätze (26/26, FINITE-ANCHOR-CLOSED)** — die geschlossene, zensus-freie Normalform q*(x) = Σ_{i 0); die Dilations-Route GESPALTEN (der v898-M2-Parent ist θ_abT-marginaler Zeuge AUF dem Kegelrand, die Schur-Kompression trägt die VOLLE Pfaffian-Mischung mit t²·3m/(1−m²) = 1/200 EXAKT; die strikte Kollar-Route familienweit exakt obstruiert, 30 Defekteinträge ALLE mit Betrag 2t); t_gap = 0.230949 THEOREM-FÖRMIG (Pf(A_dep + t·A_int) = −(t−1)(3t²−1)·q(t) EXAKT, q = 9t³+21t²−t−1 irreduzibel, Sturm-Eindeutigkeit auf (0, 1/4], Kern-Dimension exakt 2, drei kritische Flächen = Projektionen EINER Varietät, KEINE Wurzel ist 1/8); DIE ZWEI TOTEN LESARTEN als erstklassige Negative: 't = 1/8 ist ein Compiler-Wert' ist eine DEKORATION (55/55 t bestehen alle eingefrorenen v898-Gates, erlaubte Menge (0, ∞), PIN-ABSENT), 'N_fam = 3 = minimaler Mediations-Rang' ist WIDERLEGT (Rang 1 genügt per Vorzeichengesetz + Ganzzahl-Zeuge, deployter S-Rang exakt 2; die 3 pint Rand-Reinheit = Dimensions-Buchhaltung); die [O]-Prämisse von v898 bleibt UNBEWEGT.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv903_seam_rp_exclusion.py", "sourceSha256": "f9af646049e7c28530bd2f01e26cddbfd54d639732114ba9da658e240d0120a1", "linkedClaimIds": [ "SEAM.STATE.DERIVATION.01", "SEAM.CFIN.MIXING.NORMALIZATION.01", "SEAM.CFIN.MINIMAL.MEDIATOR.01", "SEAM.CFIN.TWISTED.RP.01", "SEAM.CFIN.RP.DILATION.01", "SEAM.CFIN.GAP.PENCIL.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:5ff3f529ae7be4541192", "section:6bcd4464dbd4c8f8f003", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:93b8868beb643874af75", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:e7e7f78a69bea2986c9f", "section:eb00caf29086b02d5bf5", "section:f091de1c3533bab48372" ], "activeSectionIds": [ "section:5ff3f529ae7be4541192", "section:6bcd4464dbd4c8f8f003", "section:ab9e7e520130ecc7da7c", "section:e7e7f78a69bea2986c9f", "section:f091de1c3533bab48372" ], "evidenceId": "python_verification:verification/v903_seam_rp_exclusion.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v903_seam_rp_exclusion.py", "pubMirrorHash": "f9af646049e7c28530bd2f01e26cddbfd54d639732114ba9da658e240d0120a1", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v903_seam_rp_exclusion.py" }, { "id": "v908_seam_equilibrium_wiring", "filename": "v908_seam_equilibrium_wiring.py", "path": "verification/v908_seam_equilibrium_wiring.py", "cluster": "core", "synopsis": "SEAM.CFIN.MARGINAL.STABILITY.01 + CFIN.NESS.PARENT.01: **die Seam-Gleichgewichts-Verdrahtung (22/22 + 25/25) — der Physik-Abschluss der Runde-60-Fragen** — strikte 2-Zykel-RP ist auf der GANZEN C6-kovarianten Klasse UNMÖGLICH (das Sitz-Gesetz reduziert kovariant EXAKT auf M1 = diag(a_J, −a_J), det = −a_J²: Inneres LEER — der v903-Marginal-Zeuge ist weder Limes kovarianter strikter Gleichgewichte (es gibt keine) noch isoliert: das ganze s = 0-Stratum ist marginal, sup(RP-Marge × Mischung) = 0 EXAKT); der einzige strict-enabling Ausweg ist die kovarianz-BRECHENDE X-Koordinate (exakter linearer Preis 2ε, Margen-Exponent 2) mit dem FLOOR-EXCHANGE als schärfstem exakten Objekt: Pf4(ε) = (ε − 1/200)(ε + 1/200) — das kanonische Vorzeichen-Gate IST die negative effektive RP-Marge, Crossover exakt am 1/200-Floor; die Strict-Collar-Obstruktion ist ein ZWEI-SITZ-LINEARGESETZ der Kopplung (exakter Rang 12, Kern 12 = die {J, Z}-Koordinaten des 24-dim kovarianten Kopplungsraums), die deployte Seam-Verdrahtung ist PURE-I = eine MAXIMAL obstruierte kovariante Richtung (erklärt das v903-Gesetz ‚30 Einträge, Magnitude 2t' exakt), und der Kern enthält GLEICHGEWICHTS-Zeugen: V_J/V_Z bestehen strikte θ_S-RP in exakter Arithmetik und tragen die VOLLE kanonische Pfaffian-Mischung mit J-Koordinate EXAKT t²·3m/(1−m²) = 1/200 — KEIN NESS NÖTIG: bei endlicher Größe gilt stationär ⟹ σ ≡ 0 exakt (‚NESS mit positiver Entropieproduktion' ist kategorien-unanwendbar) und Drive kauft KEINE RP — die minimale Entropieproduktion, bei der die Mischungs-Gates öffnen, ist EXAKT NULL; SEAM.CFIN.NESS.PARENT.01 schließt als NOT-NEEDED; der registrierte nächste Kontrakt SEAM.STATE.WIRING.SELECTOR.01 (ist PURE-I compiler-erzwungen?) ist in v911 GESCHLOSSEN: Deployment-Wahl, kein Compiler-Theorem; die [O]-Prämisse von v898/v903 bleibt unbewegt.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv908_seam_equilibrium_wiring.py", "sourceSha256": "8dab7fead65fc50f25eb10ab1365f005c09cfae66ca20e25513550c2ad6aa950", "linkedClaimIds": [ "SEAM.CFIN.MARGINAL.STABILITY.01", "SEAM.CFIN.NESS.PARENT.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:5ff3f529ae7be4541192", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:93b8868beb643874af75", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:e7e7f78a69bea2986c9f", "section:eb00caf29086b02d5bf5", "section:f091de1c3533bab48372", "section:f22c82858ff073c133d4" ], "activeSectionIds": [ "section:5ff3f529ae7be4541192", "section:ab9e7e520130ecc7da7c", "section:e7e7f78a69bea2986c9f", "section:f091de1c3533bab48372", "section:f22c82858ff073c133d4" ], "evidenceId": "python_verification:verification/v908_seam_equilibrium_wiring.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v908_seam_equilibrium_wiring.py", "pubMirrorHash": "8dab7fead65fc50f25eb10ab1365f005c09cfae66ca20e25513550c2ad6aa950", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v908_seam_equilibrium_wiring.py" }, { "id": "v911_wiring_freedom", "filename": "v911_wiring_freedom.py", "path": "verification/v911_wiring_freedom.py", "cluster": "core", "synopsis": "SEAM.STATE.WIRING.SELECTOR.01 (+ THETA.SELECTOR.01 + WIRING.GAUGE.RP.01): **das Verdrahtungs-Freiheits-Theorem (30/30 + 26/26 + 21/21) — die CXXXIX-Frage geschlossen, der v908-registrierte Kontrakt beantwortet: DEPLOYMENT-WAHL, kein Compiler-Theorem** — der exakte Gröbner-Zensus bestimmt GENAU EINE admissible 3-dim Verdrahtungs-Komponente mod Regel-Eichung (C_rot); Z/X sind eichinvariant durch Orientierungspropagation ausgeschlossen; pure-I ist INNERER Punkt, durch die ganzzahlige Eichung (⊕₅J2)⊕I6 mit pure-J verbunden — PURE-I IST DEPLOYMENT-REPRÄSENTANT; θ-CONVENTIONAL: keine kompilerseitige Demand zeichnet das θ_S-Frame aus (fünf Demand-Klassen silent-on-angle), der deployte Parent BESTEHT strikte Kragen-RP exakt im ganzzahlig konjugierten Frame — die Runde-58/59-Obstruktion ist FRAME-RELATIV; RP-FRAME-COVARIANT: die strict-collar RP-Grams transformieren exakt kovariant, der pure-I-Ausschluss ist eine Frame-Aussage (Option 2), KEIN Verdrahtungs-No-Go; kanonischer Satz eingefroren (sha 79950314), VERBOTEN: „pure-I ist compiler-erzwungen“; die [O]-Prämisse von v898/v903 bleibt [O]; NULL RH-Gehalt.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv911_wiring_freedom.py", "sourceSha256": "7227ee25db322726df68d6edea9cbade233099f6ccca80e94ccb3f6816aa1595", "linkedClaimIds": [ "SEAM.STATE.WIRING.SELECTOR.01" ], "sectionIds": [ "section:0739148b5a5974d0d662", "section:5ff3f529ae7be4541192", "section:848c49f799255f4cda92", "section:8872501633bb702220cd", "section:93b8868beb643874af75", "section:ab9e7e520130ecc7da7c", "section:c4cf080b9ae6f25f7a71", "section:e7e7f78a69bea2986c9f", "section:eb00caf29086b02d5bf5", "section:f091de1c3533bab48372", "section:f22c82858ff073c133d4" ], "activeSectionIds": [ "section:5ff3f529ae7be4541192", "section:ab9e7e520130ecc7da7c", "section:e7e7f78a69bea2986c9f", "section:f091de1c3533bab48372", "section:f22c82858ff073c133d4" ], "evidenceId": "python_verification:verification/v911_wiring_freedom.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v911_wiring_freedom.py", "pubMirrorHash": "7227ee25db322726df68d6edea9cbade233099f6ccca80e94ccb3f6816aa1595", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v911_wiring_freedom.py" }, { "id": "v957_ccc_crossover_kinematics", "filename": "v957_ccc_crossover_kinematics.py", "path": "verification/v957_ccc_crossover_kinematics.py", "cluster": "horizon", "synopsis": "CCC.SEAM.KINEMATICS.01 (Runden DL–DLV, 2026-08-24): **das CCC-Crossover-Kinematik-Wörterbuch (28/28 + 29/29 + 18/18 + 21/21 + 14/14 + 7/7, sechs Probes byte-exakt eingebettet)** — (1) Penroses reziproke Eichung Ω·τ(Ω) = −1 ist das Element τ = ρ²σ des bewiesenen μ4-Stabilisators D4 (τ kehrt die Clock um = Z2-Sheet-Parität; der Crossover-Kreis trägt alle vier Marken); (2) die Clock allein lässt auf der 2D-Seam genau EINEN konformen Modul, das reziproke Z2 killt ihn (Liouville-exakt; so(3,1)-Kommutanten 2/0); (3) Stinespring-Dilatation des v221-Transports exakt (V†V = 1, ‖Tⁿ−P⋆‖ = (2/3)^{6n}, globaler Overlap invariant — Entropie-Reset = reduzierter Kanal, keine Informationsvernichtung); (4) der kinematische 2D→3D→4D-Uplift: Seam-Sphäre = Hopf-Basis (stereographisch = z1/z2 exakt), Crossover X = S³/Z4 = Linsenrand des korpuseigenen A3-ALE (Deck frei; Marken = 4 verschlungene Faserkreise in 2 Sheet-Orbits, Gauss-Linking 1; so(4,1)-Deck-Kommutant = 4 Killing/0 Boosts — Yamabe-Starrheit ohne Zusatzbedingung, global via Obata-Familie), 4D-Brücke = Kegel mit Inversion als Äon-Tausch, Lorentz-Schatten Einstein R_ab = 3g_ab mit raumartigem S³-Crossover und Ω̂·Ω̌ = −1; (5) KMS-Schließung: Detailed Balance exakt, spec(−ln T) = {0, 6ln(3/2), 6ln3}, T = e^{−H_mod}, β_angle = 2π = 1/(4c3) = Gibbons–Hawking auf der Faser — diskreter Takt = modulare Zeit (freies Level); (6) Holonomie: Pol-Strings tragen die volle μ4 (i), jeder Seam-String exakt die 2-Torsion −1 = v522s GSO/Fermionparitäts-Wrap ([C]-Korrespondenz); (7) Selektor-Notwendigkeit: zulässige Spiegelachsen von M(δ) = V4 generisch, D4 GENAU bei δ = π/2; Majorana-Operator-Ebene mit Fermion-Vorzeichen: Clock-Achsen Θ-real NUR bei k = 4 — die Uniqueness-Hälfte des v534-Selektors HERGELEITET (Survival + Vorzeichen zitiert); (8) der eingefrorene Gate-6-Kernel: Top-Hat-Scheibe θ_max ≈ 1.16°, Raten ln(729/64)/ln729 (Verhältnis 2.709511), κ aus v526 hergeleitet (Band deklariert, Kontrast ≤ 3.3e−4) — speist die preregistrierte Suche ccc-crossover-disc (keine Daten berührt). Zyklische Lesart bleibt [C], WOIT.OS.TWISTOR.01 bleibt [O].", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv957_ccc_crossover_kinematics.py", "sourceSha256": "4fb069e13d4e637ed0bc58a3a3bbcc44d1c1eaf1eaf91deaa33cef15167f46ce", "linkedClaimIds": [ "CCC.SEAM.KINEMATICS.01", "CCC.SEAM.CROSSOVER.01" ], "sectionIds": [ "section:01c88746fb95cc0958d7", "section:083150cfb9ad50768449", "section:169299815207b9547d33", "section:18ed0d526d18a5853eb0", "section:2a4b108348409f980f6d", "section:2b143252250e5f0e1b6b", "section:580c8e5b415ac9b79cec", "section:5c7b501c80f2e5816761", "section:73dd631de817637ce12d", "section:76c21b1d36713cce72ac", "section:824af218b156f48374d8", "section:830ce3efdf003a4e5049", "section:84ec2c9d7a3c77ec2664", "section:98cf6dab6e992992d2c9", "section:a3401d23c565056512c5", "section:ab9e7e520130ecc7da7c", "section:c976211c2c659cc182f9", "section:dccf3e7f3250c009523d", "section:ea28e660b1549c41a88a", "section:f28a7b7a00ea958cfb53", "section:f8ad9138e39428999ab9", "section:fbf67a6377a333f71dff", "section:fd8a259cd96f2b7b4df5" ], "activeSectionIds": [ "section:01c88746fb95cc0958d7", "section:18ed0d526d18a5853eb0", "section:580c8e5b415ac9b79cec", "section:830ce3efdf003a4e5049", "section:84ec2c9d7a3c77ec2664", "section:a3401d23c565056512c5", "section:ab9e7e520130ecc7da7c", "section:c976211c2c659cc182f9", "section:dccf3e7f3250c009523d" ], "evidenceId": "python_verification:verification/v957_ccc_crossover_kinematics.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v957_ccc_crossover_kinematics.py", "pubMirrorHash": "4fb069e13d4e637ed0bc58a3a3bbcc44d1c1eaf1eaf91deaa33cef15167f46ce", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v957_ccc_crossover_kinematics.py" }, { "id": "v971_markov_embedding_generator", "filename": "v971_markov_embedding_generator.py", "path": "verification/v971_markov_embedding_generator.py", "cluster": "frontier", "synopsis": "", "publicationNotes": [ "Non-scientific synopsis omitted." ], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv971_markov_embedding_generator.py", "sourceSha256": "d375800751d102835142fc81ea465021a7b82ed161a6672d70a052228513a945", "linkedClaimIds": [ "DYN.MARKOV.EMBED.01" ], "sectionIds": [ "section:01c88746fb95cc0958d7", "section:10eb7a1a008b9b2bbd4b", "section:39807bac57329dd11bcf", "section:568b5e9acdb7b04367d3", "section:5c7b501c80f2e5816761", "section:98cf6dab6e992992d2c9", "section:a3401d23c565056512c5", "section:ab9e7e520130ecc7da7c", "section:c8d53f7c2e20223e312d", "section:f0ac30137703825661c6", "section:fdf63a1d99769ab37ccb" ], "activeSectionIds": [ "section:01c88746fb95cc0958d7", "section:a3401d23c565056512c5", "section:ab9e7e520130ecc7da7c", "section:c8d53f7c2e20223e312d", "section:fdf63a1d99769ab37ccb" ], "evidenceId": "python_verification:verification/v971_markov_embedding_generator.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v971_markov_embedding_generator.py", "pubMirrorHash": "d375800751d102835142fc81ea465021a7b82ed161a6672d70a052228513a945", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v971_markov_embedding_generator.py" }, { "id": "v972_seam_interaction_front", "filename": "v972_seam_interaction_front.py", "path": "verification/v972_seam_interaction_front.py", "cluster": "core", "synopsis": "SEAM.INT.ODDSPLIT.01 [E] + SEAM.INT.OSAVOID.01 [E] + SEAM.STATE.RPMIXING.01 [E] (+ Updates an SEAM.INT.FKTOY.01 / WOIT.OS.TWISTOR.01 / SEAM.STATE.DERIVATION.01; Konsolidierung dreier Explorationsrunden vom 2026-08-27, alle drei Sonden byte-exakt eingebettet mit gepinnten Quell-SHA-256 und wörtlich ausgeführt, 20/20 + 18/18 + 25/25, Verdikte CLASS_EMPTY_ON_BASIS + OS_VIABLE_ON_AVOIDING + RP_ADMITS_MIXING): **DIE SEAM-INTERAKTIONSFRONT** — (1) Die hinreichende Jaffe–Pedrocchi-Bedingung für Majorana-Reflexionspositivität (arXiv:1406.1384; Wei–Li–Xiang arXiv:1601.01994) wird auf dem v529-FK-Toy ENTSCHEIDBAR gemacht: die Kreuzungs-Koeffizientenmatrix B ist EINDEUTIG (Links-Monom-Paare bijektiv auf Kreuzungsmonome), also ist „B hermitesch UND −B PSD\" ein endlicher Check; der freie FK-Hamiltonian wird auf allen 8 Bond-Cuts zertifiziert (Twist η = −i erzwungen); die Konfusionsmatrix gegen gemessene RP über 35 Zellen ist PERFEKT (23 zert.&PD / 12 unzert.&fail / 0 FP / 0 FN); der μ4-kovariante Quartik-Raum (dim 464) ist auf der Basis LEER (und auf 64 geseedeten Kombinationen; der Träger-Ausschluss pinnt den vollen 1820-dim Raum) — DIE ENTDECKUNG: das v529-Straddle-Gesetz VERFEINERT sich zum ODD-SPLIT-GESETZ: JP sagte RP-Überleben auf ZENTRIERT gestraddelten Cuts voraus (m = 4-Modell, Achsen 7/15, 2+2-Spiegelsplit), die Direktmessung bestätigt ((37,0,0) bei g = 0.5/1/2); die v529-Ankerleiter exakt reproduziert. (2) Die quartett-MEIDENDE Cut-Familie des uhr-invarianten m = 4-Mitglieds erzeugt die VOLLE gerade Seam-Algebra (Rang 15, dim 32768 = 2¹⁵; Einzel-Cut-Mitglieder m = 2/6 mit typisiertem Defizit EXAKT 1), und OS/GNS auf dem meidenden Cut k = 3 bei g = 1 ist POSITIV (min +4.43e−5, GNS 37/37, Distanzen 1.044/1.386/1.650 monoton), während die gestraddelte Kontrolle ehrlich scheitert (−6.94e−2); die μ4-Uhr bildet das meidende Paar {3, 11} exakt auf sich ab — das Kill-Test-2-Gegengewicht VERENGT, hebt nicht auf. (3) Die v903-Exklusivität ist STRAHL- und SPIEGELUNGS-relativ, nicht slice-weit: auf dem vollen 33-dim C6-kovarianten Mixing-Slice sieht θ_abT genau EINE Koordinate (a_J, Kernwert −1/(1+c²) = −0.8240271368 bei c = tanh(1/2)), 32/33 unsichtbar ⇒ 32-dim MARGINALE RP-Hyperebene {a_J = 0}; die θ_S-Defektabbildung hat Rang 16 ⇒ 17-dim erstordnungs-neutraler Unterraum mit STRIKTEN finite-s-Zeugen (W_S bei s = 1/8, λ_min 0.1558 — genau die Richtung, die θ_abT tötet); der v903-Anker reproduziert (a_J = +0.04068013). Modul-eigene Exaktsektion S0 (sympy/GF(2), keine Sonden-Importe): JP-Entscheidbarkeits-Lemma am 4-Majorana-Toy (9 paarweise verschiedene Kreuzungsmasken ⇒ eindeutiges B; Falschvorzeichen-Toy SCHEITERT), Odd-Split-Arithmetik (zentriert ⇔ 2+2 exakt auf Z₁₆; der ungerade 1+3-Block [[0,b],[b*,0]] erzwingt b = 0 — die Obstruktion; Vorzeichen-Flip-Mutant CAUGHT), GF(2)-Erzeugungs-Buchhaltung (Paarrang 15, 2¹⁵ = 32768; Innerhalb-Hälften-Rang 14 — Defizit exakt 1), Fenster-Arithmetik (33 = 24 + 9, 32 + 1, 33 − 16 = 17; Kernwert symbolisch == −cosh(1/2)²/cosh(1)) plus 4 Verdikt-Bars mit Kipp-Mutanten. EHRLICH: KEINE Marker-Bewegung; SEAM.EQUIV.01 bleibt [O]; der v529-Pflichtzaun (EIN Toy, EINE Wechselwirkungsklasse, [C] Flachband-Parent) wird von allen drei Resultaten GEERBT; JP ist nur hinreichend; der S1-Zensus ist sektor-trunkiert. KEIN RH-Claim.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv972_seam_interaction_front.py", "sourceSha256": "76f0e4bb6aa5d8d7fa0cb6dcaf9a2d057b2d3352fcb064a2da6f8700319fe736", "linkedClaimIds": [ "SEAM.INT.ODDSPLIT.01", "SEAM.INT.OSAVOID.01", "SEAM.STATE.RPMIXING.01" ], "sectionIds": [ "section:00084b3039331dc8515a", "section:2db6bd35ce5c578613f3", "section:3bc2480a0b64fd3112f1", "section:46614e805445fc78e7af", "section:58f2181069f63dc9bc77", "section:5ff3f529ae7be4541192", "section:6e482b6ca2a1df5c2627", "section:7d0e50b6a6c30535730d", "section:7ee581db787f8ddbcb4a", "section:848c49f799255f4cda92", "section:8d1e955857da6655fadd", "section:93b8868beb643874af75", "section:ab9e7e520130ecc7da7c", "section:b191b0a66e5bacdc1a0e", "section:c4cf080b9ae6f25f7a71", "section:c519f45910c30ff3c0ae", "section:cac001c63c2444d31263", "section:cca5b83aae425d5f0e88", "section:ccd38232c9f484cdbcb7", "section:de8db1cd8257eab0d607", "section:e7e7f78a69bea2986c9f", "section:eb00caf29086b02d5bf5" ], "activeSectionIds": [ "section:00084b3039331dc8515a", "section:3bc2480a0b64fd3112f1", "section:46614e805445fc78e7af", "section:5ff3f529ae7be4541192", "section:8d1e955857da6655fadd", "section:ab9e7e520130ecc7da7c", "section:cac001c63c2444d31263", "section:ccd38232c9f484cdbcb7", "section:de8db1cd8257eab0d607", "section:e7e7f78a69bea2986c9f" ], "evidenceId": "python_verification:verification/v972_seam_interaction_front.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v972_seam_interaction_front.py", "pubMirrorHash": "76f0e4bb6aa5d8d7fa0cb6dcaf9a2d057b2d3352fcb064a2da6f8700319fe736", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v972_seam_interaction_front.py" }, { "id": "v973_seam_route_narrowing", "filename": "v973_seam_route_narrowing.py", "path": "verification/v973_seam_route_narrowing.py", "cluster": "core", "synopsis": "SEAM.EQUIV.MMST.01 [O-Update] + SEAM.EQUIV.TWISTOR.01 [O-Update] + SEAM.EQUIV.SKELETON.01 [E, NEU] + SEAM.EQUIV.01 [O-Update] (Seam-Adjudikationswelle, 2026-08-27): **die Seam-Routen-Verengung — drei Probes byte-exakt eingebettet (19/19 + 20/20 + 19/19; SPEC e6f392cbcd0d3ae1 / 0875f39fe1d0fa0f / 451bd470b98a9d6d), plus die modul-eigene Exaktsektion S0** — (1) MMST-ABDECKUNG ZERLEGT: der zitierte Osborne–Stottmeister-Satz (CMP 398 (2023) 219, arXiv:2107.13834) DECKT die bilineare Hälfte des Seam-Ziels — so(16)₁-Fermion-Bilinear-WZW-Ströme konvergieren STARK auf dem endlichen Teilchenkern (Thm 5.1 + Cauchy–Schwarz Gl. 229 inkl. Majorana-Algebren), Virasoro/Koo–Saleur (Thms A/4.11/4.16), Korrelatoren (Thms B/C), polynomiale Fehler Error² ≤ C·2^(−2δN), δ ∈ [0,2] — und deckt vier BENANNTE Punkte NICHT: N1 die μ₄/GSO-Erweiterung SO(16)₁ → (E8)₁ als NETZ-Aussage (die 128 Spinor-Ströme sind keine Bilineare), N2 der Twist-/Spinfeld-Sektor (vom Paper explizit verschoben), N3 das einseitige chirale Randnetz eines 2+1D-Bulks, N4 der Holomorphie-Selektor det K = 1 vs 4; NEUE MESSUNG: die Rand-Korrelator-Konvergenzrate auf dem v367-Collar p = 3.48 (Richardson 3.1–4.2, präregistriertes Band [0.5, 4.0]), Fehler 6.3e-2 → 2.7e-6 über Nx = 16..256; die M = 3-Kontrolle konvergiert NICHT zum chiralen Ziel (min rel Abw 0.836); die Abdeckungs-Gates exakt-ganzzahlig (248 = 120 + 128, 240 Wurzeln = 112 + 128, det Cartan 4 → 1, Index-Arithmetik 2·2 = 4 = |μ₄|). (2) TWISTOR-MASS-RIGIDITÄT: auf dem berechenbaren v508/v515-Sektor hat die 18-Parameter-Deformation der deklarierten Maßdaten (Kontakt-Normierung, 4 Sektorgewichte, Residuen-Normierung, 4 Linking-Ladungen, 4 Zentrumspositionen) die exekutierten Constraint-Ränge C1 Uhr 9 / C2 Lockstep+Ganzzahligkeit 8 / C3 Ladung 2 / C4 Null-Ideal 2, gemeinsamer Rang 13, 4 Eichrichtungen ⇒ der Moduli-Kern ist EXAKT 1 = der uniforme Sektorgewichts-Shift dv = (1,1,1,1), abgebildet auf das ungetwistete Okubo-Quadrat Q⁰ = 36(1,2,1,0,0), von jedem exekutierten Zertifikat-Funktional PER KONSTRUKTION annihiliert (exakt flach zu allen Ordnungen); Anker re-deriviert (A_fix = (9,−30,−15,0,32), Zertifikat (0,32,72), ψ(A_fix) = 64); Ablations-Leiter (voll,−C1,−C2,−C3,−C4,−C1&C2) = (1,3,1,2,3,10); ehrlich: der W₂:W₁₃ = 4:3-Tester ist NOT-TRANSCRIBABLE. (3) OS-SKELETT GETEILT: ALLE fünf WOIT-Killtest-Hauptinvarianten (α: erzwungenes η = +i, Θ² = +1, Bond-RP; β1: GSO-2-Torsion; β2: OS-Quotient existiert + KMS λ_max > 1; β3: Perp-Descent; γ: Spiegel-Flip, multiplizitätsfrei, Mark-Inzidenz) gelten WÖRTLICH auf der p+ip-Collar-Kante; ALLE Divergenzen kontroll-typisiert und auf EINEN Mechanismus zurückgeführt (das exakte chirale Schachbrett C(even) = 0 des Twistor-Gitters vs K(even) bis 0.1736 des Collars — bestätigt v519-R4 unabhängig von der zweiten Route); BONUS: die obere Kante realisiert den anti-chiralen Zustand EXAKT (max|K_top + K_bot| = 7.5e-16); der triviale M = 3-Collar verliert das Skelett ZUERST bei GAMMA.MARK.INCIDENCE — das Skelett folgt der topologischen Phase. Modul-eigene Exaktsektion S0: Abdeckungs-Arithmetik exakt (Wurzel-Zensus, Cartan-Determinanten, Index); die Eindeutigkeits-Lineare-Algebra als exakte Rationale auf einem unimodular gemischten 18-Raum (Ränge (9,8,2,2) → 13 → Kern 1; Ablations-Leiter exakt; der C4-Drop-Mutant öffnet den Kern auf 3 — CAUGHT); die Skelett-Mechanismen exakt (bipartit S H S = −H ⇒ ungerade Funktionen verschwinden auf geraden Distanzen; P H P = −H auf dem Streifen ⇒ K_top = −K_bot exakt); Verdikt-Bars mit Kipp-Mutanten (ein falsches COVERAGE_FULL wird vom nichtleeren N1–N4-Gate VERWEIGERT; Hash-Mutation CAUGHT). EHRLICH: die Abdeckungs-Gates sind ausführbare TRANSKRIPTIONEN einer menschlichen Literatur-Adjudikation; die Rate SUPERKONVERGIERT (p > δ_max = 2) gegen die zitierte OBERE Schranke — Band kalibrierungs-informiert; die Sektor-Eindeutigkeit ist KEINE BCOV-Herleitung; Skelett-Treue pro Test typisiert. 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(1) Das BFK-Face AUSGEFÜHRT: die Burghelea–Friedlander–Kappeler-Klebekonstante ist EXAKT 2^−N (symbolisch hergeleitet N = 1..4, allgemeine Intervalllängen, Laurent-Polynom-Identität); masselose Reassemblierung det′_ζ(Δ_S¹) = l² = 2^−N·∏(2a_j)·(l/N)·det′(R₀) mit det′(R₀) = N·l/∏a_j; an der KMS-Skala l = 2π = 1/(4c₃): R₀ = 16c₃·circ(2,−1,0,−1) (16c₃ = |μ₄|·4c₃ pro Intervall), det′R₀ = 2¹⁶c₃³, Produkt (2π)²; Sprungmatrix R(m) = (G_m|_marks)⁻¹ exakt; gegen die v484-Markenmatrix G_marks = −4c₃ln2·circ(0,1,2,1) KEINE globale Proportionalität (Kerne in VERTAUSCHTEN μ₄-Kanälen: Eich-Nullmode vs. Vorzeichendarstellung), aber kanalweise EXAKT (gleiche μ₄-Fourier-Eigenbasis, |spec|-Multimengen {0,2,2,4}, Dublett-Verhältnis 4/ln2 mit KÜRZENDEM c₃, Tr B^k = 4^k + 2·2^k spiegelt Tr C^k = 4^k + 2(−2)^k — der Vorzeichen-Flip IST der Kern-Tausch); der v485-Skalenkanal EXAKT reproduziert über die KMS-Einheit (log det′-Differenz = (1/(4c₃))·G_reg(0;l)). (2) EM1 GERECHNET: gepumpte Ladung == Rand-Spektralfluss == Streda == Chern == 1 pro Flussquant auf dem v367-Kragenmodell (Wannier-Winding-Residuum 0.0; Streda ΔN = C·n_φ exakte Ganzzahlen; der Konjugations-Mutant kippt ALLE VIER Lesarten simultan, der Falschband-Projektor bricht die Quantisierung gitterinstabil); Buchhaltung exakt: 16 Majoranas = 8 komplexe Kopien, c₋ = 8 = g_car + N_fam, k_Y = 5/3, (1/k_Y)·41/6 = 41/10 = b₁. (3) Die endliche Quillen-Identität ZWEISEITIG: Berry-Integral == Poincaré–Lelong-Divisor-Integral == +1 über dem Twist-Torus (beide Referenzen, beide Größen), Differenz eine EXAKTE Form (3.3e−16), Übergangs-Winding == Chern (Dai–Freed); typisiert konditional auf die Quasi-frei-Rigiditäts-Prämisse (gemessen, nicht bewiesen — SEAM.STATE.RPMIXING.01). S0 leitet alles unabhängig her: die BFK-Geschlossenformen aus den ζ_R-Werten, den Alpha-Anker bei 50 Stellen (8b₁ = 164/5 exakt, EINDEUTIGE Wurzel im Scanfenster, α⁻¹ = 137.03599921684071, Split-Residuum 6.4e−58), die Inflow-Buchhaltung als exakte Brüche und ein probe-freies FHS-Chern-Zertifikat. Mutanten: Hash-Mutation vom sha256-Pin gefangen; die falsche KMS-Einheit (2π → 4π) bricht die Skalenidentität um EXAKT −2ln2; der b₁-Mutant gefangen. 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Unter dem benannten TFPT-kompatiblen Axiomensatz A1 (d > 2: propagierende lokale Eichfelder), A2 (dimensionslose Yang-Mills-Kopplung), A3 (reelle selbstduale/anti-selbstduale 2-Form-Sektoren: der euklidische Hodge-Stern als involutiver Endomorphismus auf 2-Formen), A4 (chirale Weyl-Darstellungen: gerades d) ist d = 4 auf dem exakten Scanfenster d = 2..12 EINDEUTIG und MINIMAL — und der Selektor ist ÜBERDETERMINIERT: A2 allein = {4} ([g_YM] = (4−d)/2 symbolisch erzwungen, einzige Nullstelle 4) und A3 allein = {4} (expliziter 6×6-Stern auf Λ²(R⁴), *² = I, Eigenwerte ±1 mit Multiplizitäten 3/3), während A1 & A4 allein {4, 6, 8, 10, 12} geben — Chiralität selektiert 4 NICHT allein (ehrliche Ablations-Leiter). Weyl-Chiralität zertifiziert durch exakte Clifford-Algebren d = 2..7 (gerade d: γ* antikommutiert, γ*² = I, spurfrei; ungerade d: das Produkt ist ZENTRAL und skalar). Signatur ehrlich typisiert: lorentzisch ist *² = −1 auf 2-Formen — der reelle Split ist eine EUKLIDISCHE/OS-seitige Aussage. Mutanten gefangen ([g] = (6−d)/2 selektiert {6}; der 'A4 allein'-Overclaim verweigert). 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Gitter-Arithmetik-Schatten vollstaendig] (Externe Master-Objekt-Review Welle 2, 2026-08-28): **der eine Glue-Vektor lambda = (omega_s, omega_f) erzeugt den gesamten 128er-Spinorsektor — exakt auf Gitterebene** — |omega_s|^2 = 5/4, |omega_f|^2 = 3/4, |lambda|^2 = 2, konformes Gewicht h_lambda = 1 (ganzzahlig => triviale Selbstmonodromie); [lambda] hat ORDNUNG VIER in der Diskriminantengruppe Z4 x Z4 von D5 (+) A3 (4 lambda in L0, lambda und 2 lambda nicht); lambda . L0 in Z => isotrope Verklebung, geklebtes Gitter GERADE; det = 16/4^2 = 1 => UNIMODULAR Rang 8 => E8 (Klassifikation [C]; explizites Zertifikat v1). COSET-WURZEL-ZENSUS [52, 64, 60, 64] (Summe 240; +8 Cartan = 248 = (45+15) + (16,4) + (10,6) + (16bar,4bar)); die ungeraden Fusionspotenzen tragen 64 + 64 = 128 = der VOLLE fehlende Spinorsektor — EIN Feld erzeugt alle vier Cosets. KILL-TESTS FEUERN: Vektorklassen-Glue (Norm 7/4) und Fehlklassen-Glue (Norm 9/4) brechen beide die Geradheit. HOLOMORPHIE-SCHATTEN: det 1 => ein Sektor vs det(D8) = 4 => SO(16)_1 hat vier (nur der Gitter-Schatten von N4). 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MUST-FAIL FEUERT: der geschlossene Unitaer hat |U_B^2|^2 != B^2 (31/54 vs 0.2450) — die Dilatation ist notwendig. TYPISIERTE BEMERKUNG (Probenbefund GEGEN den Review-Text): eine WIEDERVERWENDETE mod-3-Addierer-Ancilla gibt diag = B^2 p weiterhin exakt (der Rekord j1+i bleibt unterscheidbar) — frische Ancillas braucht man fuer die Kohaerenzen, nicht fuer die Populationen. Der konjugierte Zweig V* dilatiert dasselbe B (sgn J = +-1/27 bleibt klassisch unsichtbar; Auswahl bleibt [O]). 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FIREWALL: nur endliche 4x4-mu4-Zirkulanten; Kontinuums-Bismut-Freed, KMS-Rigiditaet, die 2^-4/Quillen-Metrik-Kompensation und die Exaktheit von F_U(1) bleiben [O]; alpha^-1 unberuehrt; keine Marker-Bewegung.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv985_quillen_channel_swap.py", "sourceSha256": "3f09ec91b2d9ca53d1556d87661303b4d933339ed45b6d8a8cf8c0a8c6112dd0", "linkedClaimIds": [ "ALPHA.QUILLEN.EXACT.01" ], "sectionIds": [ "section:0534241ef38a39dcc3cc", "section:09b49009253acb5a0dfb", "section:1fa633590a33e985ed41", "section:3cc790136e8b9bd3c188", "section:3d3092d4174b4ba2e0ec", "section:584e87a9c163ac38f92f", "section:64a9e573649942dd32e9", "section:6a757c5701557192653a", "section:a3b94e09ceb6d6dbdae4", "section:ab9e7e520130ecc7da7c", "section:c852f8ae0a03109ca8ad", "section:ca7a45590bd2289527ff", "section:eb0bd97fda8c0fedefad" ], "activeSectionIds": [ "section:0534241ef38a39dcc3cc", "section:584e87a9c163ac38f92f", "section:64a9e573649942dd32e9", "section:6a757c5701557192653a", "section:ab9e7e520130ecc7da7c", "section:c852f8ae0a03109ca8ad" ], "evidenceId": "python_verification:verification/v985_quillen_channel_swap.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v985_quillen_channel_swap.py", "pubMirrorHash": "3f09ec91b2d9ca53d1556d87661303b4d933339ed45b6d8a8cf8c0a8c6112dd0", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v985_quillen_channel_swap.py" }, { "id": "v986_nu_scalaron_rung", "filename": "v986_nu_scalaron_rung.py", "path": "verification/v986_nu_scalaron_rung.py", "cluster": "frontier", "synopsis": "FLAV.NUSCALE.05 [C]/[N] Kandidat (Externe Master-Objekt-Review Welle 2, 2026-08-28): **die Skalaron-Spur-Sprosse M_R = N_fam M_scal = 3 c3^{7/2} Mbar — ein strukturierter Punkt IM v481-Fenster, 1.8 % von der 1-Loop-Anforderung** — 3 M_scal = 9.180e13 GeV vs das v481-geforderte 9.346e13 GeV (dieselbe eingefrorene 1-Loop-Inversion, y_nu = y_t [P]) — Abweichung -1.8 % (der Review sagte 'etwa 1 %'; der ehrliche Wert ist 1.8), m_3 am Kandidaten = 0.0512 eV (+1.9 %, innerhalb der >50 %-v482-RG-Enveloppe); EXAKTE Leiterposition 3 c3^{7/2} = (3 sqrt c3) c3^3 mit 3 sqrt(c3) = 3/sqrt(8 pi) = 0.598413, 0.26 % von der 3/5 der v482/v488-Geschichte — ADJAZENZ EHRLICH TYPISIERT: v488 toetete 3/5 als SO(10)-CLEBSCH; die Skalaron-Spur-Lesart ist eine ANDERE Mechanismusklasse (HONEST RETYPE Welle 3: Tr I = 3 ist locker, Spec(I)={1,1,1}; Operator-Lesart ist Q_+ Spec{1,2,3}; Textur DATA_CONSTRAINS_TEXTURE) und bleibt selbst [O]; ~20x schaerfer als die abgelehnte Ganzzahl-Sprosse c3^3 Mbar (0.019 vs 0.401 in m_3); dasselbe M_scal traegt bereits f_a = M_scal/128 (v185) — kein neues Skalenatom. KILL-TEST: Sigma m_nu (NO) = 0.059 eV; eine robuste Schranke darunter oder ein >~5 %-Shift der geforderten M_R toetet den Kandidaten. 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KILL: D4(+)D4 / A7(+)A1 scheitern an der Zyklizitaet (Produkt 16); Z3-Kontrolle E6(+)A2 = Z3 x Z3. [lambda]^2 = [v] EXAKT (Gitterschatten von U^2 = (-1)^F). mu4-Mittelung = EINDEUTIGE spurerhaltende bedingte Erwartung (Modul-Eigenschaft noetig: ohne sie Kern dim 36/720). P1-Arithmetik 1/(4*2pi)=c3 ist v813-Bestand; Aequiverteilung bleibt [C] von v813. 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C6 = das quasi-freie Konvergenztheorem ist jetzt AUSGESCHRIEBEN (articles/2026-08-28/psi_lambda_convergence_theorem_en.tex; 2/pi^2=0.20264 vs gemessen 0.203, 0.18%). C7 modulare Invarianz bleibt zitiert. 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Typ-III/Kontinuum bleibt zitiert/offen. 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Detline-Kruemmung -> 2pi exponentiell, Rate 0.6936 ~ ln 2 (numerischer Bismut-Freed-Schatten, kein Kontinuumstheorem). alpha_s(M_Z) bleibt externer Input. 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FK-SMG-Toy: N=8 eindeutiger Spin(7)-Singulett-Grundzustand, Schmidt-Rang 1, volumenunabhaengiges Gap 14 bei L=1,2,3; N=4-Kontrast 2^L-entartet; physische chirale Kante behaelt pi/L-Spektrum exakt. Python-only / Wolfram-Spiegel zurueckgestellt.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv997_spin2_smg_witnesses.py", "sourceSha256": "b4ea6b72fbf77d5042e26abd31ed3e911cbd41f5fd87ea88faa6c26bac496f0b", "linkedClaimIds": [ "CHIRAL4D.NOMIRROR.01", "GRAV.SPIN2.EMERGENCE.01" ], "sectionIds": [ "section:11cf2220db595f7b5339", "section:3ef64d782ddc411f1754", "section:65138c298db225aabbae", "section:7b481ee095ad252819f8", "section:81a6dc002dc46cf7b6c5", "section:970b604e67143eb148a6", "section:ab9e7e520130ecc7da7c", "section:ccd38232c9f484cdbcb7", "section:e4bb9a238c9f340ff5d1", "section:f0556283246eaeda72b3", "section:f5274c8105ff62e99dcd" ], "activeSectionIds": [ "section:65138c298db225aabbae", "section:7b481ee095ad252819f8", "section:81a6dc002dc46cf7b6c5", "section:970b604e67143eb148a6", "section:ab9e7e520130ecc7da7c", "section:ccd38232c9f484cdbcb7", "section:f5274c8105ff62e99dcd" ], "evidenceId": "python_verification:verification/v997_spin2_smg_witnesses.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v997_spin2_smg_witnesses.py", "pubMirrorHash": "b4ea6b72fbf77d5042e26abd31ed3e911cbd41f5fd87ea88faa6c26bac496f0b", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v997_spin2_smg_witnesses.py" }, { "id": "v998_seam_modular_closure", "filename": "v998_seam_modular_closure.py", "path": "verification/v998_seam_modular_closure.py", "cluster": "frontier", "synopsis": "SEAM.EQUIV.MMST.01 / SEAM.SIMPLECURRENT.GENERATOR.01 [O-Update: C7-ARITHMETIK-SCHATTEN jetzt exakt; Netz-C7 bleibt zitiert] (Review-Welle 4, 2026-08-29): Zwei-Kanten-HS-Rest <= 2.11 auf dem Plateau Nx in (16,24,32,48,64,96); Gitter-Charakter theta_E8/eta^8 EXAKT vier Ordnungen [1,0,248,0,4124,0,34752]; Theta_E8(tau)=E4(tau) q-Entwicklung >= 8 Ordnungen exakt (Jacobi vs Eisenstein); j^{1/3}-Transform bei 60 Stellen; S-Gewicht-Buchfuehrung. Netz-C7 bleibt zitiert/offen. 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Vertrag bleibt [O]. 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SK -- KMS/FDT ~1e-17, rho_0-Kontrast 3.550e-3 vs statisch 1e-16, Sattel 5-fach entartet, 3pi/5 eindeutig im mu4-Lift [C]. Beide Vertraege bleiben [O]. 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Kills: DESI-Floor, DUNE delta_CP 287.7 vs 240, JUNO. FLAV.NUSCALE.05 unbewegt. 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Python-only / Wolfram-Spiegel zurueckgestellt.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv1002_spin10_mirror_projector.py", "sourceSha256": "84f7cd7987887ee071d7e05872285ab274ae329f6bcfa693be69bb52add19a4c", "linkedClaimIds": [ "CHIRAL4D.NOMIRROR.01", "CHIRAL4D.MIRROR.DET16.01" ], "sectionIds": [ "section:11cf2220db595f7b5339", "section:33d37547e51432bedff8", "section:52fe7259f20dc261237c", "section:53d5143975a8c0ba13df", "section:5a8078e84394b902d12b", "section:6ce553746490f88b0988", "section:710760dba8520599a644", "section:7b481ee095ad252819f8", "section:845ed867739988332e9e", "section:8bcd1b39df69f2ce6417", "section:ab9e7e520130ecc7da7c", "section:c55d5c0e208b3eaef29d", "section:db01ea1aa320dae5cd00", "section:f0556283246eaeda72b3", "section:f5274c8105ff62e99dcd", "section:f989f7674214352c43f6" ], "activeSectionIds": [ "section:52fe7259f20dc261237c", "section:53d5143975a8c0ba13df", "section:5a8078e84394b902d12b", "section:710760dba8520599a644", "section:7b481ee095ad252819f8", "section:ab9e7e520130ecc7da7c", "section:f5274c8105ff62e99dcd", "section:f989f7674214352c43f6" ], "evidenceId": "python_verification:verification/v1002_spin10_mirror_projector.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v1002_spin10_mirror_projector.py", "pubMirrorHash": "84f7cd7987887ee071d7e05872285ab274ae329f6bcfa693be69bb52add19a4c", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v1002_spin10_mirror_projector.py" }, { "id": "v1003_nu_structural_nulls", "filename": "v1003_nu_structural_nulls.py", "path": "verification/v1003_nu_structural_nulls.py", "cluster": "frontier", "synopsis": "FLAV.NU.TEXTURE.MECHANISM.01 [O] (Review-Welle 5, 2026-08-29; bindende Constraints, keine Texture): [E] geladener Sektor h=(1,1,1), d=(64,60,64); [X] Schur-Texture-NULL 8/8 (K,B) scheitern, D4-Spiegelung erzwingt lambda_1=lambda_3; gefordertes K ~ [3536.998, 1768.499, 1/3] trifft keinen von 9 Komparatoren; [E] Orientierungs-Verdopplung hebt Entartung generisch; [X] Skalen-NULL 12/12, 1-|c/a|=1.885e-4 von keiner gefrorenen Konstante. Mechanismus muss D4-ungerade sein UND ~2e-4-Cancellation liefern; reine Seam-Daten ausgeschlossen. 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EXAKT ABER [C] (zirkular): eindeutiges t=2, lambda=7/3, CM J0^2=-I, Index 25=g_car^2 SNF (1,1,25) -- ABER Traeger 5 sitzt schon in den Spaltensummen von Q_2 und C: KEIN P2-Selektor. [C] Klein-Vier SNF (2,2) nur nach D=2d. AX.P2.01 unbewegt. Python-only / Wolfram-Spiegel zurueckgestellt.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv1005_relative_pencil_bridges.py", "sourceSha256": "08d6bafcc1cdef466ca50419cdb7a33e79b1726c3b5883bbae0dd15cfd64a200", "linkedClaimIds": [ "AX.P2.01" ], "sectionIds": [ "section:2cbe5d1807cd76c5e04d", "section:710760dba8520599a644", "section:789583ec50a9f61cdf33", "section:81a6dc002dc46cf7b6c5", "section:83df5fee438149d3054f", "section:86d6234f384db2b3c770", "section:89a96ea40df8ee1ce3c8", "section:ab9e7e520130ecc7da7c", "section:f5274c8105ff62e99dcd" ], "activeSectionIds": [ "section:710760dba8520599a644", "section:81a6dc002dc46cf7b6c5", "section:83df5fee438149d3054f", "section:86d6234f384db2b3c770", "section:89a96ea40df8ee1ce3c8", "section:ab9e7e520130ecc7da7c", "section:f5274c8105ff62e99dcd" ], "evidenceId": "python_verification:verification/v1005_relative_pencil_bridges.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v1005_relative_pencil_bridges.py", "pubMirrorHash": "08d6bafcc1cdef466ca50419cdb7a33e79b1726c3b5883bbae0dd15cfd64a200", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v1005_relative_pencil_bridges.py" }, { "id": "v1006_mmst_lemma_battery", "filename": "v1006_mmst_lemma_battery.py", "path": "verification/v1006_mmst_lemma_battery.py", "cluster": "frontier", "synopsis": "SEAM.MMST.TYPEIII.CHARGED.01 [O]: five in-house lemmas; Round-4 document guard requires native v1026 norm below 2.995906 at fixed M=1, Ny=8 for all even N>=16 plus explicitly open FE-GEN/ALG-EXH/MMST; historical 2.11 grid is not the proof; 68/68", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv1006_mmst_lemma_battery.py", "sourceSha256": "7ce9873c4554d1f20554ff185a88c92680d39f79074ccab93a88ef17c42b4df9", "linkedClaimIds": [ "SEAM.MMST.TYPEIII.CHARGED.01" ], "sectionIds": [ "section:2465208e294a3178e3e1", "section:710760dba8520599a644", "section:81a6dc002dc46cf7b6c5", "section:a25026597f4b790eb050", "section:ab9e7e520130ecc7da7c", "section:d185199a34886354d525", "section:eed3aaec663e71b02dd1", "section:f5274c8105ff62e99dcd" ], "activeSectionIds": [ "section:710760dba8520599a644", "section:81a6dc002dc46cf7b6c5", "section:a25026597f4b790eb050", "section:ab9e7e520130ecc7da7c", "section:eed3aaec663e71b02dd1", "section:f5274c8105ff62e99dcd" ], "evidenceId": "python_verification:verification/v1006_mmst_lemma_battery.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v1006_mmst_lemma_battery.py", "pubMirrorHash": "7ce9873c4554d1f20554ff185a88c92680d39f79074ccab93a88ef17c42b4df9", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v1006_mmst_lemma_battery.py" }, { "id": "v1007_det16_stability_battery", "filename": "v1007_det16_stability_battery.py", "path": "verification/v1007_det16_stability_battery.py", "cluster": "frontier", "synopsis": "CHIRAL4D.MIRROR.DET16.01 Kandidat [C] (Review-Welle 7, 2026-08-30): T1/T2 bewiesen (v1002); T3 Michalakis-Zwolak zitiert-verifiziert (LTQO, t*>0, Gap>=1/2). [N] Zaehlgerade n=2,3; n=2-Scan bis t=4; dynamische Z2/Z4 eindeutig gelueckt (Vollsonden-Min 0.728854416); SW 1-alpha t^2 + O(t^4); c_geo/L beschraenkt. [X] gewoehnliches Hopping nicht blockdiagonal, daher 1/192 boxed; BDL liefert keinen volumen-uniformen Gap-Rest. Bleibt [C]. Python-only / Wolfram-Spiegel zurueckgestellt.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv1007_det16_stability_battery.py", "sourceSha256": "feaf81bb4bb568cce12a972d606f93ba9eb841b986c395b677ef433574d53baf", "linkedClaimIds": [ "CHIRAL4D.MIRROR.DET16.01" ], "sectionIds": [ "section:6ce553746490f88b0988", "section:710760dba8520599a644", "section:81a6dc002dc46cf7b6c5", "section:845ed867739988332e9e", "section:ab9e7e520130ecc7da7c", "section:f5274c8105ff62e99dcd", "section:f989f7674214352c43f6" ], "activeSectionIds": [ "section:710760dba8520599a644", "section:81a6dc002dc46cf7b6c5", "section:ab9e7e520130ecc7da7c", "section:f5274c8105ff62e99dcd", "section:f989f7674214352c43f6" ], "evidenceId": "python_verification:verification/v1007_det16_stability_battery.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v1007_det16_stability_battery.py", "pubMirrorHash": "feaf81bb4bb568cce12a972d606f93ba9eb841b986c395b677ef433574d53baf", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v1007_det16_stability_battery.py" }, { "id": "v1008_master_assembly_scaffold", "filename": "v1008_master_assembly_scaffold.py", "path": "verification/v1008_master_assembly_scaffold.py", "cluster": "frontier", "synopsis": "QFT4D.LATTICE.FUNDAMENTAL.01 Decision / GAUGE.DETLINE.FIXPOINT.01 [O] (Review-Welle 7, 2026-08-30; 2+1D-Scaffold kohaerent): Prototyp K=0 Plaquette-Exponenten; Materie frozen-link q^2~4, K(q=0)=0, kontraktiver Selektor |R'|<1; Wand/Spiegel QWZ-Steigung ~-0.9989, DET-Gap >=1.5 bis t=0.6; Assembly Z6 (1,2,3,0), Uhr [0,1,1,2], chi_phys vs chi_mirror. Keine Marker-Bewegung. 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[X] V1000_CONSEQUENCE_MISMATCH (Kompression toetet die SK-Antwort vs. gefrorener Kontrast 3.550e-3) + CENTER_FLATNESS_PREMISE_FALSE. Kanonische Formel braucht eine schwaechere zulaessige Menge. Vertrag bleibt [O]. 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Bruecke Q KANONISCH: Leiter erzwingt Summen (9,5,1); C's 5 von R geerbt -- v1005-Zirkularitaetsflag als erzwungene Provenienz korrigiert. Bruecke W CHOICE aber bedingt eindeutig (1078 -> 1). Milnor-Starkbruecke NICHT existent bei F2 und allen upstairs homes; grobe D+Paarung existiert; |Aut(X)|=36864, |Aut(Y)|=8. SEAM.MILNOR.LOCALRING.01 bleibt [O]; AX.P2.01 bleibt Axiom. 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BINDEND: Matching-Skala des Kopplungsfunktionals muss im deconfined/weak Regime sitzen. QFT4D.LATTICE.FUNDAMENTAL.01 bleibt Decision; GAUGE.DETLINE.FIXPOINT.01 bleibt [O]. 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T8 rho0 8-Kandidaten NO_SET_WORKS (harte Sektoren antworttot; KMS-affine Mengen selektionsvakuoes). T6 kappa sechsfach NULL (K4 18.8x zu gross; 4D-Funktional noetig). T7 wechselwirkendes TT (Erhaltung/Positivitaet/Summenregeln/Z-Persistenz; gelueckt). FIREWALL: TFPT.TOE.COMPLETE.01 / FTRANSFER.SK.RHO0.01 / FLAV.NU.TEXTURE.MECHANISM.01 / GRAV.SPIN2.EMERGENCE.01 bleiben [O]. 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W-Bruecke: P-anch ABGELEITET (e1=R^{-1}a, Wicklungs-Lock); P-dem TEILWEISE (Z4-Mittel annihilert nichttriviale Charaktere; fehlend = charakterblinde Determinanten-Antwortabbildung, MMST/Quillen-Bein). ALPHA.QUILLEN.EXACT.01 / AX.P2.01 unbewegt. 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Zusammen mit P-anch (v1014) BEIDE W-Bruecken-Praemissen endlich abgeleitet; Axiomkern-Rest NULL modulo externalisierter MMST-Identifikation. AX.P2.01 bleibt Axiom (endliche Schatten; Kontinuums-Identifikation dasselbe externe Bein). T1-Notiz: Strukturpostulat-Route endlich praemissengestuetzt. Python-only / Wolfram zurueckgestellt.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv1015_axiom_core_closure.py", "sourceSha256": "ff1db6a6cde86bbea64ef04c6e56d3bc799bf6d676b8a820b2f35632acd59229", "linkedClaimIds": [ "AX.P2.01", "TFPT.TOE.COMPLETE.01" ], "sectionIds": [ "section:14713793ccdcb9ca035e", "section:2cbe5d1807cd76c5e04d", "section:49081b131681f01ae9d6", "section:789583ec50a9f61cdf33", "section:81a6dc002dc46cf7b6c5", "section:83df5fee438149d3054f", "section:8c44b477c1ab034d5ccf", "section:ab9e7e520130ecc7da7c", "section:ae01aeb2bb0e5a5a8b6f", "section:b9be0eca5eee141eabc7", "section:f5274c8105ff62e99dcd" ], "activeSectionIds": [ "section:81a6dc002dc46cf7b6c5", "section:83df5fee438149d3054f", "section:8c44b477c1ab034d5ccf", "section:ab9e7e520130ecc7da7c", "section:ae01aeb2bb0e5a5a8b6f", "section:f5274c8105ff62e99dcd" ], "evidenceId": "python_verification:verification/v1015_axiom_core_closure.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v1015_axiom_core_closure.py", "pubMirrorHash": "ff1db6a6cde86bbea64ef04c6e56d3bc799bf6d676b8a820b2f35632acd59229", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v1015_axiom_core_closure.py" }, { "id": "v1016_state_gap_batteries", "filename": "v1016_state_gap_batteries.py", "path": "verification/v1016_state_gap_batteries.py", "cluster": "frontier", "synopsis": "Zustands-/Luecken-Batterien (Montagmorgen 2026-08-31): R4 Naht-Modular-Kappe einzigartiger endlicher nicht-entropischer Selektor (D_tr 0.1434, SK-RMS 3.038e-3, Sattel erhalten; Finite-Proxy-Caveat). TEL-B zertifizierter Schwanz BLOCKIERT (N^2 D_N 530->19032); skalares dyadisches A_R<43 mit Faktor-350-Headroom; N-uniforme CAR-Nuklearitaet bewiesen (C_beta 67.97/29.73/12.15); ALG-EXH unveraendert. DFP volumenuniforme Luecke zitiert-verifiziert fuer Z2/Z4-offene Ketten (a=0.0233, a/16=0.00146); Rest Rotor/Wand/3+1D. FTRANSFER.SK.RHO0.01 [O] / SEAM.MMST.TYPEIII.CHARGED.01 [O] / CHIRAL4D.MIRROR.DET16.01 [C] unbewegt. Python-only / Wolfram zurueckgestellt.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv1016_state_gap_batteries.py", "sourceSha256": "99975c7c250401344bfa086e0d277d9e0a3d936ad73b0a0052ad2442c54210ab", "linkedClaimIds": [ "FTRANSFER.SK.RHO0.01", "CHIRAL4D.MIRROR.DET16.01", "SEAM.MMST.TYPEIII.CHARGED.01" ], "sectionIds": [ "section:03b9058ca08ba4829ac7", "section:0510f986f3f8ee9a5656", "section:14713793ccdcb9ca035e", "section:16a3dfffba2175d45b88", "section:2465208e294a3178e3e1", "section:6ce553746490f88b0988", "section:81a6dc002dc46cf7b6c5", "section:845ed867739988332e9e", "section:8c44b477c1ab034d5ccf", "section:a25026597f4b790eb050", "section:ab9e7e520130ecc7da7c", "section:ae01aeb2bb0e5a5a8b6f", "section:b9be0eca5eee141eabc7", "section:d185199a34886354d525", "section:d8ed1f80544bebc4760c", "section:eed3aaec663e71b02dd1", "section:f5274c8105ff62e99dcd", "section:f97072f658fe6bcec8d8", "section:f989f7674214352c43f6", "section:fd15b9954fc0175fba1b" ], "activeSectionIds": [ "section:0510f986f3f8ee9a5656", "section:81a6dc002dc46cf7b6c5", "section:8c44b477c1ab034d5ccf", "section:a25026597f4b790eb050", "section:ab9e7e520130ecc7da7c", "section:ae01aeb2bb0e5a5a8b6f", "section:eed3aaec663e71b02dd1", "section:f5274c8105ff62e99dcd", "section:f97072f658fe6bcec8d8", "section:f989f7674214352c43f6" ], "evidenceId": "python_verification:verification/v1016_state_gap_batteries.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v1016_state_gap_batteries.py", "pubMirrorHash": "99975c7c250401344bfa086e0d277d9e0a3d936ad73b0a0052ad2442c54210ab", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v1016_state_gap_batteries.py" }, { "id": "v1018_e8_directed_readout", "filename": "v1018_e8_directed_readout.py", "path": "verification/v1018_e8_directed_readout.py", "cluster": "core", "synopsis": "E8.DIRECTED.READOUT.01 [E] (2026-09-02, Runde r609): sieben exakte E8-Ablese-Zellen (C7 offen) -- neu abgeleitet (keine Proben-Importe): Seifert/Phi_30, Hamming 1+14y^4+y^8, srg(120,56,28,24), N(n)=240 sigma_3(n) n<=10, A_P/A_P(1)=tau(n), (Z/30)^x = C2 x C4, E6 oplus A2 Index 3 Smith (1^6,3,3) Glue 78/81/81. C7 Gauss-Code bleibt offen (rem:c7-audit). KEIN RH-CLAIM. Python-only / Wolfram zurueckgestellt.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv1018_e8_directed_readout.py", "sourceSha256": "25f541903f01621990cf317372f1349be22a495b1594eb12c77c64db151dc9db", "linkedClaimIds": [ "E8.DIRECTED.READOUT.01" ], "sectionIds": [ "section:4924c7863d81853eba3d", "section:81a6dc002dc46cf7b6c5", "section:ab9e7e520130ecc7da7c", "section:f091de1c3533bab48372", "section:f5274c8105ff62e99dcd" ], "activeSectionIds": [ "section:4924c7863d81853eba3d", "section:81a6dc002dc46cf7b6c5", "section:ab9e7e520130ecc7da7c", "section:f091de1c3533bab48372", "section:f5274c8105ff62e99dcd" ], "evidenceId": "python_verification:verification/v1018_e8_directed_readout.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v1018_e8_directed_readout.py", "pubMirrorHash": "25f541903f01621990cf317372f1349be22a495b1594eb12c77c64db151dc9db", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v1018_e8_directed_readout.py" }, { "id": "v1019_coxeter_euler_completion", "filename": "v1019_coxeter_euler_completion.py", "path": "verification/v1019_coxeter_euler_completion.py", "cluster": "core", "synopsis": "E8.COXETER.EULER.COMPLETION.01 [E]+Numerical (2026-09-02, Runde r617): Coxeter-Euler-Vervollstaendigung -- neu abgeleitet. Exakt: det(I-xC)=Phi_30, Tr C=-1; Moebius Phi_30=(1-x^2)(1-x^3)(1-x^5)(1-x^30)/[(1-x)(1-x^6)(1-x^10)(1-x^15)]; U=1 oplus C, Tr U=0. Global Z_C und D_E8 als Zeta-Quotienten, abs. konv. Re s>1/2. Numerisch (X=10^5): D_E8 Residual 4.76e-4 bei s=0.75, 4.16e-12 bei s=1.5. Klasse: lineares Verschwinden generisch aus Tr C=-1; E8 waehlt nur die Teiler von 30. Beurling-generisch. ZAUN: The trace-free completion is zero-free and pole-free in Re s > 1/2. The splitting into the scalar zeta channel and the Coxeter channel is open and RH-equivalent. No RH claim. NO-GO E8.COXETER.REGULARIZED_SPLIT.NO_GO.01: det_2 isoliert nicht 1/zeta(s). Python-only / Wolfram zurueckgestellt.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv1019_coxeter_euler_completion.py", "sourceSha256": "13bc603350b3bd38b45760158742406031f557c00c411b72ac0937eccb8777e0", "linkedClaimIds": [ "E8.COXETER.EULER.COMPLETION.01" ], "sectionIds": [ "section:81a6dc002dc46cf7b6c5", "section:ab9e7e520130ecc7da7c", "section:f091de1c3533bab48372", "section:f5274c8105ff62e99dcd" ], "activeSectionIds": [ "section:81a6dc002dc46cf7b6c5", "section:ab9e7e520130ecc7da7c", "section:f091de1c3533bab48372", "section:f5274c8105ff62e99dcd" ], "evidenceId": "python_verification:verification/v1019_coxeter_euler_completion.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v1019_coxeter_euler_completion.py", "pubMirrorHash": "13bc603350b3bd38b45760158742406031f557c00c411b72ac0937eccb8777e0", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v1019_coxeter_euler_completion.py" }, { "id": "v1020_spectator_sector_obstruction", "filename": "v1020_spectator_sector_obstruction.py", "path": "verification/v1020_spectator_sector_obstruction.py", "cluster": "frontier", "synopsis": "Spectator-Sektor-Hindernis (r644-Audit-Ernte 2026-09-04): endlicher freier-Fermion-Zeuge, neu abgeleitet (keine Proben-Importe). Aufschichten eines entkoppelten trivialen Gap-Sektors C (M=3, Chern 0) auf das Seam-Modell B (M=1, NY=8) laesst alle Seam-Daten identisch (Chern C_B=C_{B+C}=-1, C_C=0; Nullmoden 2/0/2 mit B-Träger 1.0; Randdispersion koinzident 1.4e-15; seam-restringierte Kovarianz 0.0; Randprofil-Ueberlapp 1.0) und aendert den Bulk (Dim 16 vs 32, E0(C)=-25.31, Rang 4 vs 8, HS 0.752536 vs 0.760202). Repariertes Kriterium: Krylov-Erzeugtheit spectator_dim(B+C)-spectator_dim(B)=16 an allen 128 Impulsen; Kommutant 1 vs 17, Pi_C im Kommutanten (Rest 0.0); Auswahl eindeutig (B ausgewaehlt, B+C verworfen). EHRLICH: spectator_dim(B)=10 nur bei p=0 -- Kriterium fast ueberall in p. SEAM.BULK4D.RECON.01 bleibt [O]; BULK.PRIME_COMPLETION.01 neu [O] registriert. KEIN MARKER-MOVE. KEIN RH-CLAIM. Python-only / Wolfram zurueckgestellt.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv1020_spectator_sector_obstruction.py", "sourceSha256": "cf62ace61ab774635e89df611336a6db6363e1c249e6d85f79431ec918c20647", "linkedClaimIds": [ "BULK.PRIME_COMPLETION.01" ], "sectionIds": [ "section:14713793ccdcb9ca035e", "section:17757402db902787518b", "section:186be605c9fda2c80784", "section:73dd631de817637ce12d", "section:81a6dc002dc46cf7b6c5", "section:9541b674d713737f6e7f", "section:ab9e7e520130ecc7da7c", "section:ae01aeb2bb0e5a5a8b6f", "section:b9be0eca5eee141eabc7", "section:c61a0a05c77babe52899", "section:dccf3e7f3250c009523d", "section:f287beabd75c01fb7360", "section:f5274c8105ff62e99dcd", "section:fbf67a6377a333f71dff" ], "activeSectionIds": [ "section:17757402db902787518b", "section:81a6dc002dc46cf7b6c5", "section:ab9e7e520130ecc7da7c", "section:ae01aeb2bb0e5a5a8b6f", "section:c61a0a05c77babe52899", "section:dccf3e7f3250c009523d", "section:f5274c8105ff62e99dcd" ], "evidenceId": "python_verification:verification/v1020_spectator_sector_obstruction.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v1020_spectator_sector_obstruction.py", "pubMirrorHash": "cf62ace61ab774635e89df611336a6db6363e1c249e6d85f79431ec918c20647", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v1020_spectator_sector_obstruction.py" }, { "id": "v1022_telb_round3_certificates", "filename": "v1022_telb_round3_certificates.py", "path": "verification/v1022_telb_round3_certificates.py", "cluster": "frontier", "synopsis": "TEL-B-Runde-3-Zertifikate (2026-09-05): natives Arb/Acb, 256 Bit, 5812 rationale Zellen; TV_p(F'') <=15.817695962988924...<15.928674 und K3_TV<2.517464500835. Die analytische C2b-Skalarreduktion plus ausführbare Arb-Arithmetik ergibt c_epsilon=0.288547359238..., c_zeta=0.110677064901..., Summe=0.399224424139...<0.400; volles C2b bleibt exakt bei CF<=0.139/sqrt(N) und DG<=0.060/sqrt(N) offen. Exaktes Einmoden-Gegenmodell widerlegt den alten ALG2-Vandermonde-Schluss; FE-GEN oder eine praezise Gauge/Code-Projektion bleibt noetig. T2/TOE [O] unbewegt; python-flint==0.9.0, nicht Pyodide. KEIN RH-CLAIM.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv1022_telb_round3_certificates.py", "sourceSha256": "3444b78527478e4b3262f98ac0d6b4ad18113fc5ccb99ede8ee0ccab11cf8ff7", "linkedClaimIds": [ "TFPT.TOE.COMPLETE.01", "SEAM.MMST.TYPEIII.CHARGED.01", "SEAM.MMST.TELB.ROUND3.01" ], "sectionIds": [ "section:13c83724c05e526a735d", "section:14713793ccdcb9ca035e", "section:17757402db902787518b", "section:2fb6cd875276a150402c", "section:6b698096745880841f4c", "section:83c8266dcbf844e64c6b", "section:9e0ba325fdce5ca83fef", "section:a25026597f4b790eb050", "section:ab9e7e520130ecc7da7c", "section:ace8f6c66089bf3029b9", "section:ae01aeb2bb0e5a5a8b6f", "section:b9be0eca5eee141eabc7", "section:bce0cf0522b937838636", "section:bd6d1336259ad1689a45", "section:be838d1d0321f5b1e358", "section:ca091ab682b2d3ecd50b" ], "activeSectionIds": [ "section:13c83724c05e526a735d", "section:17757402db902787518b", "section:6b698096745880841f4c", "section:9e0ba325fdce5ca83fef", "section:a25026597f4b790eb050", "section:ab9e7e520130ecc7da7c", "section:ae01aeb2bb0e5a5a8b6f" ], "evidenceId": "python_verification:verification/v1022_telb_round3_certificates.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v1022_telb_round3_certificates.py", "pubMirrorHash": "3444b78527478e4b3262f98ac0d6b4ad18113fc5ccb99ede8ee0ccab11cf8ff7", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v1022_telb_round3_certificates.py" }, { "id": "v1023_derivative_filtered_wall", "filename": "v1023_derivative_filtered_wall.py", "path": "verification/v1023_derivative_filtered_wall.py", "cluster": "frontier", "synopsis": "Ableitungsgefilterter Wall-Block (2026-09-05): H_df erhaelt ker(D_GW) exakt; det Block=lambda g^2 Delta s^2; das adiabatisch spiegel-kontinuierte hohe Band liegt >=Delta+lambda; der niedrige Ast ist quadratisch. Der nackte Spiegeloperator ist nicht invariant und hat fuer s>0 Niedrigbandgewicht -- kein Spiegel-Antwortgap und kein Weyl-Kegel. Gauge-Defekt 2.41e-15, Spektraldefekt 1.78e-15. Endliches quasi-freies Blocklemma; kanonische DET16/DET32-Realisierung, Vielteilchenparent, Zulässigkeit/Quasilokalitaet, Mass/Anomalie/Index, Universalitaet und 4D-Limes bleiben offen. Keine Markerbewegung. KEIN RH-CLAIM.", "publicationNotes": [], "sourceHref": "/documentation?evidence=python_verification%3Averification%2Fv1023_derivative_filtered_wall.py", "sourceSha256": "a6850b0acc2c2cd47579b290d02aeb8b48ba32836f4141570c6daaad8f35f69a", "linkedClaimIds": [ "CHIRAL4D.NOMIRROR.01", "TFPT.TOE.COMPLETE.01", "CHIRAL4D.MIRROR.DET16.01", "CHIRAL4D.MIRROR.DFILTER.BLOCK.01" ], "sectionIds": [ "section:14713793ccdcb9ca035e", "section:17757402db902787518b", "section:6ce553746490f88b0988", "section:845ed867739988332e9e", "section:ab9e7e520130ecc7da7c", "section:ae01aeb2bb0e5a5a8b6f", "section:b9be0eca5eee141eabc7", "section:f989f7674214352c43f6" ], "activeSectionIds": [ "section:17757402db902787518b", "section:ab9e7e520130ecc7da7c", "section:ae01aeb2bb0e5a5a8b6f", "section:f989f7674214352c43f6" ], "evidenceId": "python_verification:verification/v1023_derivative_filtered_wall.py", "reviewState": "registered-source-not-executed", "pubMirrorHref": "/verification/v1023_derivative_filtered_wall.py", "pubMirrorHash": "a6850b0acc2c2cd47579b290d02aeb8b48ba32836f4141570c6daaad8f35f69a", "pubMirrorMatchesSnapshot": true, "snapshotSourceHref": "/verification/v1023_derivative_filtered_wall.py" }, { "id": "v1024_parent_internal_boundaries", "filename": "v1024_parent_internal_boundaries.py", "path": "verification/v1024_parent_internal_boundaries.py", "cluster": "frontier", "synopsis": "Parent-interne T6--T8-Grenzen (2026-09-05): endlicher A3--D4 Seam/Neutrinopaar-Intertwiner ohne neuen Faktor; positiv, gerade, gauge-kompatibel, nichtadditiv, lokaler Gap 0.25 konditional auf ererbte volle Parent-Schranke, gemischte Resolvente 0.104712041885. Interner 12D-Z5-Cap Gap 0.197423715893, aber beliebig, D4-brechend und kein globales rho0. Exakte Grenzen: projektiver Full-Fock-D4-Lift; relativer Kommutant bei unitaler Erweiterung; volles Z5-Weylpaar verlangt 5|D nur unprojiziert; uniformer voller Gap schliesst masselosen Spin-2-Pol aus; TT-Projektion nicht endlichreichweitig. 49/49; T6--T8/TOE [O] unbewegt. 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