Original ledger status
E8.CODESEM.01
The code-semantics rounds, kill + stage 2 (one module, 27 checks, ~3 s; discovery probes code_semantics_kill_probe.py 13/13 CODE-SEMANTICS-RELABELLED and code_semantics_stage2_probe.py 27/27 DICTIONARY-SHARP). Stage 1 (kill): the naive v626 placement is DEAD for the family 3-cycle pisig; exactly 2/30 S8-placements of the extended Hamming code carry BOTH compiler symmetries mod 2 (piJ = mu4 in-pair swap, pisig = family pair 3-cycle), exchanged by the anchor transposition (67) -- ONE placement C* up to anchor orientation. Stage 2 (the dictionary, DICTIONARY-SHARP): under binary position labels C* IS Reed-Muller RM(1,3) on AG(3,2) (piJ = translation by 001, pisig affine, the 14 weight-4 supports = the 14 planes; 30 = |S8|/|AGL(3,2)|); NO equivariant 4+4 block split exists (all 6 pair-unions are codeword supports), the UNIQUE minimal Z6-orbit of information sets is the transversal pair 'one bit per mu4 pair, anchor-flipped' (3 family bits + 1 anchor bit); the 12 sigma-fixed roots reduce mod 2 to exactly {0, t_even, t_odd} (4 each); the clock-orbit fibration reproduces 60 = 7 x 4 + 4 x 8 and the sigma census 3 + 19 (the v629 tower 240 -> 60 -> 3+19); SYNDROME SEMANTICS: all 3840 single-coordinate errors sit at squared distance EXACTLY 1 with the tie pair collapsing mod 2; the syndrome space factors as the flag 0 < <q> < F2^4 (q = the universal in-pair bit) with sigma acting on the pair directions as the 3-CYCLE + fixed anchor (P3 = P0+P1+P2) and piJ trivial on the quotient; DECODE = PROJECTION verbatim on the single-error class (3840/3840, exact Fraction arithmetic; boundary regime honest: mismatches need >= 2 rounding errors). KILL CONTROL: {universal in-pair syndrome} = {zero fragmented Z6 orbits} = {both-invariant} = the two C* relabellings -- the equivariance is load-bearing; the whole dictionary dies for every non-equivariant placement. [2026-08-02 XLIII: the reverse reading executed -- v646: the sigma-fixed syndromes carry the anchor decomposition exactly (leader weights (0,1,1,2), norm 6, anchor = family sum; the SELECTION is equivariance-specific, the raw (1,1,2)/norm-6 weights are generic for any [8,4,4] placement), while the bytecode p-sequence p_n = 2 + 2^n has NO code reading (0/11 families; 18/27/81 without any hit -- the bingo is buried); the kill control fires selectively; see E8.RM13REV.01.] [2026-08-02 XLV: look-elsewhere quantification -- v664: the CODESEM number battery (anchor norm 6 et al.) carries p_max = 0.593 under the conservative null model -- the v646 finding quantified: the numeric coincidences of this row are observations without statistical weight; the [E] structure theorems (RM(1,3) dictionary, decode = projection) are untouched.] [2026-08-03 L: the message space is IDENTIFIED as a lattice congruence -- v689: E8(Z[i])/(1+i) = F2^4 carries this module's RM(1,3) info-bit semantics exactly (240 = 15 x 16 census, zero class provably empty; sigma = c^4 = the family 3-cycle + fixed anchor on the quotient; residual gauge order 18; coordinate block = F1+F2+F3), presentation-independent and with all must-fail controls firing; see E8.GAUSSCODE.01.]
Recorded status: Exact [E] code/dictionary identities + [E, kill] the 30-census control (exact arithmetic; Python-only per GATE.WOLFRAM.02).
Dependencies, status detail and source
Canonical status: DICTIONARY-SHARP: the equivariant placement is RM(1,3) on AG(3,2) with an exact dictionary (information bits one per mu4 pair, syndrome flag with the sigma 3-cycle, decode = projection); only 2/30 placements carry it; residual: the anchor-pair orientation; no physics claim, no marker moves.
Dependencies: E8.CODE.01; E8.INCIDENCE.01; v626; v629
Scripts: v638_code_semantics.py
Location: tfpt_3
Original CSV, line 647Original ledger status
QGEO.TWISTOPE.01
The twist-field/OPE round (one module, 25 checks, ~1 s; discovery probe orbifold_twist_ope_probe.py 25/25, verdict TWIST-OPE-COHERENT-RP-OPEN). The interacting/CFT-level slice of the Z3 orbifold residue (v623/v628): h_sigma = 1/36 from THREE independent exact routes (v628 Casimir coefficient = 2(h - c/24); zeta-function mode sum -zeta(-1,nu)/2; bosonization pair h(1/2-eta)+h(1/2+eta) = eta^2/2), with the convention traps resolved exactly (eta(1-eta)/2 = the Ramond-deficit identity); lattice dictionary Delta = eta^2 = 1/9 = 4 h_sigma; the lattice twist two-point (U(1) string determinants on the half-filled NS seam double; equal-time covariance = half the v519 seam kernel, dev 8e-16) hits 2 Delta = 2/9 at 0.06% (N -> 1536) and 0.11% (within-ring); Ising control (eta = 1/2) at 0.02%; the four-point: exact lattice crossing (gap rotation = w -> 1-w, |G4| invariant at 1.4e-14: symmetry-protected), conformal collapse onto w (< 1%), the exact closed form A^2 [w(1-w)]^{-2 Delta} at < 0.1% after N^{-2/3} extrapolation (deviation identified as the Fisher-Hartwig artifact, ratio 0.637 vs 2^{-2/3}); OPE data: cross-channel block (1-w)^{-2/9} at 0.19%, c1 = 2 Delta = 2/9 model-bound at 0.19% (the exact vertex value 2 eta^2), identity normalization C -> 1 at 0.07%; HONEST OPEN [O]: the model-free c1 extractors bracket 2/9 only within +-15%; the Majorana-level block split not fixed by G4 alone. REFLECTION POSITIVITY DIFFERENTIATED: all mirror Grams Hermitian at machine precision; POSITIVE CONTROL: the real Z2 string class exactly PSD at every N; HONEST NEGATIVE [X-slice]: the naive antiunitary Z3 pairing fails positivity by an N-STABLE amount (-4.5e-3 charged; indefinite already in the continuum) -- the positivity-carrying pairing (parafermionic Klein twist, Jaffe-Pedrocchi-type) is a named OPEN item. [2026-08-02 XLIII: the named open item is RESOLVED at the lattice OS level -- v645: the positivity-carrying pairing IS the parafermionic Klein twist (mirror composed with charge conjugation, omega^{k q} zero-mode phases, eta = (1,1) unique among the 36 scanned pairs), all charged blocks real symmetric and PSD, N-stable 48..384, both axes, full mixed identity+twist+dipole OS Gram PSD; the naive pairing keeps its -4.5e-3 violation as the must-fail control; continuum OS reconstruction/modularity stay typed open; GATE.QGEO does not move; see QGEO.KLEINRP.01.] [2026-08-02 XLV: the orbifold front is COMPLETE at the lattice level -- modular data (v650: nine Z[g,h] vs |theta/eta|^2 < 1%, S measured at N^{-4}, T exact as the Z6 Dehn shift, deck^3 = -1 as exact Z6 trace arithmetic), assembly (v651: H^2(Z3,U(1)) = 0 enumerated, exactly one seam assembly B, T kills the naive Z3 exactly), Arf/GSO hardening (v652: the 6^6 classification leaves {B, C3}, the one-Fock-space pin forces B, the mu6 ladder measures the C3-excised states directly), and the bond-defect premise as a lattice theorem (v653); the [C] remainder is the continuum CFT statement + the seam-identification premise; no marker moves.]
Recorded status: Exact [E] weights/crossing + [E-float] two-/four-point and OPE + [O] typed open items + [X-slice] honest RP negative (Python-only per GATE.WOLFRAM.02).
Dependencies, status detail and source
Canonical status: TWIST-OPE-COHERENT-RP-OPEN: the interacting slice stands at the abelian vertex level (weights 1/36, exponent 2/9, crossing, closed four-point, OPE data); RP validated in the real Z2 class, the complex Z3 pairing typed open (parafermionic Klein twist); GATE.QGEO does not move.
Dependencies: QGEO.ORBCAS.01; QGEO.COVERSEAM.01; QGEO.SEAMID.01; v519; v622; v623; v628
Scripts: v639_twist_ope.py
Location: tfpt_3
Original CSV, line 648Original ledger status
QGEO.KLEINRP.01
Parafermionic Klein-twist reflection positivity of the Z3 twist sector (one module, 17 checks, ~30 s; discovery probe parafermion_klein_rp_probe.py 17/17, verdict KLEIN-RP-POSITIVE). The named open item of QGEO.TWISTOPE.01 (the naive antiunitary Z3 pairing fails positivity N-stably at -4.5e-3) is RESOLVED at the lattice OS level: the positivity-carrying pairing composes the mirror with CHARGE CONJUGATION -- Theta_K(sigma_k(x)) = eta_k sigma_{3-k}(r(x)) with omega^{k q} zero-mode phases (q = half-position mod 3). MACHINERY [E]: the dressed-string reality identity (particle-hole I - C = DCD at half filling) makes every Klein Gram entry EXACTLY real (1.4e-15 over 40 mixed configs); for lam = pi the naive and Klein pairings coincide identically (the v639 Z2 control could not distinguish them); the naive glue pins a spurious 2 lam = 4 pi/3 defect on the axis bond, the Klein glue is defect-free. POSITIVITY [E-float, central]: every charged Klein block is real symmetric AND PSD (worst min/max 2.9e-12), k = 1, 2, BOTH diameter axes, N = 48/96/192/384 (N-stable, no drift); charge blocks coincide exactly. UNIQUENESS [E]: over the 36 pairs (eta_1, eta_2) in {+-1, +-w, +-w^2}^2 exactly ONE satisfies consistency + Hermiticity + PSD: eta = (1, 1); no phase rescues the naive pairing (the fix is structural). MUST-FAIL [E]: the naive pairing reproduces the v639 violation (-4.4e-3..-4.5e-3 N-stable); eta = -1 loses PSD, eta = omega breaks Hermiticity. THE LATTICE OS STATEMENT [E-float]: the FULL mixed Gram over {1, sigma_1, sigma_2, dipoles} with NO sector projection is real symmetric and PSD at N = 48/96 (min/max -5e-17), stable at N = 192. HONEST TYPING [C]: continuum OS reconstruction, R/fermion-parity sectors (deck^3 = -1), modular invariance, chiral factorization, non-abelian content stay NAMED, not claimed; GATE.QGEO does not move. [2026-08-02 XLV: the modularity/assembly successors land -- v650 (S measured with a clean N^{-4} rate, T exact), v651 (the seam assembly is B, matching this row's Klein phase eta = (1,1)), v652 (Arf hardening; the half-twist tau sector is Klein-PSD too), v653 (bond defect = lattice theorem); the orbifold front is complete at the lattice level; GATE.QGEO does not move.]
Recorded status: Exact [E] reality/uniqueness/must-fail structure + [E-float] PSD Grams (N-stable) + [C] typed continuum remainder (Python-only per GATE.WOLFRAM.02).
Dependencies, status detail and source
Canonical status: KLEIN-RP-POSITIVE: the Z3 twist sector is reflection positive on the seam-double lattice under the parafermionic Klein-twist pairing (mirror x charge conjugation, omega^{k q} phases, eta = (1,1) unique among 36), N-stable 48..384, both axes, including the full mixed OS Gram; the naive pairing keeps its N-stable violation (must-fail); continuum OS/modularity typed open; GATE.QGEO does not move.
Dependencies: QGEO.TWISTOPE.01; QGEO.ORBCAS.01; QGEO.COVERSEAM.01; v519; v622; v623; v628; v639
Scripts: v645_klein_rp.py
Location: tfpt_3
Original CSV, line 649Original ledger status
E8.RM13REV.01
The RM(1,3) reverse reading -- are compiler numbers CODE operations? (one module, 20 checks, ~1 s; discovery probe rm13_reverse_probe.py 20/20; exact integer arithmetic). An honestly TWO-PART answer. THE ANCHOR IDENTITY [E, central]: the sigma-fixed syndromes of the equivariant placement C* are EXACTLY {0, s(e6), s(e7), q} with coset-leader weights (0, 1, 1, 2) and norm-square sum 6 = (1,1,2).(1,1,2); the anchor is the family sum in the quotient (P3 = P0+P1+P2); ALL four pair sectors carry (1,1,2)/norm 6 but ONLY the anchor pair is sigma-stable (pointwise fixed) -- the sigma action SELECTS the anchor copy. HONEST SPLIT [E]: the (1,1,2)/norm-6 weights per pair sector are GENERIC for any [8,4,4] placement (R3.2: the naive placement carries them too); equivariance-specific are ONLY q-universality, the sigma-fixing of the anchor sector, and anchor = family sum (R3.1: all die for the naive placement). THE BYTECODE NEGATIVE [E, honest]: the 42-entry invariant battery lands the structural anchors exactly (240 = #roots, 8 = n, 248 = roots + n, 60 = roots/4, 12 = #sigma-fixed roots, 6 = anchor norm = #pair-unions) -- but the p-sequence (4, 6, 10, 18) of p_n = 2 + 2^n has NO code reading (0/11 natural families), 27 and 81 have no hit at all, 18 no hit, 10 only as a C*-specific Z6-orbit count: the bingo is buried. KILL CONTROL [E]: fires selectively -- the orbit censuses (6, 10) and the sigma/anchor selection die for non-equivariant placements, the pure-code invariants and even the sigma-fixed-root COUNT 12 do not (R3.6 honest correction: naive also has 12; only the mod-2 fibration is C*-structure). No marker moves.
Recorded status: Exact [E] anchor identity + honest [E] generic/specific split + honest negative (no code reading of the p-sequence) + selective kill control (Python-only per GATE.WOLFRAM.02).
Dependencies, status detail and source
Canonical status: RM13-REVERSE-TWO-PART: the anchor decomposition (0,1,1,2)/norm 6 is exact with the sigma action selecting the anchor sector (selection equivariance-specific, weights generic); the bytecode p-sequence has NO code reading (0/11 families, 18/27/81 no hit) -- honest negative, route closed; kill control selective; no marker moves.
Dependencies: E8.CODESEM.01; E8.CODE.01; EXTREV.LATTICE.01; v624; v626; v638
Scripts: v646_rm13_reverse.py
Location: tfpt_3
Original CSV, line 650Original ledger status
E8.ST31DEG.01
The ST31 degree-24/-20 round (one module, 25 checks, ~4 s; discovery probe st31_degree24_probe.py 25/25; exact Fraction/Z[i] arithmetic). THE REGULAR 24-CLOCK [E, structural]: an explicit w with free census {24:10} and |C_G31(w)| = 24 (Springer); on the 60 lines it reads as the free 6-clock {6:10}; EXACT center relations w^12 = -1 and w^6 = J^3 -- the mu4 center is a POWER of the regular 24-clock (mu4 = <w^6>, <w>/mu4 = Z6 = the line 6-clock); chi_w = x^4 + i x^2 - 1 EXACT (Gaussian-integral quartic factor of Phi_24; divides x^24 - 1 and no proper x^d - 1: all four eigenvalues PRIMITIVE zeta24); the half-clock w^2 is the REGULAR 12-element ({12:20}, |C| = 288), NOT the compiler clock. THE CLOCK KILL [E, parity theorem]: c = w^2 is IMPOSSIBLE for any order-24 w, even in S_240 -- the 12-cycles of any square come in PAIRS from 24-cycles (4-cycles in pairs from 8-cycles) and census(c) = 19 x 12 + 3 x 4 has ODD counts; the full power-census scan over all 46080 elements confirms: the only (census, k) with census(x^k) = census(c) are order-12 elements with census(c) itself and k coprime to 12. THE 20-DEGREE [E]: regular u with census {20:12}, |C(u)| = 20; u^5 = J^3 CENTRAL (stronger than J-class); u^4 of order 5 acts FREELY with census {5:48} = 240/5 EXACTLY, lines {5:12}, |C(u^4)| = 20; chi_u primitive-zeta20 exact. HONEST TYPING [C]: the equality 48 = seam sites stays an OBSERVATION (number coincidence, no structural bridge in this module); g_car = 5 has only the census side; no marker moves. [2026-08-02 XLV: v654 completes the degree census (order-8 landscape 10560/4800/480, the unified d/4-theorem, 'free => regular' killed at d = 8 and already at order 4); LEAN ROUND 3: the order statements of the regular words are machine-proved (G31WordOrders.lean: chi_w | X^24 - 1 and chi_u | X^20 - 1 via the conjugate-quartic witnesses chi x conj = Phi_24 / Phi_20, and NO proper-divisor X^d - 1 by companion-matrix kernel decide -- all eigenvalues primitive; W^24 = U^20 = 1), and the combinatorial kernel of the c = w^2 parity kill is certified at the multiset level (SquareParity.lean: the exact count law #{L-cycles of rho^2} = 2 #{2L-cycles of rho} for even L + census_not_square; the permutation-level bridge honestly typed as not formalized); lake build green, 3383 jobs, no sorry.]
Recorded status: Exact [E] structural clock relations + [E] parity-theorem kill + [C] typed observations (Python-only per GATE.WOLFRAM.02).
Dependencies, status detail and source
Canonical status: ST31-DEGREE-ANCHORED: the mu4 center is a power of both regular clocks (w^6 = +-J, chi_w = x^4 + i x^2 - 1 primitive-zeta24; u^5 = +-J central); c = w^2 killed by the parity theorem (19/3 odd -- proof-grade); u^4 free with census {5:48}, 48 = 240/5; 48 = seam sites stays a typed observation; no marker moves.
Dependencies: E8.ST31.01; E8.ZIQUOTIENT.01; E8.INCIDENCE.01; v629; v633; v634
Scripts: v647_st31_degree24.py
Location: tfpt_3
Original CSV, line 651Original ledger status
META.DISCIPLINE.01
The discipline audit (one module, 17 checks, ~200 s; discovery probe discipline_audit_probe.py 17/17, verdict DISCIPLINE-MEASURED). The suite parses ITSELF and freezes its process-discipline metrics as minimum bars. [E] D1 LEDGER CENSUS: 715 rows / 710 active (display classes E/C/O/X/AXIOM/OTHER = 169/222/282/37/2/3 at freeze), and 214 rows documenting kills / honest negatives / ill-posed retirements / retypes (keyword census over claim + canonical_status) -- a project that documents its own buried hypotheses is not a confirmation-bias generator. [E] D2 MUST-FAIL CENSUS: 643 modules (every one carries checks), 6040 static check() call sites (clears the published 5452 counter), 1469 must-fail/kill/scramble keyword occurrences across 233 modules, typing marks [E] x 3579 vs [C] x 1323 -- negative controls are corpus-wide, not decorative. [E] D3 PRE-REGISTRATION CENSUS: 47 contract rows in the ledger (29 naming kill criteria BEFORE execution; 20 mentions in the contracts paper); executed chains verified in the ledger: FTR.PGL2.01 (v533 -> executed v632), PRIME.WEIL.OPERATOR.01 (kill tests K1-K3 named -> W1 theorem-closed v643), REG.FREEZE.01 (registry frozen 2026-06-09, re-derived each run by v84). [E] D4 REPRODUCIBILITY: deterministic replay 12/12 on the DECLARED sample v55/v91/v108/v205/v305/v405/v505/v555/v600/v634/v643/v648 (two fresh subprocess runs each, identical output up to timing lines); 396 modules sympy-exact, 77 with explicit seeds. [E] D5 EXTERNAL ANCHORS: five classical results recomputed here against the literature the suite quotes -- Jacobi 1834 four-square counts (exact, n = 1..40), Construction A [8,4,4] -> E8 with 240 minimal vectors, the Shephard-Todd G31 degrees (8,12,20,24), the Suzuki archimedean constants psi(1/4)/L/A to 25+ digits, and the completed-zeta functional equation (worst rel dev 3e-31). [E] D6 LEAN LAYER: 54 committed TfptCarrier proof modules (git ls-files; uncommitted sandbox WIP excluded); lake build honestly NOT re-run in-suite (last green build quoted: 3380 jobs, no sorry). [C] D7 THE LIMIT, honest: this module measures PROCESS discipline, NOT the truth of the physics; typed [C] observations stay observations; the open gates stay open (278 class-O rows incl. SEAM.THEOREM.01, PRIME.WEIL.OPERATOR.01 W2-W4, the QGEO premise family and the GATE.METRIC family); a discipline certificate is a necessary, not a sufficient, condition against numerology. Read-only; no marker moves.
Recorded status: Exact [E] machine census + deterministic replay + external anchor recomputes + [C] typed limit (read-only meta-module; Python-only per GATE.WOLFRAM.02).
Dependencies, status detail and source
Canonical status: DISCIPLINE-CERTIFIED: frozen minimum bars -- 214 kill/negative rows, 1469 negative-control occurrences in 233 of 643 modules, 47 contract rows (29 with named kill criteria; FTR.PGL2 and the W1 chain verified as executed), replay 12/12 deterministic, 5 classical anchors recomputed, 54 committed Lean modules; the limit typed [C]: process discipline, not physics truth -- the open gates stay open.
Dependencies: REG.FREEZE.01; FTR.PGL2.01; PRIME.WEIL.OPERATOR.01; AUDIT.NULLMC.01; v84; v100
Scripts: v649_discipline_audit.py
Location: tfpt_3
Original CSV, line 652Original ledger status
QGEO.ORBMOD.01
The modular data of the Z3 orbifold of the seam on the lattice (one module, 17 checks, ~25 s; discovery probe orbifold_modular_probe.py 17/17, verdict ORB-MODULAR-COHERENT). SECTORS [E]: all nine twisted-sector partition functions Z[g,h] of the seam double (free complex fermion, N x L cylinder) are real positive with exact conjugation degeneracies and match the continuum |theta[g/3,h/3]/eta|^2 at < 1% on ln Z (N = 48; tau = i/2, i, 2i); the Casimir slopes reproduce the v628 coefficients per deck class (C_g/4 = (-1/24, 1/72, 1/72)). S MEASURED [E-float, central]: modular S-covariance converges with a clean common N^{-4} rate (4.06-4.32 over N = 24/48/96) while the single-lattice deviation falls at N^{-2}: the leading lattice artifact is itself S-covariant and CANCELS in the S-relation. T EXACT [E]: T is the discrete Dehn twist -- the Z6 sector map (g,h) -> (g, g+h) x (-1)^F at machine precision (3.6e-13); continuum T-phases not resolvable in the real-positive trace convention (honest scope). CHARACTERS [E]: h_sigma = 1/36 (rel 5.6e-4), parafermionic 1/6 gap (multiplicity 2), omega^{k q} charge weights. SPIN STRUCTURE [E]: deck^3 = (-1)^F closes exactly as Z6 trace arithmetic (1.4e-13) incl. the cover factorization; positive bookkeeping = Z6 charge projection, ground class c = 0 in every sector. TYPED [C]: chiral phases, continuum T-phases, assembly (-> v651), continuum OS; GATE.QGEO does not move.
Recorded status: Exact [E] sectors/characters/spin structure + [E-float] measured S-covariance (N^{-4}) + [C] typed continuum remainder (Python-only per GATE.WOLFRAM.02).
Dependencies, status detail and source
Canonical status: ORB-MODULAR-COHERENT: nine sectors match |theta/eta|^2 at < 1%, S measured with a clean N^{-4} rate (the N^{-2} artifact is itself S-covariant and cancels), T exact as the Z6 Dehn shift, h_sigma = 1/36 with the 1/6 gap, deck^3 = -1 exact as Z6 trace arithmetic; chiral phases/continuum OS typed open; GATE.QGEO does not move.
Dependencies: QGEO.TWISTOPE.01; QGEO.KLEINRP.01; QGEO.ORBCAS.01; v622; v623; v628; v639; v645
Scripts: v650_orbifold_modular.py
Location: tfpt_3
Original CSV, line 653Original ledger status
QGEO.ORBASM.01
The full Z3-orbifold assembly of the seam (one module, 17 checks, ~35 s; discovery probe orbifold_assembly_probe.py 17/17, verdict ORB-ASSEMBLY-SEAM). COHOMOLOGY [E]: H^2(Z3, U(1)) = 0 by machine enumeration (27 mu3-valued 2-cocycles = 9 coboundaries x 3 classes, every cocycle symmetric) -- NO discrete torsion for a pure Z3 orbifold; residual phase tables are exact charge-class relabelings. GRID [E]: all 35 nonvanishing Z6 sectors match |theta[gt/6,ht/6]/eta|^2 at < 1% (beyond v650: the odd deck powers). THE CENSUS [E, central]: of SIX assembly candidates the survivors of {integer spectrum, unique vacuum, S measured clean, T exact} are EXACTLY {B, C3} -- A (the naive Z3) dies by an exact T violation 3.5e-3 (= its charge-3 content: T kills the naive Z3 exactly), C1 by S stalling at 1.7e-3, C2 has no vacuum, A' by exact T violation 4.6e-1 AND the wrong first twisted exponent (5/18, not 1/9). THE PICK [E/C]: the seam data discriminate B from C3 -- B keeps every measured c = 0 sector ground and the Klein phase eta = (1,1) (v645); C3 excises all odd-sector grounds: THE SEAM ASSEMBLY IS B, the Z6 deck quotient with uniform charge-0 projection (data-backed [C] here; hardened structurally by v652). MEASURED [E]: the chiral phase e^{-2 pi i a~ b} (spectral-flow-reduced branch). GATE.QGEO does not move.
Recorded status: Machine [E] cohomology/census + [E-float] S rates and exact T + data-backed [C] B-vs-C3 pick (hardened by v652) (Python-only per GATE.WOLFRAM.02).
Dependencies, status detail and source
Canonical status: ORB-ASSEMBLY-SEAM: H^2(Z3,U(1)) = 0 enumerated (no discrete torsion), six candidates -> exactly {B, C3} survive {integer spectrum, vacuum, S, T} (T kills the naive Z3 exactly at 3.5e-3), the seam data pick B (measured c = 0 grounds + Klein eta = (1,1)); chiral phase measured; GATE.QGEO does not move.
Dependencies: QGEO.ORBMOD.01; QGEO.KLEINRP.01; QGEO.TWISTOPE.01; v622; v623; v628; v639; v645
Scripts: v651_orbifold_assembly.py
Location: tfpt_3
Original CSV, line 654Original ledger status
QGEO.ORBARF.01
Arf/GSO hardening of the B-vs-C3 discriminator (one module, 15 checks, ~30 s; discovery probe orbifold_arf_probe.py 15/15, verdict ARF-B-STRUCTURAL). THE LADDER [E]: the mu6 defect ladder on the seam double measures the C3-excised states DIRECTLY -- exponents 2 Delta = (1/18, 2/9, 1/2) at rel devs < 8e-4 (N = 96..1536 and within-ring), the half-twist (tau) Klein Gram exactly real symmetric and PSD, exact charge-resolved minima (0, 1, 4, 9, 4, 1)/36 = the measured sector grounds. THE EXCISION VERDICT [E, central]: the measured exponents hit B's c = 0 minima in every sector (< 3%); C3's odd-sector predictions 85/18 and 81/18 exceed the measurements by factors 85.0 and 9.0 -- the defect string is occupation-diagonal, hence exactly charge-neutral: C3 excises states that exist on the lattice seam with positive Klein norm and measured dimension. THE PIN [E]: the cover circle is NS (sympy closed form); among ALL 6^6 = 46656 sector-character wirings exactly {B, C3} survive the exact lattice degeneracies, and the single-Fock-space requirement forces B. HONEST: the earlier v639 2/9 read alone is B-vs-C3-BLIND (B and C3 coincide exactly on the even sectors); the new tau datum: OPE exponent 1/18 (rel 2.9e-3). TYPED [C]: the bond-defect premise (-> v653); GATE.QGEO does not move.
Recorded status: Exact [E] classification/pin/excision data + [C] typed premise remainder (resolved by v653) (Python-only per GATE.WOLFRAM.02).
Dependencies, status detail and source
Canonical status: ARF-B-STRUCTURAL: B vs C3 decided structurally -- the 6^6 classification leaves {B, C3}, the one-Fock-space pin forces B, and the mu6 ladder measures the C3-excised states directly (factors 85.0/9.0); the v639 2/9 read is B-vs-C3-blind; new tau datum 1/18; GATE.QGEO does not move.
Dependencies: QGEO.ORBASM.01; QGEO.ORBMOD.01; QGEO.KLEINRP.01; QGEO.TWISTOPE.01; v622; v623; v628; v639
Scripts: v652_orbifold_arf.py
Location: tfpt_3
Original CSV, line 655Original ledger status
QGEO.BONDDEF.01
The bond-defect premise upgraded to a lattice THEOREM (one module, 18 checks, ~40 s; discovery probe bond_defect_premise_probe.py 18/18, verdict BOND-DEFECT-CANONICAL). THE THEOREM [E]: the deck-character blocks of the covered seam ARE the one-bond-defect chains, unitarily and exactly (A_r = sqrt(3) R P_r on all modes, exact in Q(zeta_6), at 16/48 AND 48/144; defect phase = deck character): twist sector = deck boundary condition = bond defect, canonically; D_can = L^4 and D_can^3 = -1 as exact operator identities (the quarter clock fixes the canonical section lift); NS-vs-R bookkeeping exact. GAUGE + PIN [E]: the defect position is pure gauge (symbolic telescoping theorem in all 16 free bond phases; all positions exactly isospectral); the geometry pins the gauge class -- sheet reduction = one uniform twist unit per mark (cocycle support = the v622 mark set), window boundary at a crossing <=> defect at a mark, clock covariance selects the mark-uniform field. EXCLUSION CENSUS [E + honest]: every unit-phase configuration with the sector holonomy is gauge-equivalent to the bond defect; the base chain has NO other Z3; site potentials/amplitude defects killed by exact traces, sign defect = the R sector (v628 kill), alternating weights trivialize (v623 kill); an isospectral real NN chain EXISTS (7.8e-16) -- honestly documented: purely spectral data cannot exclude it, but it is no Z3-twist realization and the measured string/correlator data discriminate it (0.26/0.066); the charge-string bridge makes the measured defect ladder bond-defect spectroscopy. TYPED [C]: the continuum/CFT-level statement + the v622/v623 seam identification; GATE.QGEO does not move.
Recorded status: Lattice theorem [E] (exact unitary equivalence + gauge pin + exclusion census, honest isospectral documentation) + [C] typed continuum remainder (Python-only per GATE.WOLFRAM.02).
Dependencies, status detail and source
Canonical status: BOND-DEFECT-CANONICAL: twist = deck = bond defect as a lattice theorem in Q(zeta_6) (exact unitary equivalence, D_can = L^4, D_can^3 = -1 operator identities), position = gauge + mark pin, alternatives census complete incl. the honest isospectral chain (string data discriminate); continuum CFT + seam identification stay [C]; GATE.QGEO does not move.
Dependencies: QGEO.ORBARF.01; QGEO.ORBASM.01; QGEO.TWISTOPE.01; v622; v623; v628; v639
Scripts: v653_bond_defect.py
Location: tfpt_3
Original CSV, line 656Original ledger status
E8.ST31D8.01
The ST31 degree-8 round + the unified d/4-theorem (one module, 30 checks, ~10 s; discovery probe st31_degree8_probe.py 30/30; exact Fraction/Z[i] arithmetic). ORDER-8 LANDSCAPE [E]: 10560 order-8 elements, 4800 with free census {8:30}, only 480 with x^2 central; the regular witness has |C| = 192 (Springer), chi_v = (x^2 + i)^2 EXACT (all eigenvalues primitive zeta8, doubled), v^2 a GENERATOR of mu4; HONEST KILL: 'free => regular' is FALSE at d = 8 (4320 free elements with x^2 noncentral; witness chi = Phi_8, |C| = 32) -- and already at order 4 (510 noncentral free 4-elements, none regular). THE d/4-THEOREM [E, central]: for every degree d in {8, 12, 20, 24} the Springer-regular d-clocks satisfy x^{d/4} = +-i Id, a GENERATOR of mu4, never +-1 (one formula: all exponents of G31 are 3 mod 4); regular sets = 2 Galois classes each with sign split J vs J^3; THE CONVERSE is exact at d in {8, 20, 24} (extras 0) with the UNIQUE exception at d = 12: exactly 1280 extra elements = the classes of the COMPILER CLOCK c and its Galois twin -- chi_c = (x - i)^2 (x^2 + ix - 1) is half the regular-12 Springer block plus a doubled i, all eigenvalues satisfy lambda^3 = -i (exactly why c^3 = J^3 is central): the compiler-clock classes are the ONLY non-regular clocks in all of G31 whose d/4-th power generates the center. CONTROLS [E]: full order census (max 24); free orders = the divisors > 1 of the degrees; degrees = free orders divisible by 4 above 4 (honest: NOT the maximal free orders). No marker moves.
Recorded status: Exact [E] census/theorem/controls + honest kill ('free => regular' false) (Python-only per GATE.WOLFRAM.02).
Dependencies, status detail and source
Canonical status: D4-THEOREM: every Springer-regular d-clock has x^{d/4} = +-i Id (generator of mu4; exponents 3 mod 4); converse exact at d in {8, 20, 24}, unique exception at d = 12 = the compiler-clock class (chi_c = (x-i)^2(x^2+ix-1), c^3 = J^3); order-8 landscape complete; 'free => regular' killed; no marker moves.
Dependencies: E8.ST31.01; E8.ST31DEG.01; E8.ZIQUOTIENT.01; v629; v633; v634; v647
Scripts: v654_st31_degree8.py
Location: tfpt_3
Original CSV, line 657Original ledger status
META.LOOKELSEWHERE.01
The look-elsewhere audit -- the bingo budget of the typed [C] numeric coincidences, quantified (one module, 14 checks, ~2 s; discovery probe look_elsewhere_probe.py 14/14, verdict LOOKELSEWHERE-QUANTIFIED; seed 20260802, 100k MC, exact Poisson-binomial tails). THE BUDGET [E]: N = 42 structure slots, K = 19 hits against the compiler target list FROZEN before the computation; the 6 killed readings enter as 0-hit trials. GLOBAL [E]: family-corrected p = 5.08e-3 in the most conservative of three null models (uniform 7.5e-13, divisor-weighted 8.4e-13, size-windowed 5.08e-3); empirical control: 0.2%/0.3% of 2000 size-matched pseudo-target lists reach the real hit count / the real p. THE TRIAGE [E, the point]: NO single observation is significant on its own -- suggestive (0.01..0.1): 60 = D_start, 12 sigma-fixed roots = 12 marks, the G31 degrees, 48 = 240/5 = Omega_adm; unremarkable (p > 0.1): 6 = p_2(a) (p = 0.169) and the CODESEM number battery (p = 0.593); FORCED: 14 = A_4, 16 = |C| (their value is the theorem, not the number). RE-TYPES executed as dated ledger notes (EXTREV.LATTICE.01, E8.CODESEM.01, E8.CODE.01). The substance of the rounds lies in the [E] structure theorems, not in the number bingos; kills confirm the discipline (6 of 12 readings killed).
Recorded status: Exact [E] budget census + MC quantification + executed re-types (read-only meta-module; Python-only per GATE.WOLFRAM.02).
Dependencies, status detail and source
Canonical status: LOOKELSEWHERE-QUANTIFIED: 42 slots / 19 hits / 6 kills, global p = 5.08e-3 conservative (ensemble significant), pseudo-theory control 0.2%/0.3%, NO single observation significant; re-types executed (6 = p_2(a) p = 0.169; CODESEM battery p = 0.593; 14/16 FORCED); the substance is the [E] theorems.
Dependencies: META.DISCIPLINE.01; EXTREV.LATTICE.01; E8.CODE.01; E8.CODESEM.01; E8.INCIDENCE.01; E8.ST31.01; v100; v624; v626; v629; v633; v634; v638; v646; v647
Scripts: v664_look_elsewhere.py
Location: tfpt_3
Original CSV, line 658Original ledger status
QGEO.ORBOS.01
The first continuum-OS slice of the seam orbifold B -- the Osterwalder-Schrader reconstruction data measured at the CONVERGENCE level (one module, 19 checks, ~3 s; discovery probe orbifold_continuum_os_probe.py 19/19, verdict ORB-OS-CONTINUUM-SLICE). MACHINERY [machine]: Toeplitz == mode-sum covariance (1.2e-15); zero-mode-dressed Klein reality for the full mu6 angle family (5.4e-15); the NEW Euclidean-time machinery validated (NS bond Hamiltonian == eps6 at 6.7e-16; G(tau) via thin-QR-stabilized determinant ratio: == 1 identically at lam = 0 and at tau = 0, matches the naive complex determinant at 1.7e-13, det(V+ U_D V) == covariance-route string at 6.0e-15); ONE fitted constant (the non-universal amplitude A^2, N = 1536 vs 768 consistent at 5.7e-6). CONVERGENCE [E, central]: at fixed continuum data over N = 48..384 all six sigma-channel observables share the uniform raw rate 0.659 (spread 0.020) = the predicted Fisher-Hartwig branch exponent rho_sigma = 2/3; the tau-channel contrast measures 1.298 vs rho_tau = 4/3 (the channel law rho = 2(1-beta)^2 - 2 beta^2: the rates are UNDERSTOOD, not fitted; the honest answer to 'all rates >= 1?' is NO -- the leading artifact is the smooth FH branch, the same for every observable); after removing the ONE known FH term the residuals sit at the N^{-4/3} level; the extrapolated limits hit the CFT chord/cross-ratio values at < 0.05% (devs 3.9e-4 .. 5.1e-5); the epsilon/current channel is EXACT on the lattice (8.9e-15 -- no artifact at half filling). RP IN THE LIMIT [central]: the correlation-normalized Klein Grams are PSD at every N (worst floors 2.9e-12 / 4.3e-13 / 1.3e-12) AND the resolvable spectra converge with lambda_min extrapolations bounded away from zero -- sigma 1.357e-3 (margin 7x the uncertainty band), tau 2.800e-4 (margin 358x), mixed OS Gram {1, sigma_1, sigma_2} 1.337e-3 (margin 31x; the dipole-extended mixed Gram PSD too); must-fail: eta = -1 flips the sigma Klein Gram negative definite (floor -1.00). CLUSTER [E]: space -- the free-exponent chord fit at N = 1536 gives 2 Delta = 0.222220 vs 2/9 at 8.1e-6 (the chord/sin form beats the plain power law by 5 orders: the compact two-point IS the tau = 0 slice of the cylinder cosh form), and the N-extrapolated connected ratio equals the exact CFT law (1-w)^{-2/9} - 1 pointwise < 2%, falling like w^1.017; Euclidean time -- the connected C(tau) decays exponentially with the fitted gap = the exact transfer-matrix neutral gap at < 0.5% on BOTH lattices (Delta_exch = 0.99933 vs 1: the epsilon/current level IS the gap), the cosh/cylinder form holds pointwise (FH-extrapolated ratio 1 within 2.2e-3), the amplitude FH-extrapolates to 0.9977x the closed form. CHARACTERS [E]: h_sigma -> 1/36 and Delta_sigma -> 1/9 at 1.7e-12, the charged level 5/18 at 6.8e-13, the neutral level 4/9 at 3.9e-13 -- exact mode sums with the measured N^{-2} rate (2.001/2.000/2.000). TYPED [C]: OS axioms E0 (temperedness), E2 (reflection positivity), E3 (hermiticity), E4 (cluster) are now MEASURED at the convergence level; E1 (Euclidean invariance) is exact only for the discrete lattice symmetries -- full rotation invariance is EMERGENT (cross-ratio collapse + the N^{-4} S-covariance of v650); WHAT REMAINS for the formal limit: uniform bounds over ALL point configurations, tightness/equicontinuity, the GNS limit Hilbert space, operator (not Gram-entry) convergence, the R/parity sectors in the OS frame, and the assembled orbifold-B correlators beyond the twist blocks -- named, not claimed; GATE.QGEO does NOT move, no marker change.
Recorded status: Machine-exact wiring + Exact [E] convergence/cluster/character slices + [MEASURED] RP-limit extrapolations with must-fail control + [C] honest typing of the formal-limit remainder (Python-only per GATE.WOLFRAM.02).
Dependencies, status detail and source
Canonical status: ORB-OS-CONTINUUM-SLICE: correlator convergence with understood FH rates (2/3 sigma, 4/3 tau channel law; limits < 0.05% at CFT after one FH term), RP survives the limit (lambda_min extrapolations bounded away from zero, margins 7x..358x, must-fail flips), the cluster property exact in space and Euclidean time (2 Delta = 0.222220 vs 2/9 at 8e-6; time gap = the epsilon level), characters at 1e-12 with the measured N^-2 rate; E0/E2/E3/E4 measured at the convergence level, E1 discrete; the formal limit (GNS, uniform bounds, operator convergence) is the named remainder; GATE.QGEO does not move.
Dependencies: QGEO.ORBMOD.01; QGEO.ORBASM.01; QGEO.ORBARF.01; QGEO.BONDDEF.01; QGEO.KLEINRP.01; QGEO.TWISTOPE.01; GATE.QGEO.01; v622; v623; v639; v645; v650
Scripts: v679_orbifold_continuum_os.py
Location: tfpt_3
Original CSV, line 659Original ledger status
E8.GAUSSCODE.01
The Gaussian code bridge (review contract E8.GAUSSIAN.CODE.01) -- E8(Z[i])/(1+i) IS the information space of RM(1,3): the mu4 complex structure J makes E8 a rank-4 Z[i]-lattice L; reduction modulo the ramified Gaussian prime (1+i) gives L/(1+i)L = F2^4 EXACTLY (one module, 26 checks, ~3 s, exact integer/Fraction arithmetic, sympy only for the Smith normal form; discovery probe gaussian_code_bridge_probe.py 26/26, verdict GAUSSIAN-CODE-BRIDGE-EXACT). THE QUOTIENT [E]: SNF exact; standard-model cross-check: basis |det| = 256 = 2^8 (doubled coordinates), SNF [1,1,1,1,2,2,2,2] -- presentation-independent. THE CENSUS [E]: 240 roots fall 15 x 16 over the nontrivial classes (the zero class PROVABLY EMPTY); each class = a union of 4 of the 60 G31 lines (60 = 15 x 4). THE SEMANTICS [E]: sigma = c^4 acts on the quotient as the RM(1,3) family permutation (3-cycle F1 -> F2 -> F3 + fixed anchor, exactly the v638 info-bit action); residual gauge = the order-18 centralizer of the family 3-cycle in GL(4, F2); the coordinate block = the sum-of-families label F1 + F2 + F3. MUST-FAIL CONTROLS [E, kill]: the naive placement keeps the 15 x 16 census (a property of (E8, J) alone) but the sigma-bit semantics becomes UNDEFINED (witness codeword lift off the lattice); a non-piJ placement has NO Z[i]-module; Z[i]^4 trivializes (16 minimal vectors, 11 classes empty). No marker move. [2026-08-03 LI: formally verified -- the algebraic core (Z[i]-module + SNF certificate with unimodular P/Q both directions, the 240-root census 15 x 16 with the zero class provably empty, mu4 stability, the sigma = order-3 family action with coordinate block = F1+F2+F3) is kernel-checked in Lean 4 (experiments/lean4-carrier-rigidity/TfptCarrier/GaussianCodeBridge.lean, lake build green, no sorry / native_decide).]
Recorded status: Exact [E] SNF/census/semantics identities + [E, kill] three must-fail controls (exact arithmetic; Python-only per GATE.WOLFRAM.02).
Dependencies, status detail and source
Canonical status: GAUSSIAN-CODE-BRIDGE-EXACT: E8(Z[i])/(1+i) = F2^4 (SNF exact, presentation-independent), 240 = 15 x 16 census (zero class provably empty), 60 = 15 x 4, sigma = RM(1,3) family permutation (18 equivariant gauges), coordinate block = F1+F2+F3; all must-fail controls fire (naive placement, non-piJ placement, Z[i]^4).
Dependencies: E8.CODE.01; E8.CODESEM.01; E8.ST31.01; E8.ZIQUOTIENT.01; v626; v634; v638
Scripts: v689_gaussian_code_bridge.py
Location: tfpt_1;tfpt_2;tfpt_3
Original CSV, line 660Original ledger status
E8.QUARTICHALF.01
The quartic invariant restriction (review contract E8.QUARTIC.HALF.01) -- is G31 the holomorphic mu4 shadow of the E8 Coxeter compiler? ALIVE, with the honest split (one module, 22 checks, ~1 s, exact Gaussian-integer/Fraction arithmetic, no floats; discovery probe quartic_half_probe.py 22/22, verdict QUARTIC-HALF-ALIVE). THE VANISHING HALF [PROOF, typed honest]: {2,14,18,30} is TRUE but TRIVIAL -- W(J alpha) = -i W(alpha) for all 240 roots => every J-orbit contributes t^d (1 + (-i)^d + (-1)^d + i^d) = 0 for every d != 0 mod 4 (holds for 6, 10, 22, 26 too: mu4 orbit factor, NOT degree-list-specific); degrees 4/6 vanish on ANY q-isotropic subspace (f_4 = 576 q^2, f_6 = 1920 q^3 symbolically); F_4| has all 35 monomial coefficients = 0 exactly (the first G31-consistency point: mod-4 alone would allow F_4 != 0). THE LOAD-BEARING CONTENT [E, central]: F_8|, F_12|, F_20|, F_24| are G31-invariant (60/60 hermitian reflections + clock generators, exact), ALGEBRAICALLY INDEPENDENT (exact Jacobian != 0 off the mirrors), degrees (8,12,20,24) Molien-unique with product 46080 = |G31| => by Chevalley [cited] a system of BASIC INVARIANTS: the holomorphic restriction of the W(E8) invariant ring generates the FULL G31 invariant ring; the Jacobian carries the 60 mirror lines (deg Jac = 60 = sum(d_i - 1), on-mirror vanishing point-verified 60/60; the full factorization = cited standard theorem, NAMED residual). MUST-FAIL CONTROLS [E, kill]: J' = RJR^T (orthogonal, NOT root-preserving) breaks the informative half {14,18,22,26,30} while the trivial isotropy layers persist; the root-preserving J'' keeps the full pattern (the theorem is about the W(E8)-conjugacy class of compiler-compatible J); a random non-isotropic 4-space breaks even F_2; honest negative: signed-permutation J-conjugates canNOT serve as controls (they stay in W(D8)). No marker move. [2026-08-03 LI: formally verified -- the mu4-orbit vanishing mechanism (orbit factor 1 + (-i)^d + (-1)^d + i^d = 0 iff d != 0 mod 4, per-pair weight law, the full vanishing half incl. the trivial extras) and the quartic power sum Sum <alpha,x>^4 = 576 (Sum x_i^2)^2 over the explicit 240 roots (+ holomorphic isotropy) are kernel-checked in Lean 4 (experiments/lean4-carrier-rigidity/TfptCarrier/QuarticHalf.lean, lake build green, no sorry / native_decide); the Chevalley basic-invariant step remains CITED, not formalized.]
Recorded status: Symbolic [PROOF] mu4-orbit vanishing + [E] G31 invariance/independence/mirror census + [E, kill] complex-structure controls + [cited] Chevalley basic-invariant theorem (exact arithmetic; Python-only per GATE.WOLFRAM.02).
Dependencies, status detail and source
Canonical status: QUARTIC-HALF-ALIVE: the vanishing half {2,14,18,30} proven symbolically but TRIVIAL (mu4 orbit factor, honest typing); the substance: F8/F12/F20/F24 algebraically independent G31 basic invariants (holomorphic restriction generates the FULL G31 ring, Chevalley cited); Jacobian carries the 60 mirrors (60/60 point-verified); controls fire exactly as demanded.
Dependencies: E8.ST31.01; E8.ST31DEG.01; v634; v647; v654
Scripts: v690_quartic_half.py
Location: tfpt_1;tfpt_2;tfpt_3
Original CSV, line 661Original ledger status
E8.GAUSSIAN.CODE.01
Review contract (external review, theorem candidate, registered 2026-08-03): E8(Z[i])/(1+i) is the information space of RM(1,3) -- the mu4 complex structure J makes E8 a rank-4 Z[i]-lattice; the (1+i)-quotient is F2^4; the 240 roots fall 15 x 16; sigma acts as the RM(1,3) family permutation. FIRST SLICE EXECUTED by v689 (26/26, GAUSSIAN-CODE-BRIDGE-EXACT): the full 6-step census verbatim, exact arithmetic, all must-fail controls firing. REMAINING: the paper-level theorem writeup (the census IS the proof skeleton; the residual gauge order 18 documented). NOTE (2026-08-04, v736/v737 -- marker UNCHANGED): the ORBIT PACKET lemma is machine-closed [E] (Burnside 7 = (15+3+3)/3, the canonical 5 x 48 split, the (1,1,2) anchor from the fixed-syndrome leader weights (0,1,1,2), the q = 16 normal form 240 = 16*15 / 248 = 240+8; P1/P2 typed as EXACT-INTERNAL-RECONSTRUCTION behind the circularity fence; companion Lean module OrbitPacket.lean, 34 theorems kernel-checked), and the seam-48 intertwiner sharpening is DEAD (v737: incidence distribution 0:96/1:64/2:64/3:16 instead of == 1, representative-independent over all 2304 order-5 elements) -- 240 = 48 x 5 remains a factorization WITHOUT coordinatization. NOTE (2026-08-05, v782/v783 -- marker UNCHANGED): the code bridge acquires its operational identification -- the 60 Gaussian lines ARE the 60 two-qubit stabilizer rays entry-exactly over Z[i] with U G31 U^-1 an index-2 subgroup of the Clifford matrix group (classes = the 15 Pauli contexts, spreads = the MUB pentads; the index bit is the sqrt2/Hadamard Galois bit, NOT J <-> -J; v783), and the 240 = 16 x 15 transition reading is settled at TORSOR level (each class fiber a canonical v_perp pair-torsor; the frozen predicate reproduces all 57600 inner products; NO deck-equivariant 16-state labeling exists -- proof-grade obstruction; v782).
Recorded status: Review contract; first slice machine-closed [E] (v689); remaining: theorem writeup.
Dependencies, status detail and source
Canonical status: EXECUTED (first slice): v689 closes the census + semantics exactly (26/26); remaining: theorem writeup.
Dependencies: E8.GAUSSCODE.01; E8.CODESEM.01; E8.CODE.01
Scripts: See original ledger entry
Location: tfpt_research_contracts
Original CSV, line 662Original ledger status
E8.QUARTIC.HALF.01
Review contract (external review, theorem candidate, registered 2026-08-03): restricting the W(E8) invariant root power sums to the holomorphic mu4 eigenspace V^{1,0} kills exactly the half {2,14,18,30} and keeps {8,12,20,24} = Deg(G31) -- 'G31 is the holomorphic mu4 shadow of the E8 compiler'. FIRST SLICE EXECUTED by v690 (22/22, QUARTIC-HALF-ALIVE) WITH the honest correction: the vanishing half is TRUE but TRIVIAL (mu4 orbit factor -- holds for all d != 0 mod 4, not degree-list-specific); the substance is F8/F12/F20/F24 as a system of basic G31 invariants (Chevalley cited; the holomorphic restriction generates the FULL G31 ring). REMAINING: the symbolic degree-60 Jacobian factorization (cited standard theorem, named residual) and the paper-level writeup.
Recorded status: Review contract; first slice machine-closed [E]/[PROOF] with honest typing correction (v690); remaining: Jacobian factorization symbolics + writeup.
Dependencies, status detail and source
Canonical status: EXECUTED (first slice): v690 proves the vanishing half (trivial, honestly typed) and establishes the basic-invariant substance; remaining: symbolic Jacobian factorization + writeup.
Dependencies: E8.QUARTICHALF.01; E8.ST31.01
Scripts: See original ledger entry
Location: tfpt_research_contracts
Original CSV, line 663Original ledger status
E8.ORBIT60.01
The ORBIT60 census -- the 60 mu4-lines of E8 as a combinatorial object: quotient graph, sigma/clock/Coxeter dynamics on the ORBIT SPACE, and a STRICT park test for the cascade 60 -> 6 (one module, 18 checks, ~1 s; discovery probe orbit60_census_probe.py 18/18, verdict ORBIT60-PARKED). THE FIVE ROUTES, all adjudicated: (i) degree rules DEAD (all quotient graphs regular -- no distinguished pair sequence from incidence degrees); (ii) sigma structure DEAD (sigma-orbit sizes {3,1} on the lines, no 2-blocks); (iii) THE INVOLUTION WITNESS DOES NOT EXIST: the full involution census of the line group LG (order 11520; 375 involutions, 21 conjugacy classes) shows NO element of cycle type 2^27 1^6 (fixed-line census {0: 120, 4: 180, 12: 15, 16: 60}) -- the one-shot group-action carrier of the cascade is absent; (iv) reflection/Coxeter DEAD: W(E8) Coxeter dynamics does not descend (reflection cycle types on the lines all equal, no distinguished element with 27 disjoint 2-blocks); (v) the MUST-FAIL numerology control fires as designed: rule-free lexicographic pair removal reproduces the counting 60 - 2n in exactly 27 steps and > 10^70 equally 'successful' sequences exist -- the counting carries no structural information (v633 Q8.2 reproduced). A5 one-liner (as instructed, no expedition): order-5 elements exist (2304) but <sigma, sample order-5> has order 960 -- no visible natural A5 action attached to the compiler data. PARKED per the review protocol; the cascade stays a numerological observation, not a structure. Deterministic (fixed seed for the generating-set search only).
Recorded status: Honest [E, park] five-route adjudication with the involution-witness census and the must-fail numerology control (exact group computations; Python-only per GATE.WOLFRAM.02).
Dependencies, status detail and source
Canonical status: ORBIT60-PARKED: all canonical cascade routes dead; no involution of cycle type 2^27 1^6 in the line group (order 11520; 375 involutions, 21 classes); W(E8) Coxeter does not descend; no A5 signature (order-5 elements exist but nothing natural); the must-fail numerology control fires -- parked per the review protocol.
Dependencies: E8.ST31.01; v629; v633; v634
Scripts: v700_orbit60_census.py
Location: tfpt_3
Original CSV, line 664Original ledger status
QGEO.DECKSECTOR.01
TFPT scope of original v705: only D1 NS-circle clock/deck finite algebra, 48 modes with three 16-mode sectors. The prime/digamma application is maintained in Prime Front.
Recorded status: Exact [E] deck-sector trace identity (3.4e-16, scalar forced 1, must-fail x82); deterministic (Python-only per GATE.WOLFRAM.02).
Dependencies, status detail and source
Canonical status: The three digamma channels ARE the three deck sectors of the 48-site NS lift (exact tower traces, dev 3.4e-16, scalar forced 1, must-fail x82) -- the geometry anchor of the chain arc; GATE.QGEO untouched; no RH statement.
Dependencies: PRIME.KEYSTONE.01; QGEO.ORBIFOLD.01; v623; v628
Scripts: v705_chain_deck_sector.py
Location: tfpt_3
Original CSV, line 665Original ledger status
QGEO.CARLIMIT.01
QGEO-CAR -- the quasi-free CAR route to the formal orbifold continuum limit (GATE.QGEO), first slice (one module, 22 checks, ~10 s; discovery probe qgeo_car_continuum_probe.py 22/22, verdict QGEO-CAR-RATES-SUMMABLE). THE STRATEGY EXECUTED: not measure compactness -- the orbifold correlators are DETERMINANTS of a one-particle covariance, so the limit runs through SCHATTEN-NORM control plus Araki's quasi-free CAR theory. THE MEASUREMENTS: all 6+1 deck/twist sector covariances AND all dressed twist channels are Schatten/shadow-norm CAUCHY on eps-separated configurations (N up to 3072 / 6144), with geometrically summable rates; the FH renormalization is FIT-FREE LATTICE-DERIVED (Barnes G, deviation 8.8e-7); the RP cone margins do NOT degenerate along the ladder; all four kill criteria are clear. THE REMAINDER NAMED: the majorant lemma (L1)-(L3) is stated with constants and the CLASSICAL proof route -- named, not claimed: GATE.QGEO does NOT move. Deterministic (no RNG); self-contained. No marker move.
Recorded status: [MEASURED] Schatten-norm Cauchy rates (6+1 channels, geometrically summable) + [E] lattice-derived FH renormalization (Barnes G, 8.8e-7) + named (L1)-(L3) majorant lemma; deterministic (Python-only per GATE.WOLFRAM.02).
Dependencies, status detail and source
Canonical status: QGEO-CAR-RATES-SUMMABLE: all 6+1 channels Schatten-norm Cauchy (N up to 3072/6144), FH renormalization fit-free lattice-derived (Barnes G 8.8e-7), RP cone stable, kill criteria clear; majorant lemma (L1)-(L3) named with constants + classical proof route; GATE.QGEO does NOT move.
Dependencies: GATE.QGEO.01; QGEO.CONEDYN.01
Scripts: v715_qgeo_car_continuum.py
Location: tfpt_3
Original CSV, line 666