Original ledger status
CURVE.CODE.2TORSION.01
The curve/code 2-torsion decider (33/33 checks, ~9 s; discovery probe curve_code_2torsion_probe.py CURVE-CODE-PARTIAL, 2026-08-05). The frozen CM-model route through the seam curve C: y^3 = x^4 - 1 (genus 3, Jacobian splits per v610): exact differential characters (zeta^11, zeta^7, zeta^10) reproduce v610 L1; A = the zeta_12 CM abelian surface with EVERY generator period certified as an integral O = Z[zeta_12] recognition (mpmath dps 120, residual tolerance 1e-35, recognition margin > 10^25 x residual, HNF index 1 -- the numerics END in certified integer recognitions); A[2] = O/2O = F2^4 exact from there on; the deck tau = multiplication by zeta^4 is DERIVED as the only order-3 automorphism class (Aut(C) = C12, monodromy forcing); the minimal ODD tau-invariant polarization is type (1,3) with Pfaffian 3 -- NO principal form exists in the tau-invariant cone (unit-sign obstruction: the fundamental unit 2+sqrt3 of the real subfield is totally positive) and the curve-induced Prym type (1,2) is mod-2 DEGENERATE (typed [C]); q_Theta = the unique tau-fixed quadratic refinement (exists and is unique since N(omega-1) = 9 is odd). THE DECIDER: (A[2], e_2) and (V, hbar) are isomorphic as BARE symplectic F2^4 (720 = |Sp(4,2)| transporters -- content-free), but the full correspondence DIES at two exact layers: (1) SIGMA LAYER: tau acts FREELY on A[2] (fixed space 0, realization-independent) with cycle type [3,3] on the 6 odd theta characteristics (SYNTHEME side), while the code family cycle sigma-bar fixes a 2-plane with cycle type [3,1,1,1] (DUAD side) -- the two order-3 classes are exchanged only by the OUTER automorphism of S6, never by conjugation; equivariant census 0 (tau and tau^2). (2) REFINEMENT LAYER: the curve's canonical deck-invariant theta refinement q_Theta is EVEN (Arf 0, 10 zeros, stabilizer 72, decomposition 1+6+9) while the code's arf-certified selector q* is ODD (Arf 1, 6 zeros, stabilizer 120, decomposition 1+5+10) -- Arf is a transport invariant, census 0. Joint census 0 with the positive control (code clone) at exactly 6 = the code-side stabilizer order; all must-fire controls fire. ROOTCLASS-MIXED (v775) fence respected: finite exact algebra on 2-torsion, no physical labeling. No marker move, NO RH claim. NOTE (2026-08-06, v796 -- marker UNCHANGED): the INNER identification stays dead exactly as recorded, and the OUTER twist is now decided CANONICAL (CURVE.CODE.OUTERSPIN.01 / v796): the Sylvester bridge beta with beta sigma = tau beta and beta(q*) = S* is unique up to the order-6 joint stabilizer, pulls q_Theta back to q_even* = q* + hbar(., A) (the anchor shift resolves the Arf mismatch), and transports 1+5bar+10 / 3+2 / t_A -> rho = J exactly -- both breaking layers of this row are thereby explained as the two faces of the outer automorphism of S6, not repaired.
Recorded status: Exact [E] finite algebra + certified-recognition CM layer; the correspondence honestly PARTIAL with both breaking layers named exactly (syntheme-vs-duad and Arf 0-vs-1); no marker move (Python-only per GATE.WOLFRAM.02).
Dependencies, status detail and source
Canonical status: CURVE-CODE-PARTIAL: (A[2], e_2) = (V, hbar) as bare symplectic spaces only; the correspondence dies at two exact layers -- deck acts syntheme-side [3,3]-free vs code duad-side [3,1,1,1] (outer S6), and curve theta even/Arf-0 (1+6+9) vs q* odd/Arf-1 (1+5+10); joint census 0 with positive control 6; every period certified as integral O-recognition; no RH statement.
Dependencies: v610; v611; v752; v753; ARF.SPINORCOMPILER.01; ARF.ROOTCLASS.01
Scripts: v784_curve_code_2torsion.py
Location: tfpt_1;tfpt_3
Original CSV, line 687Original ledger status
FTRANSFER.KMSCOSET.01
the coset assignment of the fibered clock functor is a THEOREM from KMS/modular typing (18/18 checks incl. the three must-fire controls, ~3 s; discovery probe ftransfer_kms_coset_probe.py, 2026-08-05, verdict KMS-COSET-THEOREM; frozen before the first run). THE THEOREM: S_transported = -(ln lambda)^2/2 with lambda the PGL2 multiplier of the flow's time-1 holonomy per clock e-fold -- the coset is COMPUTED from the typing datum lambda, never case-inspected. THE CLASSIFIER uses NO Schwarzian and NO derivative of any order (non-circularity gate on its own source): (i) the holonomy grounded as an exact functional identity y(x+1) = T(y(x)), (ii) the PGL2 class of T (scalar -> degenerate; parabolic -> autonomous, lambda = 1; else hyperbolic candidate), (iii) the detailed-balance multiplier cross-ratio m(x) -- the discrete KMS signature -- exactly constant -> modular with lambda = m. DERIVATION CHAIN sympy-exact: Lemma A {M(e^{ax}), x} = -a^2/2 identically for GENERIC Moebius M; Lemma B {M(x), x} = 0; Lemma C -a^2/2 = -Delta^2/2 iff a = +-Delta, affine dictionaries change nothing. BLIND PROTOCOL: the four deployed clock charts classify F_pole/F_Boltzmann MODULAR with |ln lambda| = Delta = 6 log(3/2) exactly, F_QCD AUTONOMOUS (parabolic), F_relic DEGENERATE; unblinding: predicted cosets == transported Schwarzians EXACTLY (sympy zero) -- the fiber classification of the executed contract (v777, FTRANSFER-FIBERED-CARRIES) is now DERIVED. CONTROLS: C1 fake-KMS witness caught (functional identity fails AND the ratio is non-constant); C2 affine reparametrization x -> -x + c leaves typing and |ln lambda| unchanged; C3 the v578 Moebius clock t = e^{Delta sigma} flips the QCD chart to modular and the theorem PREDICTS -Delta^2/2, confirmed by the transported Schwarzian -- the K1-duty transplant as the positive case. Completes the three-probe chain executor -> fibered groupoid -> coset theorem: the CONTRACT.F.01 fibered refinement's clock-fiber classification is a derived statement. Freeze guards: prereg YAML + both data tables byte-identical. No marker move, NO RH claim. Python-only per GATE.WOLFRAM.02.
Recorded status: Theorem-grade [E] sympy-exact derivation chain + blind classification with the non-circularity of the classifier gated on its own source; completes the fiber classification of the executed clock contract; no marker move (Python-only per GATE.WOLFRAM.02).
Dependencies, status detail and source
Canonical status: KMS-COSET-THEOREM: S = -(ln lambda)^2/2 from the time-1 PGL2 holonomy multiplier per clock e-fold; classifier Schwarzian-free and derivative-free (non-circularity gated); blind assignment F_pole/F_Boltzmann modular (|ln lambda| = Delta), F_QCD autonomous, F_relic degenerate; unblinding exact (sympy zero); controls fire incl. the Moebius-clock positive case; the executor -> groupoid -> coset chain whole; no RH statement.
Dependencies: CONTRACT.F.01; FTRANSFER.CLOCKS.01; v777; v578; v99; v425
Scripts: v792_ftransfer_kms_coset.py
Location: tfpt_research_contracts;tfpt_3
Original CSV, line 688Original ledger status
CURVE.CODE.OUTERSPIN.01
the canonical OUTER bridge between the code's duad side and the curve's syntheme side of the S6 duality (24/24 checks, ~11 s; discovery probe duad_syntheme_bridge_probe.py, 2026-08-05, verdict BRIDGE-CANONICAL). THE CONSTRUCTION (Sylvester duality made explicit): a bridge is a bijection beta: Omega_code -> T_curve (code odd Arf forms -> curve isotropic spreads/totals), canonically inducing the incidence-preserving duality Delta_beta: V\{0} -> IsoLines(A[2]) through the K6 duad model and the shared-syntheme rule (every pair of totals shares exactly one line -- verified). THE CENSUS: 18 + 18 bridges intertwine sigma with tau|T resp. tau^2|T (each family a torsor under C_S6(3-cycle), order 18); after pinning beta(q*) = S* -- the UNIQUE curve spread fixed by the FULL <tau, rho> automorphism image (rho = the mu4 rotation = the complex structure J = mult by zeta^9; existence + uniqueness COMPUTED, not assumed) -- exactly 6 + 6 remain = ONE ORBIT (torsor) under the order-6 code joint stabilizer, with the tau/tau^2 families exchanged by an inner code symmetry (one statement). B2 ARF RESOLUTION: the pullback of the curve's even q_Theta through the two frozen even<->3|3-split dictionaries is CONSTANT over all 36 B1 bridges and equals q_even* = the unique sigma-invariant even code refinement, with the NAMED operation q* = q_even* + hbar(., A) EXACT -- the anchor shift resolves the v784 Arf mismatch canonically. THE OUTER WITNESS exact: sigma is [3,1,1,1] on odds but [3,3] on spreads, tau the reverse, the anchor transvection t_A is [2,1,1,1,1] on odds but [2,2,2] on spreads, and the class swap is UNIFORM (0 violations over all 720 group elements) -- the twist IS the outer automorphism of S6, not an inner accident. TRANSPORTS (structure labels only): {q* = 0}\{0} maps EXACTLY onto the 5 lines of S* (5bar) and the 10 onto the complement; the 3+2 split maps onto the [3,1,1] tau-orbit structure of S*; t_A maps to rho = J on every census bridge; chi_NSR transports as an honest exact TWO-VARIANT torsor ('incidence with one of the two tau-fixed lines of S*') -- it is pinned code-side by the v752 NS/R lattice parity, a datum the bare quadruple (V, hbar, sigma, q*) does not carry, and rho swaps the two candidate lines (the two-fold ambiguity intrinsic). CONTROLS: inner cross-side census 0 (class mismatch), same-side census 0, no bridge pulls q_Theta to an ODD form (never to q*), scrambled sigma census 0. The v784 INNER identification stays dead (CURVE-CODE-PARTIAL untouched); the bridge is a NEW statement about the outer twist. NO matter semantics (5bar/10, 3+2, chi_NSR are structure labels; ROOTCLASS-MIXED v775 stands). No marker move, NO RH claim. Python-only per GATE.WOLFRAM.02. CONTRACT DECIDED (registered here as the decided outer-bridge statement): the outer identification is CANONICAL; the residual is the intrinsic two-variant chi_NSR ambiguity (pinned only by the v752 NS/R lattice parity, which the bare 2-torsion quadruple does not carry) -- typed, not open work; cross-referenced with CURVE.CODE.2TORSION.01, whose inner-identification kill stands unchanged.
Recorded status: Exact [E] finite census theorem (torsor uniqueness incl. the tau/tau^2 swap; constant Arf resolution; exact transports) behind the structure-label fence; the inner identification stays dead (v784); no marker move (Python-only per GATE.WOLFRAM.02).
Dependencies, status detail and source
Canonical status: BRIDGE-CANONICAL: the Sylvester duality beta (code odd forms -> curve spreads) with beta sigma = tau beta and beta(q*) = S* is unique up to the order-6 joint stabilizer (18 + 18 -> 6 + 6, one orbit incl. the tau/tau^2 swap); q_Theta pulls back constantly to q_even* = q* + hbar(., A) -- the anchor shift resolves the v784 Arf mismatch; 5bar/10, 3+2 and t_A -> rho = J transport exactly; chi_NSR an exact two-variant torsor; inner identification stays dead; no RH statement.
Dependencies: CURVE.CODE.2TORSION.01; ARF.SPINORCOMPILER.01; v784; v774; v752; v610; v611; ARF.ROOTCLASS.01
Scripts: v796_duad_syntheme_bridge.py
Location: tfpt_1;tfpt_3;tfpt_research_contracts
Original CSV, line 689Original ledger status
SEAM.CLIFFORD.MODULAR_S.01
the missing Clifford index-2 bit IS the metaplectic lift of the modular S transformation at its fixed point tau = i -- coset decision positive, deck placed, anchor named; the frozen uniqueness decider fails sharply (27/27 checks, ~50 s; discovery probe seam_clifford_modular_s_probe.py, 2026-08-06, verdict MODULAR-S-PARTIAL). COSET DECISION POSITIVE (exact cyclotomic arithmetic): the per-binary-factor Weil/metaplectic lift K1 = H (x) I (and K2 = I (x) H) lands EXACTLY in the missing coset zeta8 G31 of v783 (BFS membership certificates for zeta8^{-1} K_i in G31), with the exact tau = i fixed-point relations S^2 = +I, T^2 = the Pauli parity element, and (T K)^3 = zeta8 I -- the Weil constant gamma = zeta8, c = 1 per binary factor. R2 SOLVED (deck placement): the TOTAL symplectic Fourier K3 = H (x) H (the toric-code modular S) lies INSIDE G31 (chi = 0) and its metaplectic anomaly is (T3 K3)^3 = i I = J -- THE DECK IS THE METAPLECTIC ANOMALY OF THE TOTAL MODULAR LIFT (c = 2); zeta8 = (1 + J)/sqrt2 is the real orthogonal HALF-DECK ((1+J)^2 = 2J exact) swapping the seam pair {L, zeta8 L}: lift = half-deck turn x lattice automorphism. The Z4 deck-clock Fourier F4 is NOT a carrier symmetry (fails the Clifford gate; typed out). OS reflection gate exact: Theta K1 Theta = K1 and Theta T1 Theta = T1^{-1} -- the antiunitary reality involution acts as the GL(2,Z) orientation flip tau -> -tau-bar, which FIXES tau = i. THE FROZEN UNIQUENESS DECIDER FAILS SHARPLY (the PARTIAL): the strict census over all 46080 coset elements (order gate 480 -> Theta-reality 96 -> q*-fixed + metaplectic pairing) is EMPTY (0/46080) -- NO Theta-real metaplectic involution in the missing coset fixes the v774 Arf refinement q*: the Arf defect q* -> q* + hbar(., c) is UNAVOIDABLE; the retyped census (defect recorded instead of forbidden) has 32 survivors = 16 (+-1)-pairs = EXACTLY ONE G31-conjugacy class (w1 ~ w2; tier-A 4 = the Pauli/phase gauge fiber of H (x) I). R3 NAMED, NOT FIXED: the sigma-orbit of lifts {w1, sigma w1 sigma^{-1}, w2} has Arf defects EXACTLY {A + F_Sigma + F_i : i = 1, 2, 3} (one per family) whose XOR is THE ANCHOR A itself; the total Fourier's defect is A + F_Sigma; every retyped survivor's defect carries the anchor flag chi_NSR(c) = 1 -- the lift does not fix the anchor, it NAMES it through the Arf defects. CONTROLS: CZ (real, order 2, Clifford, non-metaplectic) lies INSIDE G31 (chi = 0); the wrong phase convention zeta8 K1 breaks S^2 in {+-I} ((zeta8 K1)^2 = iI); census selectivity 480 -> 96 -> 32 of 46080. ROOTCLASS-MIXED (v775) unaffected -- finite stabilizer/Weil mathematics about the carrier, no physics claim. No marker move, NO RH claim. Python-only per GATE.WOLFRAM.02. CONTRACT (registered, partial state): coset decision POSITIVE and R2 solved (the deck = the metaplectic anomaly of the total Fourier); R3 NAMED through the sigma-orbit Arf defects (XOR = the anchor A); remaining: derive the physical selection of the defect class (the anchor naming from seam data) or type the two-variant/defect residue as intrinsic gauge; kill: a Theta-real metaplectic coset element fixing q* (excluded here by the exhaustive 0/46080 census) would falsify the defect law.
Recorded status: Exact [E] cyclotomic coset/metaplectic identities (BFS certificates; exact tau = i relations) with the strict uniqueness census EMPTY by its own frozen gate -- the Arf defect unavoidable, a sharp typed fact; R2 placed, R3 named; no marker move (Python-only per GATE.WOLFRAM.02).
Dependencies, status detail and source
Canonical status: MODULAR-S-PARTIAL: the per-factor Hadamard IS the metaplectic S-lift at tau = i, landing exactly in the missing coset zeta8 G31 (S^2 = I, T^2 = Pauli parity, (TK)^3 = zeta8 I); the deck J = the metaplectic anomaly of the total Fourier (R2 solved); zeta8 = (1+J)/sqrt2 the half-deck swapping the seam pair; strict census EMPTY (0/46080 fix q*), one G31-conjugacy class of retyped survivors, sigma-orbit Arf defects XOR to the anchor A (R3 named, not fixed); no RH statement.
Dependencies: E8.CLIFFORD2Q.01; ARF.BOUNDARY.CODE.01; ARF.SPINORCOMPILER.01; v783; v774; v752; v689; ARF.ROOTCLASS.01
Scripts: v798_seam_clifford_modular_s.py
Location: tfpt_1;tfpt_3;tfpt_research_contracts
Original CSV, line 690Original ledger status
SEAM.CODE.TYPEII.01
Type II (doubly-even self-dual) is FORCED from three physical seam axioms -- the direct attack on residual R1 of ARF.BOUNDARY.CODE.01, decided exhaustively (19/19 checks, ~5 s; discovery probe seam_code_typeii_probe.py, 2026-08-06, verdict TYPEII-FORCED). THE THREE EQUIVALENCE CENSUSES, exhaustive over ALL 308,993 subspaces of F2^8 of dim 0..4 (totals = the Gaussian binomials 1, 255, 10795, 97155, 200787; dim > 4 excluded by rank-nullity): (1) MUTUAL LOCALITY of the Construction-A boundary vertex words <=> C self-orthogonal, ZERO exceptions (braiding exponent <(c+2m)/sqrt2, (c'+2m')/sqrt2> = c.c'/2 + Z -- the lift-shift identity verified exhaustively; word-pair census all 65536 pairs; survivors per dim 1/28/165/280/135); (2) INTEGER CONFORMAL SPIN (all T sector phases i^{wt(c)} trivial, |c+2m|^2 == wt(c) mod 4 exhaustive; the eta^8 multiplier typed universal/code-independent) <=> C doubly even, ZERO exceptions (survivors 1/8/38/52/30); (3) HOLOMORPHY / INDEX ONE (|disc| = det(rescaled Gram) = 2^{8-2k} exact in Fractions; |disc| = 1 = single modular-closed sector) <=> C self-dual <=> k = 4 -- and EVERY non-self-dual doubly-even code has a word in C-perp \ C of weight != 0 mod 4, i.e. a discriminant sector of FRACTIONAL conformal weight on which the S-image cannot close (proved exhaustively; detailed witness: the [8,3] subcode of the boundary-selected C* with exact coset theta series to h <= 2, theta_{L*} != 2 theta_L). THE KILL EXCLUDED: the survivor set of (locality, integer spin, |disc| = 1) over ALL subspaces IS the Type II set = the 30 e8-hat copies (weight enumerator 1 + 14x^4 + x^8); no boundary-legal non-Type-II code exists at length 8. R1 -> R1': the universe premise 'the boundary realizes a doubly-even self-dual code' is REPLACED by the three physical axioms A1 mutual locality (trivial monodromy / bose statistics), A2 integer conformal spin (bosonic T-alignment), A3 holomorphy / index one (single modular-closed sector) -- each a standard physical demand, not a coding-theory premise; given A1-A3 the chain boundary axioms + deck + orientation bit -> unique code -> E8 -> F2^4 -> g_car = 5 stands with this single sharpened [C] residual. IMPORTED INGREDIENTS typed and machine-verified in every instance used (I1 Frenkel-Kac-Segal braiding factor, FLM 1988/Kac, Adamo-Moriwaki-Tanimoto arXiv:2407.18222; I2 h = |lambda|^2/2 lattice-VOA grading; I3 Conway-Sloane/Ebeling theta S-transform with L* = A(C-perp) verified); the OPE-linearity scope note (admissible word sets are linear codes) typed as a scope assumption. Controls: braiding monodromy -1 witness; T-phase witnesses i and -1; the [8,3] S-closure violation. Uniqueness (30 copies; the boundary data select ONE) CITED from v776, count echo verified. NO P2 marker move. No marker move, NO RH claim. Python-only per GATE.WOLFRAM.02. CONTRACT (registered; the sharpened [C] residual replacing R1 of ARF.BOUNDARY.CODE.01): the physical seam satisfies A1 mutual locality (trivial monodromy of admissible boundary vertex words), A2 integer conformal spin (bosonic T-alignment), A3 holomorphy/index one (a single modular-closed sector); given A1-A3, Type II is FORCED at length 8 (this module), e8-hat is unique (30 copies) and the v776 boundary data select one copy -> E8 -> F2^4 -> g_car = 5; kill: a seam construction violating A1-A3 while staying boundary-legal, or a boundary-legal non-Type-II code at length 8 (excluded exhaustively here).
Recorded status: Exact [E] exhaustive finite equivalence chain at length 8 (all 308,993 subspaces) modulo the cited classical lattice-VOA/theta ingredients, each machine-verified in every instance used; the OPE-linearity scope note typed; R1 -> R1' [C] residual registered; NO P2 marker move (Python-only per GATE.WOLFRAM.02).
Dependencies, status detail and source
Canonical status: TYPEII-FORCED: exhaustively over all subspaces of F2^8 (dim <= 4), locality <=> self-orthogonal, integer spin <=> doubly even, S-closure/|disc| = 1 <=> self-dual; survivor set = exactly the 30 e8-hat copies; no boundary-legal non-Type-II code; R1 -> R1' = the three physical axioms A1-A3; imported ingredients classical, cited, instance-verified; NO P2 marker move; no RH statement.
Dependencies: ARF.BOUNDARY.CODE.01; AX.P2.01; ARF.SPINORCOMPILER.01; v776; v752; E8.GAUSSCODE.01
Scripts: v799_seam_code_typeii.py
Location: tfpt_1;tfpt_2;tfpt_3;tfpt_research_contracts
Original CSV, line 691Original ledger status
E8.TORSOR.FOURIER.01
the projective Fourier modes of the 15 Gaussian root torsors -- carrier-block purity at CHARACTER level with the mutually-unbiased honest cap (30/30 checks, ~60 s; discovery probe e8_torsor_fourier_probe.py, 2026-08-06, verdict TORSOR-FOURIER-PARTIAL; FROZEN_SPEC SHA-hashed before any root data). THE CONSTRUCTION: because the v782 class fibers are torsors WITHOUT origin, their character data is canonical where their point data is not -- 120 = 15 x 8 projective Fourier rays m(v, u) with coefficients (-1)^{hbar(u, x(r))} on the 16-root fiber; PHASE LAW EXACT on all 960 origin shifts (a shift by t multiplies by the GLOBAL sign (-1)^{hbar(u,t)}: the rays are canonical); orthogonal ray basis of the (-1)-symmetric 120-dim pair space (integer Gram = 16 I; the antisymmetric half receives NO canonical mode -- the v782 sign theorem). EQUIVARIANCE: deck J diagonal with eigenvalue (-1)^{hbar(u,v)} (60 even + 60 odd, 4 + 4 per fiber); ALL 16 Pauli translations diagonal by characters (15 x 15 x 8 exact); G31 MONOMIAL (7200 generator matches; label action closes to Sp(4,2), order 720, kernel 64 = mu4 x Pauli16; label orbits {15 uniform, 45 deck-even, 60 deck-odd}); Burnside exact (transitive on pairs and on lines); sigma (Z3) multiplicities integral. THE CARRIER BLOCK CLEAN AT CHARACTER LEVEL (P1a/P1b/P2): the spinor sector = EXACTLY the 8 R-fibers (split-independent), so M_S = the span of their 64 whole Fourier rays -- a Fourier-ALIGNED invariant block (impossible at point level per v775); M_S factorizes as a W(D5) x W(A3)-set as 16 x 4 (W(D5)/W(A3) rebuilt by BFS from the certified v775 split, 1920/24), W(D5) transitive of permutation rank 3 on the 16 half-spinor weight pairs with the folded-5-cube/CLEBSCH charpoly (x-5)(x-1)^10(x+3)^5 EXACT => isotypic dimensions 1 + 5 + 10 -- the carrier Pascal AT CHARACTER LEVEL -- and the tetrad is S4-NATURAL (faithful, transitive, stabilizer S3, permutation rep 1 + standard 3) with sigma = the family 3-CYCLE + fixed anchor; W(A3)-tables exact (the 20 D5-adjoint pairs family-invariant; M_S = (1+5+10) x (1+3)); W(D5) Burnside on the spinor pairs: 4 orbits (the tetrad), sum m_i^2 = 48. P3 FAILS AS PREDECLARED (the honest cap): every mode has full 16-root support and |<pair|mode>|^2 = 1/8 EXACTLY on every cell -- the D5-weight basis and the character basis are MUTUALLY UNBIASED on each carrier fiber; no weight axis is a Fourier ray; the pointwise code -> matter reading stays dead (ROOTCLASS-MIXED v775 intact, re-confirmed). OVERLAP CENSUS: every certified stabilizer ray expands exactly in the 4 deck-even modes of its fiber (squared overlap 1/4 each; deck-odd and foreign fibers orthogonal -- the deck-odd half is a pure phase register invisible to stabilizer rays); the 45 nontrivial deck-even modes ARE, under the certified chart U, the 45 (context, Pauli) incidences (each nonzero Pauli covered exactly 3x; uniform modes -> identity, Sum z z^dag = 4I) -- a canonical G31-equivariant operator dictionary, noted (report only) as exactly the SHAPE the v791 carrier-intertwiner demand asks for on the finite register. CONTROLS: fiber scramble destroys deck equivariance; the wrong character group F2^4 = V collides 2:1 (rank 8 < 16); seeded random sign systems fail the certificates. Everything exact integer/Fraction/Z[i]/F2 (sympy gated to two charpolys). No marker move, NO RH claim. Python-only per GATE.WOLFRAM.02.
Recorded status: Exact [E] integer/cyclotomic character theory (canonical rays, exact Clebsch spectrum, exact overlap census) with the predeclared P3 failure typed -- the weight and character gradings mutually unbiased; ROOTCLASS-MIXED (v775) intact and re-confirmed; no marker move (Python-only per GATE.WOLFRAM.02).
Dependencies, status detail and source
Canonical status: TORSOR-FOURIER-PARTIAL: 120 canonical projective Fourier rays (phase law exact on 960 shifts, Gram = 16 I); deck/Pauli diagonal, G31 monomial through Sp(4,2); the carrier block = the 8 R-fibers' 64 rays = (1+5+10) x (1+3) under W(D5) x W(A3) with sigma = family 3-cycle + anchor -- the carrier Pascal at character level, impossible at point level (v775); weight/character bases exactly mutually unbiased (the honest cap); the 45 deck-even modes = the 45 context Pauli observables under the certified chart; no RH statement.
Dependencies: E8.TRANSITIONBUS.01; E8.CLIFFORD2Q.01; ARF.ROOTCLASS.01; PRIME.POSITIVE_DESCENT.01; v782; v783; v775; v752; v791
Scripts: v800_e8_torsor_fourier.py
Location: tfpt_1;tfpt_3
Original CSV, line 692Original ledger status
GNET.MARTINGALE.LIMIT.01
the noncommutative-martingale route to the G_net GNS limit -- its finite hypotheses MEASURED, all met (15/15 checks, controls 4/4, ~7 s; discovery probe gnet_martingale_probe.py, 2026-08-06, verdict MARTINGALE-HYPOTHESES-MET). THE PROGRAMME: replace continuum heuristics by martingale convergence -- if the local-state defects along the certified Haar inductive system are SUMMABLE in trace norm, the limit state exists uniquely by elementary Banach telescoping; the operator-algebra content becomes a typed list of analytic steps with finite evidence in hand. S1 FILTRATION EXACT: Haar isometry V*V = 1 with support coherence iota(win(N,0,l)) inside win(2N,0,2l) EXACT (leak 0); the Watatani quasi-basis explicit at the predeclared depths (185 elements at l = 2, 3041 at l = 3, sum v v* = 4*1); martingale compatibility omega_k o E = omega_k at every level; window data literally level-independent (H_W identical at N = 48 and N = 3072 -- one index-4 expectation for the whole tower). HONEST TYPING: the omega_k are an ALMOST-martingale (approximate, with measured defects); the convergence mechanism is norm summability + dual-space completeness (Umegaki expectations; Cuculescu cited as context, not used). S2 SUMMABLE DEFECTS (load-bearing): delta_k = ||rho_{k+1} - rho_k||_1 geometric with fitted rates 0.250 / 0.263 / 0.265 per doubling for l = 1/2/3 -- ONE POWER BETTER than the 2^{-l} dim-law envelope (reported against 0.5, not forced; bar 0.55); envelope delta_k <= 8 delta_1 2^{-k} quantifies summability (l = 2 tail sum 2.9e-2). S3 TELESCOPING / UNIQUE LIMIT: the Cauchy tail bound holds on every rung against the Richardson extrapolant; the frozen 6-observable battery gaps fall at <= 0.6; extrapolation uniqueness within 2.25 delta_5. S4 SPLIT/NORMALITY PRECURSORS uniform along the tower: sector-resolved cross-window profiles anchored with shrinking tails; determinant witness D_k = det(1 - X X*) >= 0.985 and stabilizing at 0.992756 -- the uniform estimate a normality/split argument consumes. STEPS 5-7 TYPED, NOT EXECUTED (the analytic remainder): GNS reconstruction of omega_inf, local normality (S4 witnesses as the finite input), split property + the mu4 simple-current extension (GATE.METRIC.11) on the limit net. THE QGEO ARCHITECTURAL NOTE (typed, no gate): the open majorant residues (b) 'L2 uniform FH/RH' and (c) 'L3 uniformity' of QGEO.GRIDSUP.01/v745 are NOT needed for limit EXISTENCE (summable state-norm defects suffice) -- the route relocates them into the typed normality step: an architectural reallocation, not a proof of (b)/(c). CONTROLS: the shifted-bond isometry leaks out of the doubled window (0.707 > 0.3 -- the filtration breaks); the Z2-only average has lambda = 1/2 != 1/4; the scrambled sea gives O(1) defects (summability breaks); DECIMATION CONVERGES TO THE WRONG DEGENERATE LIMIT (||rho_dec - 1/16||_1 < 1e-3 vs Haar 0.1+) -- a summable filtration with the wrong bond data forgets the sea: the coherent Haar bond is load-bearing. Every measurement is finite-level evidence FOR the cited continuum steps, never the theorems. No marker move, NO RH claim. Python-only per GATE.WOLFRAM.02. CONTRACT (registered OPEN [O], the analytic remainder = steps 5-7): GNS reconstruction of omega_inf on the quasi-local algebra (existence/uniqueness finite-level delivered here); local normality of the GNS representation on each A(W) (nuclearity-type estimate; the uniform S4 witnesses are the finite input); split property and the mu4 simple-current extension (GATE.METRIC.11, [B:A] = 4 = |mu4|) on the limit net; kill: non-summable defects at a deeper reachable rung or a determinant-witness collapse.
Recorded status: Measured [MEASURED] martingale hypotheses under frozen gates (all met; rate one power better than the dim-law envelope, reported not forced) + typed analytic remainder; the QGEO majorant residues relocated into the normality step, not proven; no marker move (Python-only per GATE.WOLFRAM.02).
Dependencies, status detail and source
Canonical status: MARTINGALE-HYPOTHESES-MET: exact Haar filtration with one index-4 expectation for the whole tower; state defects summable at measured rate ~0.25 per doubling (<= the 2^-l envelope, one power better); unique limit by telescoping verified on every rung; split/normality precursors uniform (determinant witness >= 0.99); decimation converges to the WRONG degenerate limit (coherent bond load-bearing); QGEO residues (b)/(c) bypassed for existence, relocated into normality; steps 5-7 typed open; no RH statement.
Dependencies: GNET.GNSLIMIT.01; GATE.METRIC.11; QGEO.GRIDSUP.01; v779; v746
Scripts: v802_gnet_martingale.py
Location: tfpt_2;tfpt_3;tfpt_research_contracts
Original CSV, line 693Original ledger status
E8.RAMIFIED.JETCODE.01
E8.RAMIFIED.JETCODE.01 (+ E8.AFFINE.NSR.01): the jet-code normal form of the Gaussian E8 compiler + the NS/R bit as an affine 8-point geometry, ONE module from two probes (18/18 + 15/15 checks, ~3 s; discovery probes e8_ramified_jetcode_probe.py JETCODE-EXACT and e8_affine_nsr_probe.py AFFINE-NSR-EXACT, both 2026-08-06, FROZEN_SPEC SHA-hashed before any root data). PART 1, THE JET CODE (all [E neu], machine-certified): Z[i]/(2) = F2[eps]/(eps^2) with eps = 1 + i and 2 = -i(1+i)^2 (2 RAMIFIES; the ring iso is UNIQUE -- the only nonzero nilpotent is 1+i -- and the wrong split ring F2 x F2 is NOT isomorphic: all 24 bijections fail, control C1); W = L/2L is FREE of rank 4 over the dual numbers (explicit Z[i]-basis by Hermite reduction over the Euclidean domain Z[i], covolume-certified index 1; the 4^4 = 256 dual-number combinations enumerate W bijectively); 0 -> eps W -> W -> V -> 0 is an exact SELF-extension with V = eps W canonically and ker(eps) = im(eps) -- the self-dual differential code; the deck IS the jet unit J = 1 + eps, whence the certified v782 transition-bus torsor translation rho(Jr) = rho(r) + iota(v) on ALL 240 roots (the full 15-row fiber-translation table re-derived from ring algebra); the extension admits ZERO mu4-equivariant splittings among all 65536 = 16^4 linear sections (-1 = +1 mod 2 makes mu4-equivariance = J-equivariance) -- the no-canonical-origin obstruction IS non-splitness; the 120 root pairs are EXACTLY the q = 1 unit shell of the plus-type quadratic form (census 120/136, Arf 0, polarization b = <x,y>/2 mod 2 with trivial radical), so every root is canonically the triple (address v, admissible error jet in the affine v_perp coset, orientation +-): 240 = 15 x 8 x 2. PART 2, THE AFFINE NS/R GEOMETRY (A1-A6 [E neu], chain reading [H neu]): V \ {0} = (7 NS classes = ker chi_NSR \ 0) u (8 R classes = the affine F2^3-torsor A = chi^{-1}(1)); the 7 NS classes carry EXACTLY the 112 D8 roots and the 8 R classes the 128 Ramond spinor roots -- 248 = (112 + 8) + 128 anchored in v148/v227/v301; Stab_GL(4,2)(chi_NSR) has order 1344 = 20160/15 and EQUALS -- as a permutation group with its natural 8-point action -- AGL(3,2) = Aut(H8) (brute force over all 40320 coordinate permutations; the chart composition is the explicit iso of actions); the evaluation code of affine functions on the 8 points of A is the [8,4,4] code RM(1,3) = H8 with EXACTLY 1344 equivalence permutations; the deployed Sp(4,2) stabilizes chi in an order-48 subgroup acting INSIDE AGL(3,2) (the kill does not fire). HONEST TYPING: the reconstruction chain NS/R bit -> affine 8-point space -> H8 SHARPENS the ARF.BOUNDARY.CODE.01 attack surface but the route to V still passes through Gaussian E8 -- an exact internal reconstruction, NOT a P2 removal. Controls fire in both parts (wrong ring, seeded scrambles, unique parity functional 14/14, flipped code bit). No matter semantics (v775 ROOTCLASS-MIXED cited). No marker move, NO RH claim. Python-only per GATE.WOLFRAM.02.
Recorded status: Exact [E] ring/module/extension structure theorems (integer/F2/Z[i] arithmetic, exhaustive censuses) behind the interpretation fence; the reconstruction-chain reading typed [H neu]; carries E8.AFFINE.NSR.01
Dependencies, status detail and source
Canonical status: JETCODE-EXACT + AFFINE-NSR-EXACT: Z[i]/(2) = F2[eps]/(eps^2) unique iso; W = L/2L free rank 4 (Hermite-certified); exact self-extension with ker eps = im eps; J = 1 + eps reproduces the v782 torsor on all 240 roots; 0/65536 mu4-equivariant splittings -- non-splitness IS the no-origin obstruction; 240 roots = oriented q = 1 unit jets (15 x 8 x 2); Stab(chi_NSR) = AGL(3,2) order 1344 = Aut(H8), same natural 8-point action; affine functions = RM(1,3) = H8 (1344 equivalences); typed internal reconstruction, no P2 removal; no matter semantics.
Dependencies: E8.TRANSITIONBUS.01; ARF.BOUNDARY.CODE.01; v752; v689; v782; v776; v646; v148; v227; v301
Scripts: v803_e8_jetcode_affine_nsr.py
Location: tfpt_1;tfpt_3
Original CSV, line 694Original ledger status
E8.SYNDROME.ALGEBRA.01
E8.SYNDROME.ALGEBRA.01: the honest kill -- E8 is NOT an error-correction hull in the sharpest sense, one probe (13/13 checks incl. the 3 must-fire controls, ~6 s; discovery probe e8_syndrome_algebra_probe.py, 2026-08-06, verdict SYNDROME-DEAD, the kill fired exactly as preregistered). THE QUESTION: do the 240 root operators U_r |x> = i^{c(r).x} |x XOR v> plus the 16 neutral kernels form a 256-dimensional mu4-twisted V-graded basis of End(S+)? THE KILL FIRES: the frozen mu4-linear-lift realization family reaches max rank 222/256 over ALL FOUR frozen phase conventions (Im/Re 222, Re+-Im 160; sympy-exact over Q(i)) -- with a STRUCTURAL obstruction: any phase rule Z-linear in the root gives c(-r) = -c(r), so +-r pairs with c in {0,2}^4 produce PROPORTIONAL operators (collision witness printed; 240 - 228 = 12 c-vector collisions), unreachable for the ENTIRE diagonal-phase x translation family; TWO post-hoc diagnostics score WORSE (nonlinear BFS transversal 215, zeta8-linear float 160) -- the death is robust, not a convention artifact; a successor would need root-individual (non-linear-in-r) operator data. WHAT SURVIVES: the syndrome-table counting 16 + 240 = 256 = 1x16 + 15x16, the neutral sector (the 16 v112 kernels ARE the diagonal maximal abelian subalgebra; same-class products land in A_0 with mu4 coefficients EXACTLY), the fine (class, d, k) groupoid composition law (associative on all 3375 section triples), and the W(3,2) commutation skeleton (scalar commutators 15.1%, matching (-1)^hbar on only 51.5% -- the class-level symplectic reduction fails in this realization). NO scalar V-cocycle exists (section closure 0/210). Controls fire (scrambled classes, wrong cocycle i^hbar fails the 2-cocycle identity on 960/4096 triples, random c-assignments). The sharpest E8-is-a-hull form (twisted V-graded basis) is DEAD as frozen; successor criterion named. No matter semantics (v775 ROOTCLASS-MIXED stands). No marker move, NO RH claim. Python-only per GATE.WOLFRAM.02.
Recorded status: DEAD as frozen [E kill, preregistered adjudication fired]: the twisted V-graded basis reading of E8 killed at rank level; the surviving structures typed exactly; successor criterion named
Dependencies, status detail and source
Canonical status: SYNDROME-DEAD: max rank 222/256 over all four frozen phase conventions (two post-hoc diagnostics score worse: 215/160); the +-r proportionality obstruction structural for the whole diagonal-phase family; SURVIVES: 16 + 240 = 256 counting, the 16 v112 neutral kernels ARE the diagonal MASA, same-class products A_0-valued with mu4 coefficients exactly, the fine groupoid law associative 0/3375; successor needs root-individual (non-linear-in-r) operator data; no matter semantics.
Dependencies: E8.PROJHAMMING.01; ARF.ROOTCLASS.01; v752; v111; v112; v775
Scripts: v805_e8_syndrome_algebra.py
Location: tfpt_1;tfpt_3
Original CSV, line 695Original ledger status
CARRIER.PETERSEN.RADIAL.01
CARRIER.PETERSEN.RADIAL.01 (+ TRANSPORT.SIXTHROOT.01): the K5 edge machine, the Petersen carrier geometry with the radial dynamics whose sixth power IS the deployed transport spectrum, + the bit-exact decider on the PSD sixth root, ONE module from two probes (19/19 + 16/16 checks, ~1 s; discovery probes carrier_petersen_radial_probe.py PETERSEN-RADIAL-EXACT and transport_sixthroot_probe.py SIXTHROOT-SPECTRAL-ONLY, both 2026-08-06). PART 1, THE K5 EDGE MACHINE (all exact integer/Fraction): X = (-2,-2,-2,3,3) is the UNIQUE primitive traceless block-constant charge for the F|W = 3+2 split (sign pinned by the certified v774 table); E(K5) = 10 pairs carry the charge census {-4: 3, +1: 6, +6: 1} = the SU(5) decuple 3_{-4} + 6_{+1} + 1_{+6}, every pair cross-checked against the certified v774 hypercharge table (classes u_c/Q_up/Q_dn/e_c); under disjointness the pairs form the PETERSEN graph SRG(10,3,0,1) (charpoly (x-3)(x-1)^5(x+2)^4 exact, girth 5, |Aut| = 120 by full backtracking census = the faithful S5); the distance shells around the W vertex are (1, 3, 6) and CHARGE-PURE (+6/-4/+1 = e^c/u^c/Q), and the distance-2 shell induces a C6 -- THE FLAVOR HEXAGON AS GRAPH GEOMETRY [E neu] (explicit cycle verified edge by edge; 6 = |R+(A3)| = the transfer exponent, v124); the shell partition is EQUITABLE with quotient [[0,3,0],[1,0,2],[0,1,2]] whose eigenvector (6,-4,1) -> -2 IS the hypercharge vector, and P = Q_Pet/3 has spec(P^6) = {1, 64/729, 1/729} == the deployed TFPT transport spectrum EXACTLY (v54/v56/v171/v317; v124 lambda_n = (1-n/3)^6; GATE.METRIC.18). THE PREDICTION [H neu]: the full 10-dim Petersen walk has spec(P10^6) = {1, (1/3)^6 x5, (2/3)^6 x4} -- fast mode multiplicity 5 = g_car, slow hypercharge mode 4 = |mu4| (trace crosscheck 990 = 729 + 5 + 256); NO corpus 10-dim operator exists (T is 3-dim on the cusp space) -- a prediction, not a verification. PART 2, THE SIXTH ROOT (exact Fractions): B = (1/18)[[13,1,4],[1,13,4],[4,4,10]] -- every entry a compiler number (18 = p4(anchor), 13 = N_fam^2 + |Z2|^2, 4 = |mu4|, 10 = A_Lambda, 1 = N_Phi) -- is the UNIQUE symmetric doubly stochastic PSD sixth root with the frozen corpus-basis eigen-assignment ((1,1,1) -> 1, (1,-1,0) -> 2/3, (1,1,-2) -> 1/3; spectral reconstruction entry-exact; exactly 2 assignments in the corpus basis, a 1-parameter circle without the pin); B^6 carries the deployed spectrum exactly BUT the decider lands SPECTRAL-ONLY: B^6 is GL(3,Q)-conjugate to v486's lazy-walk M^6 (exact rational W and orthogonal O conjugations verified) and to the cusp-diagonal canonical form, yet bit-equal to NEITHER -- the corpus freezes the SPECTRUM, not the basis; the stochastic types differ (doubly vs sub-stochastic with absorbing channel). Controls fire in both parts (wrong edge 4+1 kills the (1,3,6) structure; Johnson complement kills the hexagon; both matrix perturbations break the spectrum). Typed carrier representation geometry -- ROOTCLASS-MIXED (v775) cited, no particle semantics. No marker move, NO RH claim. Python-only per GATE.WOLFRAM.02. [2026-08-06 LXVI dated correction + addendum, v814: the sixth-root census missed the deployed v221 evaluation -- T_v221 (the exact spectral sum of v221's transfer (1-w)^6) == B^6 BIT-EXACTLY, so the TRANSPORT.SIXTHROOT.01 verdict upgrades from SPECTRAL-ONLY to BITEXACT-vs-v221 (the frozen SPECTRAL-ONLY stands as the probe's adjudication; ABEL-DEAD correction precedent); and the [H neu] 10-dim prediction now has a promotion-ready canonical PROPOSAL: T10 = P10^6 in the Lambda^2 basis passes all gates with the equitable v774 quotient == (Q_Pet/3)^6 bit-exact (TRANSPORT10-PROPOSED, no deploy claim), while the six-step composition is typed CLOCK-ONLY -- the deployed 6 is the clock exponent, every spatial route carries a typed obstruction.]
Recorded status: Exact [E neu] finite graph/matrix structure theorems (integer/Fraction; charpolys sympy-gated) behind the carrier-geometry fence; the 10-dim multiplicity prediction typed [H neu]; carries TRANSPORT.SIXTHROOT.01 (spectral-only decider)
Dependencies, status detail and source
Canonical status: PETERSEN-RADIAL-EXACT + SIXTHROOT-SPECTRAL-ONLY: charges (-4,+1,+6) = the SU(5) decuple against v774; Petersen SRG certified, |Aut| = 120 census; shells (1,3,6) charge-pure; the flavor hexagon = the distance-2 shell edge-by-edge; equitable quotient with hypercharge eigenvector (6,-4,1) -> -2; spec(P^6) = {1, 64/729, 1/729} = the deployed transport spectrum; 10-dim multiplicities (x5 = g_car fast, x4 = |mu4| slow) typed [H neu] -- no corpus 10-dim operator; B unique symmetric doubly stochastic PSD sixth root in the corpus basis, B^6 GL(3,Q)-conjugate to v486's M^6 and the cusp-diagonal form but bit-equal to neither -- the corpus freezes the spectrum, not the basis.
Dependencies: ARF.SPINORCOMPILER.01; v774; v54; v56; v124; v486; v327; v212; v397; v14; v700
Scripts: v808_petersen_sixthroot.py
Location: tfpt_2;tfpt_3
Original CSV, line 696Original ledger status
CURVE.CODE.DOILY.01
CURVE.CODE.DOILY.01: the certified outer bridge sharpened into an incidence-operator statement with a spectral payoff, one probe (21/21 checks incl. the 3 must-fire controls, ~1 s; discovery probe curve_code_doily_probe.py, 2026-08-06, verdict DOILY-EXACT). THE EXACT IDENTITY: the K6 doily incidence N (15 duads x 15 synthemes on the six odd Arf refinements) satisfies NN^T = 3I + A_KG(6,2) = B + 2I entrywise, with B the certified v752/v774 symplectic incidence (synthemes <-> isotropic lines bijectively; row and column sums 3; two duads share a syntheme iff disjoint, then exactly one). THE SPECTRAL PAYOFF: spec(NN^T) = spec(N^T N) = {9^1, 4^9, 0^5} exact (annihilating polynomial + traces + rank over Q), so the normalized channel N/3 has singular values {1, 2/3, 0} -- THE RECOVERY BASE RATE 2/3 (v221) as the unique nontrivial singular value of the canonical duad-to-syntheme incidence; the identification with the corpus rate (2/3)^6 = 64/729 is TYPED [H neu -> decidable, not decided here]: it requires the six-step composition semantics (the hexagon). PETERSEN LOCALIZATION: at the q*-distinguished point the 15 duads split 5 + 10, the 10 internal duads form the Petersen graph, and syntheme -> internal pair is a BIJECTION onto E(Petersen) 15/15 -- Petersen vertices = code duads, Petersen edges = curve synthemes under the certified bridge. THE REFINED BRIDGE: every census bridge (rebuilt with the frozen BRIDGE-CANONICAL conditions, census 6) factors EXACTLY through N -- Delta(d) = {Gamma(s) : d in s} and the matrix identity N_code = P_Delta^T N_curve^T P_Gamma: the outer bridge conjugates the code incidence to the TRANSPOSE of the curve incidence, a DUALITY, not an isomorphism (control C3: 720 symplectic isomorphisms exist, 0 intertwine sigma with tau -- the inner route stays dead). THE ARF LAYER in doily coordinates: the switch set T6 = the six within-block duads of the q_Theta point-split, bijective onto the 6 odd theta characteristics -- the census-6 anchor. N/3 is doubly stochastic (typed CLASSICAL incidence channel, not CPTP; 1 + 9 + 5 spectral decomposition, rate 2/3 on the 9-dim window) -- measured, no descent claim. No matter semantics (ROOTCLASS-MIXED, v775); the inner identification stays CURVE-CODE-PARTIAL/dead. No marker move, NO RH claim. Python-only per GATE.WOLFRAM.02.
Recorded status: Exact [E] incidence-operator identities and spectra (integer/Fraction, annihilator-certified) with the (2/3)^6 identification typed [H neu -> decidable] pending the six-step composition; the inner identification stays dead
Dependencies, status detail and source
Canonical status: DOILY-EXACT: NN^T = B + 2I entrywise; spec {9, 4^9, 0^5}; N/3 singular values {1, 2/3, 0} -- the recovery base rate as the unique nontrivial singular value, (2/3)^6 typed pending six-step composition; Petersen edges = synthemes 15/15; every census bridge factors exactly N_code = P_Delta^T N_curve^T P_Gamma -- a duality, not an isomorphism (inner route 0/720); Arf switch set T6 = the six within-block duads; N/3 doubly stochastic, typed classical not CPTP.
Dependencies: CURVE.CODE.OUTERSPIN.01; CURVE.CODE.2TORSION.01; v752; v774; v796; v221; v240; v425
Scripts: v809_curve_code_doily.py
Location: tfpt_3
Original CSV, line 697Original ledger status
CARRIER.CUTCODE.01
CARRIER.CUTCODE.01 (+ CARRIER.MOMENT.INCIDENCE.01): the Arf split as the cut classification of K5 + the one-line master moment with the frozen 210 decision, ONE module from two probes (17/17 + 16/16 checks, ~1 s; discovery probes carrier_cutcode_probe.py CUTCODE-EXACT and carrier_moment_incidence_probe.py MOMENT-INCIDENCE-PARTIAL, both 2026-08-06). PART 1, THE CUT CODE [E neu]: the cut map delta: F2^5 -> F2^10 (edges of K5) is INJECTIVE on C_even(5) and ISOMETRIC (delta(x).delta(y) = x.y mod 2 on all 256 pairs; kernel = the repetition code; control C2: the isometry fails on exactly the 256 odd x odd pairs), with the quadratic identity q*(v) = wt(delta iota v)/2 mod 2 on all 16 words -- so the Arf split 16 = 1 + 5bar + 10 IS the cut classification (0|5) + (1|4) + (2|3) (the five wt-4 words = the elementary vertex cuts, the ten wt-2 words = the duad cuts, both bijections certified); the Clebsch graph SRG(16,5,0,2) (40 edges = |R(D5)|, tfpt_1 Theorem 2) grades over the Arf shells as 40 = 5 + 20 + 15 with forbidden blocks EMPTY, and the within-10 edge graph IS the Petersen graph (full isomorphism census 120 = |S5|); the 240 Gaussian roots / 60 mu4-lines grade 80 + 160 / 20 + 40 over the shells -- typed as Arf/cut grading, explicitly NOT a matter split (ROOTCLASS-MIXED, v775; the 5/20/15 readings are audit fingerprints [C]). PART 2, THE MASTER MOMENT: the symbolic identity sum_{i<j}(x_i + x_j)^2 - 3 sum x_i^2 = (sum x_i)^2 for ALL 5-vectors gives the one-line derivation Tr_{S+} X^2 = 4|X|^2 = 4 h(E8) = 120 (|X|^2 = 30 = h(E8), Tr_10 = 90, Tr_5bar = 30; the chain 120/3 + 1 = 41 = 10 b1 re-anchored); chi_X(t) = (t+2)^3 (t-3)^2 exact with elementary symmetric values (0, -15, 10, 60, -72) typed audit fingerprints [C] (72 AUDIT-ONLY, no morphism). THE 210 DECISION (frozen rule, either outcome the deliverable): p4(X) = 210 = C(10,4) stays DECORATIVE -- the equivariant-bijection candidates are KILLED by the exhaustive fixed-point obstruction (both groups S3xS2 and Z2^5:(S3xS2), both indexings: the fixed 4-subset exists, no G-fixed slot does, total equivariant maps = 0), none of the six frozen slot-local weight families reproduces p4, and only the PARTIAL miss-slot map survives (80 type-(1,1,1,1) subsets -> missed slot with uniform fibers 16 = 2^4, exact on the colour slots, deficit 65/65 on the weak slots) plus the Newton tie p4 = 2 e2^2 - 4 e4 (generic symmetric-function algebra, [C] audit). Controls fire in both parts. No physics claim, no marker move, NO RH claim. Python-only per GATE.WOLFRAM.02.
Recorded status: Exact [E neu] cut-map/shell-grading censuses (F2/integer, exhaustive) + the frozen 210 decision landing PARTIAL (decorative, per the preregistered rule); the 5/20/15 and charpoly readings audit fingerprints [C]; carries CARRIER.MOMENT.INCIDENCE.01
Dependencies, status detail and source
Canonical status: CUTCODE-EXACT + MOMENT-INCIDENCE-PARTIAL: delta injective isometric on all 256 cells; Arf split = the (0|5)+(1|4)+(2|3) cut classification; Clebsch 40 = 5 + 20 + 15 with forbidden blocks empty and within-10 = Petersen (census 120); roots/lines grade 80 + 160 / 20 + 40 -- Arf/cut grading, NOT matter; Tr_{S+}X^2 = 4|X|^2 = 4 h(E8) = 120 from one symbolic identity; charpoly exact, 72 audit-only; the 210 = C(10,4) map DECORATIVE -- equivariant bijection killed by the fixed-point obstruction (exhaustive); the partial 80 -> 5 x 16 miss-slot map and Newton tie survive as audit.
Dependencies: ARF.SPINORCOMPILER.01; ARF.ROOTCLASS.01; v774; v2; v55; v109; v111; v700; v752
Scripts: v810_cutcode_moment.py
Location: tfpt_1;tfpt_3
Original CSV, line 698Original ledger status
FLAVOR.GRAPH.FILTRATION.01
FLAVOR.GRAPH.FILTRATION.01: the flavor-matrix filtration Q -> K -> L as an incidence-compiler fingerprint -- budgets exact, entries NOT reconstructible, one probe (16/16 checks incl. the 4 must-fire controls, ~1 s; discovery probe flavor_graph_filtration_probe.py, 2026-08-06, verdict FILTRATION-FINGERPRINT-ONLY). THE BUDGET IDENTIFICATIONS ARE EXACT AND ORDER-EXACT: Q row budgets (4, 5, 6) = (|E(K3) u E(K2)|, |V(K5)|, |E(K_{3,2})|), K row budgets (6, 9, 10) = (|E(K_{3,2})|, |E(L(K_{3,2}))| with the line graph certified isomorphic to the triangular prism AND the hexagon circulant C6(2,3), |E(K5)|), L row budgets (10, 14, 16) = (|E(K5)|, #wt-4 words of H8, |H8|) -- with the level-wise additivity (4, 5, 6) + (6, 9, 10) = (10, 14, 16) mirroring the deployed L = K + Q (v37/v4) exactly; the deployed matrices located (v11/v12/v37/v4; v11 uniqueness re-derived in pure integers); control C1 certifies the identifications hold in EXACTLY the identity order. THE DECISIVE BAR (frozen: row sums alone do NOT count): NO frozen structural candidate -- 25/20/47 flag- classifier and operator-quotient candidates per level, entry-exact comparison with all 6 column permutations -- reproduces ANY of the three deployed matrices entry-wise (per-row matches recorded as fingerprint data; K rows 2-3 and all L rows have ZERO candidates). THE CONTROLS MAKE THE MISS INFORMATIVE: the exhaustive false-positive census over ALL nonneg-integer matrices with the deployed row sums gives rates 0.748% / 0.035% / 0.005% (Q/K/L) -- the candidate set is not vacuously flexible, so the entry-level failure is a real structural boundary, not a weak test; the wrong split 4|1 and the non-extended Hamming [7,4] break the Q/K/L identifications as predeclared. TYPED: the identification is an AUDIT FINGERPRINT at the budget level, not an entry-level incidence construction. Matrix-structure archaeology only -- no mass/physics claim. No marker move, NO RH claim. Python-only per GATE.WOLFRAM.02.
Recorded status: Exact [E] order-exact budget identifications (pure integers, exhaustive false-positive controls) with the entry-level reconstruction NEGATIVE; typed audit fingerprint at budget level
Dependencies, status detail and source
Canonical status: FILTRATION-FINGERPRINT-ONLY: Q (4,5,6) / K (6,9,10) / L (10,14,16) = exact counts of the K_{3,2}/prism/K5/H8 incidence chain, order-exact, with level-wise additivity mirroring L = K + Q; deployed matrices located (v11/v12/v37/v4); NO entry-level reconstruction from any frozen candidate (25/20/47 per level); exhaustive false-positive rates 0.005-0.75% -- the misses are informative; typed audit fingerprint.
Dependencies: FLAV.PENCIL.01; v11; v12; v37; v4; v752
Scripts: v812_flavor_graph_filtration.py
Location: tfpt_2;tfpt_3
Original CSV, line 699Original ledger status
P1.INDEX.KMS.01
P1.INDEX.KMS.01: the closed normalization identity c3 = 1/(I_Jones * beta_angle) = 1/(4 * 2pi) = 1/(8pi), its convention audit, and the sharpened P1 contract, one probe (13/13 checks incl. the 2 must-fire controls, ~0.1 s; discovery probe p1_index_kms_probe.py, 2026-08-06, verdict P1-IDENTITY-CLOSED). THE IDENTITY [E]: I * beta * c3 = 4 * 2pi * 1/(8pi) = 1 EXACT in formal Fraction x pi^k arithmetic (no floats; S2.1-S2.3 are one identity in three rearrangements, counted as one content; the v208 area-entropy factor 1/4 = 1/I; the AX.P1.01 anchor route 1/(2 e1(a) pi) with e1 = 4 aligns anchor-4 with index-4). THE DEPENDENCY AUDIT (the load-bearing honesty step): the index I = 4 = |mu4| is an INDEPENDENT c3-free theorem (ZERO 'c3' occurrences in all four sources v154/v726/v746/v779, gated by file scan); beta_angle = 2pi is an INDEPENDENT measurement (v526: beta = N clock steps by detailed balance, wrong-beta {N/2, N/4, 2N} excluded; the v519 radian pin is the ONE shared convention and CANCELS in the unit-invariant statement 'response per full modular circle = 1/I'); c3 STAYS the P1 axiom -- the identity EXPLAINS its value, it does not derive it. THE FINITE EVENNESS PRECURSOR (measured, real): the tracial weight per mu4 deck sector on the l-windows satisfies w_1 = w_3 = 1/4 EXACTLY at every level l = 1..6, with the w_0/w_2 offset the symmetric zero-sum pair +-2^-(l+1) halving per level -- equal quarters asymptotically, NO anomaly offset (= the no-anomaly shape the contract's bridge needs); the index-4 conditional expectation is trace-preserving (dev < 1e-12); and the SEA STATE does NOT equidistribute (deviation 0.188 from 1/4 at the N = 1536 Haar pullback) -- the bridge must normalize the MODULAR RESPONSE, not vacuum weights. THE CONTRACT (registered [O]): an index-I simple-current extension carries per modular period exactly the normalized response 1/(I * beta_angle) = c3; the ONE open bridge is the even distribution of the modular-response (Quillen/determinant-line) normalization over the I deck sectors; KILL: any asymmetric sector offset (w_1 != w_3 at any level, or a non-vanishing offset as l -> inf). Controls fire: the wrong index 2 gives 1/(4pi), which the corpus books elsewhere (un-halved Gauss-Bonnet; SdS 1/(4pi) = 2 c3); wrong beta = pi breaks the chain at 1/2. c3 remains the P1 axiom; no marker move, NO RH claim. Python-only per GATE.WOLFRAM.02. NOTE (2026-08-28, v993): unique finite CE does NOT close the equidistribution bridge -- that identification stays the open [C] of this row.
Recorded status: Exact [E] identity chain (formal Fraction x pi^k) + gated independence audit + measured finite evenness precursor; OPEN [O] contract with the one open bridge (even modular-response normalization) and the kill criterion named; c3 stays the P1 axiom
Dependencies, status detail and source
Canonical status: P1-IDENTITY-CLOSED: I*beta*c3 = 1 exact; the index c3-free (zero occurrences, four sources), beta independently measured (v526, wrong-beta excluded; the radian pin is the one shared convention and cancels); c3 stays the P1 axiom the identity EXPLAINS; finite evenness precursor measured: w1 = w3 = 1/4 exactly every level, symmetric zero-sum offset +-2^-(l+1) -- the no-anomaly shape; the sea state does NOT equidistribute (dev 0.188) -- the bridge must normalize the modular response; controls: index 2 -> 1/(4pi), booked elsewhere by the corpus; contract registered OPEN [O], kill = an asymmetric sector offset.
Dependencies: AX.P1.01; GATE.METRIC.11; GATE.METRIC.12; ANCHOR.GEN.01; v154; v726; v746; v779; v526; v239; v208; v8; v23
Scripts: v813_p1_index_kms.py
Location: tfpt_3;tfpt_research_contracts
Original CSV, line 700Original ledger status
K5.SIXSTEP.TRANSPORT.01
K5.SIXSTEP.TRANSPORT.01: the six-step composition and the 10-dim transport deploy -- the (2/3)^6 rate is canonical on three spatial routes, the deployed six is the clock exponent, and the canonical T10 proposal passes every gate, one probe (23/23 checks incl. the 3 must-fire controls, ~0.2 s; discovery probe k5_sixstep_transport_probe.py, 2026-08-06, verdicts SIXSTEP-CLOCK-ONLY / TRANSPORT10-PROPOSED). THE CORRECTION (dated note on the v808/TRANSPORT.SIXTHROOT.01 row): the deployed transport is LOCATED -- v221's transfer (1-w)^6 IS the exact spectral sum T_v221 = J/3 + (2/3)^6 u2 u2^T + (1/3)^6 u3 u3^T, and T_v221 == B^6 == (1/4374)[[1651,1267,1456],[1267,1651,1456],[1456,1456,1462]] BIT-EXACTLY -- the v808 sixth-root census missed v221, so the SIXTHROOT verdict upgrades from SPECTRAL-ONLY to BITEXACT-vs-v221 (the frozen SPECTRAL-ONLY stands as that probe's adjudication; ABEL-DEAD correction precedent). TASK A (all exact): the rate (2/3)^6 arises CANONICALLY on three independent spatial routes -- the doily alternation (three PSD double-steps duad -> syntheme -> duad: spec {1, (2/3)^6 x9, 0^5}), the hexagon compression (Pi_2 (A_Pet/3) Pi_2 == A_C6/3 with spec((A_C6/3)^6) = {(2/3)^6 x2, (1/3)^6 x4} -- BOTH deployed decay rates from pure hexagon geometry), and the hexagon circulation (((2/3) S6)^6 = (2/3)^6 I) -- but each route is blocked by a TYPED obstruction (doily: wrong space, decay multiplicity 9, no (1/3)^6 mode; hexagon: NO unit mode -- ||(A_C6/3)^6||_op = (2/3)^6 < 1 kills every norm-nonincreasing intertwiner [E neu]; radial: the bipartite sign -2/3, P NOT similar to the clock root B, and the exact conjugation S with S T_v221 S^{-1} = P^6 is deployed NOWHERE -- the missing shells -> cusp isomorphism); SIXTH-POWER BLINDNESS [E neu]: (A_C6/3)^6 and (A_{2K3}/3)^6 have IDENTICAL spectra -- the sixth power erases the cyclic geometry AND the sign, so only per-step data can distinguish walk from clock: the deployed six is the CLOCK EXPONENT (v124 lambda_n = (1-n/3)^6, v486 hand, fixed eigenbasis (1,1,1)/(1,-1,0)/(1,1,-2)). TASK B: corpus census -- NO deployed 10-dim transport operator exists (v37's Pluecker apparatus is 3x3, re-derived; v44/v45 carry Lambda^2(5) = 10 as dimension only); the CANONICAL PROPOSAL T10 = P10^6 in the Lambda^2 basis (v774 cut-code dictionary, a permutation conjugation) passes ALL gates: symmetric doubly stochastic PSD, spectrum {1^1, (1/3)^6 x5, (2/3)^6 x4} exact (multiplicities (5, 4) = (g_car, |mu4|)), the v774 class partition (e_c | u_c | Q) EQUITABLE, exact quotient == (Q_Pet/3)^6 bit-exact with the deployed spectrum {1, 64/729, 1/729} and reversibility -- a promotion-ready PROPOSAL, no deploy claim (Q6 != T_v221 bit-exact, not symmetric -- recorded: this is WHY PROPOSED, not REALIZED). Controls fire (wrong per-step rate 1/2, Johnson-complement scramble, non-equitable partition). ROOTCLASS-MIXED (v775) cited: carrier representation geometry, no physics claims beyond operator identities. No marker move, NO RH claim. Python-only per GATE.WOLFRAM.02.
Recorded status: Exact [E neu] operator identities and censuses (three spatial routes, sixth-power blindness, corpus census, bit-exact v221 location); [H neu] the walk-vs-clock reading and the T10 deployment proposal; dated BITEXACT correction to TRANSPORT.SIXTHROOT.01 carried
Dependencies, status detail and source
Canonical status: SIXSTEP-CLOCK-ONLY + TRANSPORT10-PROPOSED: the (2/3)^6 rate canonical on three spatial routes, each with a typed obstruction; the deployed 6 is the clock exponent (sixth-power blindness makes per-step data mandatory); T_v221 == B^6 bit-exact (SIXTHROOT upgrades to BITEXACT-vs-v221, dated note on the v808 row); T10 = P10^6 in the Lambda^2 basis passes all gates -- proposal, no deploy claim; NO RH claim
Dependencies: CARRIER.PETERSEN.RADIAL.01; TRANSPORT.SIXTHROOT.01; CURVE.CODE.DOILY.01; v221; v124; v486; v37; v774; v808; v809
Scripts: v814_k5_sixstep_transport.py
Location: tfpt_1;tfpt_3
Original CSV, line 701Original ledger status
TFPT.POSITIVE_DESCENT.MASTER.01
Abstract positive-descent theorem and G_net finite hypothesis checks; the prime packet instance is maintained by Prime Front. Original module ID retained; original complete mixed record is preserved in extraction provenance.
Recorded status: Abstract master theorem with kernel-checked Lean core (PositiveDescentMaster.lean: telescoping + tail, positivity closure, sector commutation); both instances measured at finite level; hypotheses (6)/(7) typed per instance; positivity a separate hypothesis (K4)
Dependencies, status detail and source
Canonical status: MASTER-BOTH-INSTANCES: G_net hypotheses re-verified (Choi PSD, delta rate 0.267/doubling); THE NEW NUMBER -- prime packet state defects summable at 0.701/doubling ~ sqrt-dilution 2^{-1/2}, mh2(p) = -1/15 exact for every odd prime; the selection problem eliminated on both sides; K4: positivity NOT implied by summability; open per instance: G_net normality/split, prime sector floor (-> PRIME.FLOOR.RATIO.01); NO RH claim
Dependencies: PRIME.POSITIVE_DESCENT.01; GNET.MARTINGALE.LIMIT.01; PRIME.FLOOR.RATIO.01; v791; v802; v793
Scripts: v817_positive_descent_master.py
Location: tfpt_3;tfpt_research_contracts
Original CSV, line 702Original ledger status
ANCHOR.AFFINE.01
ANCHOR.AFFINE.01 + FLAVOR.BIDIR.01: the anchor affine normal form and the flavor bidirectional checksum -- two exact corpus compressions, ONE module from two probes (18/18 + 15/15 checks, verdicts ANCHOR-AFFINE-EXACT and FLAVOR-BIDIR-CHECKSUM (selective); discovery probes anchor_affine_probe.py and flavor_bidir_probe.py, 2026-08-07, re-run identically at promotion, promoted VERBATIM). PART A: the anchor a = (1,1,2) has power sums p_n = 2 + 2^n satisfying the affine recursion p_{n+1} = 2 p_n - 2 identically in n (sympy); T(x) = 2x - 2 has the UNIQUE fixed point 2 = |Z_2| (the sheet), and the T-orbit of 4 is exactly the compiler quintet (4, 6, 10, 18, 34) = (|mu4|, |R+(A3)|, A_L, N_fam |R+(A3)|, Z6-lift) with p_0 = 3 = N_fam prepended. THE BUDGET FROM ONE RECURSION: |R(E8)| = p1 p2 p3 = 240, dim E8 = 240 + q3 = 248 (ladder identity p4 - p3 = p3 - 2 = 8 = h(D5) = rank E8), h(E8) = p2 p3/2 = 30, |R(D5)| = p1 p3 = 40, Omega_adm = 2 p1 p2 = 48, chi_a(t) = (t-1)^2(t-2) with (e1,e2,e3) = (4,5,2) = (|mu4|, g_car, |Z_2|), 10 b1 = e1^2 + e2^2 = 41 -- every number a word in the T-orbit and the fixed point. PART B: R = [[1,3,0],[1,5,2],[2,5,3]] decodes the SAME anchor on both sides -- R a = (4, 10, 13) = (p_1, p_3, N(3+2i)) and R^T a = (6, 18, 8) = (p_2, p_4, p_3 - 2); tr R = 9 = p_0^2, det R = 8, principal 2-minors {2,3,5}, chi_R = t^3 - p_0^2 t^2 + p_3 t - (p_3 - 2), ||R||_F^2 = 78, SNF diag(1,1,8). THE SIBLING ABLATION: of the 12 down-row candidates (all orderings of {1,2,5} and the sibling {1,3,4}) EXACTLY ONE -- the accepted (1,5,2) -- satisfies the full identity set; the anchor contraction (R a)_2 = 10 = p_3 kills both siblings (11 and 12). Controls fire (wrong map, wrong anchor, sibling (1,4,3) reproducing tfpt_2's failure numbers verbatim, scrambled ordering). A normal form / compression, NOT a new claim: no marker moves. Exact sympy/integer; no floats, no RNG, no fit. Python-only per GATE.WOLFRAM.02.
Recorded status: Exact identity-grade compression [Identity]: both parts exact sympy/integer arithmetic; the compression is a normal form of existing corpus surfaces (tfpt_1 anchor power compiler + budget lines, tfpt_2 flavor spectral selector + bilinear table); no marker move (Python-only per GATE.WOLFRAM.02)
Dependencies, status detail and source
Canonical status: ANCHOR-AFFINE-EXACT + FLAVOR-BIDIR-CHECKSUM (selective): the whole compiler budget from ONE affine recursion T(x) = 2x - 2 (orbit 4, 6, 10, 18, 34; fixed point 2); the flavor matrix R decodes the same anchor bidirectionally (rows p_1, p_3, 13; columns p_2, p_4, 8) and the accepted down-row (1,5,2) is the UNIQUE candidate of 12 passing the full identity set -- the kill test is the anchor contraction (R a)_2 = 10 = p_3
Dependencies: v1; v2; v6; v222; v230; v415
Scripts: v832_anchor_flavor_checksum.py
Location: tfpt_1;tfpt_2;tfpt_3
Original CSV, line 703Original ledger status
GAUSSIAN.RAMLADDER.01
GAUSSIAN.RAMLADDER.01: the (1+i) ramification ladder -- the four documented roles of the ramified Gaussian prime pi2 = 1+i are ONE machine-checked object with four rungs, each re-certified from scratch, ONE module from one probe (33/33 checks, verdict RAMIFICATION-LADDER-EXACT; discovery probe gaussian_ramification_probe.py, 2026-08-07, re-run identically at promotion, promoted VERBATIM, ~5 s). RUNG 1, NORM DOUBLING: N(pi2) = 2 and (pi2^2) = (2); on the Gaussian E8 lattice (the unique mu4/sigma-equivariant Construction-A placement, 2 of 30, rebuilt) (1+J)^T (1+J) = 2 I_8 EXACTLY; min L = 4 by exhaustive census, the zero class of L/(1+i)L carries NO root (0/240 directly), 240 = 15 x 16 over the nonzero classes (each a union of 4 of the 60 Gaussian lines), elementary divisors (1,1,1,1,2,2,2,2), index 16 = N(pi2)^4. RUNG 2, THE FOUR-BIT ADDRESS: L/(1+i)L ~= F2^4 with the deck J acting TRIVIALLY on all 240 roots. RUNG 3, THE NON-SPLIT JET: Z[i]/(2) ~= F2[eps]/(eps^2) (ring iso UNIQUE among all 24 bijections); W = L/2L FREE of rank 4 over the dual numbers (256/256 combinations distinct); the self-extension 0 -> V -> W -> V -> 0 exact with deck = JET UNIT 1 + eps, and of ALL 65536 linear sections EXACTLY 0 are deck-equivariant -- the no-canonical-origin obstruction IS non-splitness (v803); plus-type form census 136/120, Arf 0, the 120 root pairs ARE the q = 1 shell (240 = 15 x 8 x 2). RUNG 4, THE METAPLECTIC LIFT: zeta8 = (1+i)/sqrt2; (1+J)^2 = 2J; (S H)^3 = zeta8 I per binary factor and (T3 K3)^3 = i I = THE DECK (v798); exact Z[zeta8] BFS census: |C2/mu8| = 11520 = 16 x 720 with ZERO Galois-mixed classes, |C2| = 92160 = 2 x 46080, C2 = K u zeta8 K (K = U G31 U^-1, v783 chart theorem cited [E]); witness parities chi(H(x)I) = 1 (the RM-CSS zeta8 phase bit, v819 S4 -> v798 [E]), chi(H(x)H) = chi(CZ) = 0. Controls fire (split ring F2 x F2 admits 0 ring isos -- 2 must ramify; split self-extension admits 65536/65536 sections; scrambled nilpotent breaks ker = im). A compression: the four corpus roles (note_e8_gaussian_code Thm 1/v689, v689, v803, v783/v798/v819) are ONE ladder -- the same ramified prime read at (pi2), (pi2^2) and pi2/sqrt2. Exact integer/Fraction/sympy; no floats, no RNG. Python-only per GATE.WOLFRAM.02.
Recorded status: Exact identity/lattice-grade compression [Identity/Lattice]: all four rungs re-certified from scratch in exact arithmetic; unifies note_e8_gaussian_code/v689 (census, norm doubling), v803 (non-split jet), v783/v798/v819 (metaplectic zeta8, Clifford coset, RM-CSS phase bit); no marker move (Python-only per GATE.WOLFRAM.02)
Dependencies, status detail and source
Canonical status: RAMIFICATION-LADDER-EXACT: the four documented roles of pi2 = 1+i -- norm doubling / empty zero class, the 4-bit address, the non-split jet with deck = 1 + eps, the metaplectic zeta8 with the Clifford index-2 coset and the RM-CSS phase bit -- are ONE ladder (33/33 exact); defect-free controls (split ring, split extension, scrambled nilpotent) all fire
Dependencies: v689; v783; v798; v803; v819
Scripts: v833_gaussian_ramification_ladder.py
Location: tfpt_1;tfpt_3
Original CSV, line 704Original ledger status
PG32.FLAGS.01
PG32.FLAGS.01: the PG(3,2) flag normal form for the 105 + 35 vacuum completion, with the incidence kill test typed as a split, ONE module from one probe (26/26 checks, verdict PG32-FLAGS-EXACT + INCIDENCE-SPLIT; discovery probe pg32_flag_completion_probe.py, 2026-08-07, re-run identically at promotion, promoted VERBATIM, < 1 s). COUNTING NORMAL FORM: [4 choose 2]_2 = 35; 140 affine 2-flats of AG(4,2) = 35 through the origin + 105 not; PG(3,2) has 15 points, 35 lines, 105 = 35 x 3 point-line flags, canonically bijective to the C(15,2) = 105 point pairs via {x,y} <-> (x+y, {x,y,x+y}). RM LAYER (v819 S4 / v821 / v822 rebuilt, all set equalities): [15,10,4] weight enumerator 1 + 105z^4 + 280z^6 + 435z^8 + 168z^10 + 35z^12 EXACT; the 105 weight-4 words ARE the flats avoiding 0; the 140 weight-4 words of RM(2,4) ARE all flats; Grams 22I + 6J, 6I + J, 28I + 7J entrywise. VACUUM READING: origin planes puncture to weight 3, NONE in the shortened code, ONE unshortens dim 10 -> 11 -- the vacuum coordinate is ORIGIN RESTORATION. THE INCIDENCE SPLIT (the kill, typed): with the corpus symplectic form (v774) the 105 = 45 + 60 split is the Sp(4,2)-ORBIT decomposition on BOTH sides (|Sp(4,2)| = 720 brute force); on the 60 NON-ISOTROPIC rungs the polarity map PHI: (U,t) -> ((t+U) n U^omega, U^omega) is well-defined, bijective, Sp(4,2)-EQUIVARIANT (all 60 x 720) and INCIDENCE-PRESERVING; on the 45 DOILY rungs the obstruction is typed: U^omega = U and (t+U) n U = EMPTY for 45/45 flats, the unique abstract equivariant bijection matches flags with support n line = 0, and the flag Gram is 18I + 3J != 22I + 6J. TYPED CONCLUSION: '105 checks = 105 flags' is exact as a deck-equivariant BIJECTION, NOT an incidence isomorphism -- the obstruction sits exactly on the doily (the typed reason v822's continuum dilation died). VACUUM CARRIER CONTENT: the zero class carries NO E8 root (0/240 rebuilt, v689 [E]) -- the vacuum point repairs the label Gram but adds no carrier content; v822's frozen continuum kill cited as the companion negative. Controls fire (scrambled plane row, degenerate form, the 45-sector obstruction as its own control). Exact integer; no floats, no RNG, no fit. Python-only per GATE.WOLFRAM.02.
Recorded status: Exact lattice/identity-grade compression with the kill typed as a split [Identity/Lattice]: 60-sector exact via the symplectic polarity (equivariant incidence dictionary), 45-sector obstructed on the doily (typed negative); compresses v819 S4 / v821 / v822 RM surfaces into the PG(3,2) normal form; no marker move (Python-only per GATE.WOLFRAM.02)
Dependencies, status detail and source
Canonical status: PG32-FLAGS-EXACT + INCIDENCE-SPLIT: 105 = 45 + 60 is the Sp(4,2)-orbit decomposition on both sides; the polarity dictionary is exact, equivariant and incidence-preserving on the 60 non-isotropic rungs; the 45 doily rungs carry the typed obstruction ((t+U) n U empty 45/45, flag Gram 18I+3J != 22I+6J) -- '105 checks = 105 flags' is a deck-equivariant bijection, NOT an incidence isomorphism
Dependencies: v689; v774; v819; v821; v822
Scripts: v834_pg32_flag_completion.py
Location: tfpt_3
Original CSV, line 705Original ledger status
MESSAGE.LADDER.01
v844 -- MESSAGE.LADDER.01 + DOILY.PASCAL.RANK.01: the E8 addressing formula and the Doily-Pascal rank theorem -- two exact corpus compressions, ONE module from two probes (23/23 + 16/16 checks, verdicts MESSAGE-LADDER-EXACT and DOILY-PASCAL-RANK-EXACT; discovery probes binary_message_ladder_probe.py and doily_pascal_rank_probe.py, 2026-08-07, re-run identically at promotion, promoted VERBATIM with no downscoping, ~2 s). PART A, THE MESSAGE LADDER: M_n = 15 * Delta p_n = 15 * 2^n (anchor a = (1,1,2) with p_n = 2 + 2^n, v832 [E]; 15 = the nonzero classes of V = L/(1+i)L, v833 [E]) certified against the ACTUAL rebuilt objects with ONE NAMED STRUCTURE PER RUNG: M_0 = 15 = the address space (classes); M_1 = 30 = h(E8) derived HERE from the rebuilt root system, not cited (exactly 8 simple roots; connected simply-laced Cartan matrix, det 1, degree sequence [1,1,1,2,2,2,2,3] = the E8 diagram; every positive root with exact nonnegative INTEGER simple-root coordinates; the highest root UNIQUE at height 29 with marks {2,2,3,3,4,4,5,6}; h = 1 + 29 = 30 = |R|/rank); M_2 = 60 = the Gaussian root lines (mu4 orbits, all of size 4, exactly 4 per class); M_3 = 120 = |R+(E8)| (exact generic functional f(v) = Sum v_k 10^k) = the sign pairs; M_4 = 240 = |R(E8)| with the census 240 = 15 x 16 (zero class EMPTY); the CODA 248 = 15*16 + 8 = M_4 + rank checked against the actual census and the actual HNF rank; the structural doubling 60 -> 120 -> 240 (each line = exactly 2 sign pairs, each pair = 2 roots) and the halving 60 -> 30 = |mu4| vs rank typed. The tfpt_1 budget lines |R| = 240 / dim E8 = 248 / h = 30 and v832 S3.1-S3.3 are ALL instances of this one formula. Controls fire: the wrong anchor (1,2,2) gives (45,105,225,465) missing all four targets with recursion offset 1; the wrong multipliers 14 (the weight-4 codeword count) and 16 (the class size) miss all four targets and break the coda (232/264 != 248). PART B, THE DOILY-PASCAL RANK THEOREM: the duad-syntheme incidence N of the Cremona-Richmond doily (15 duads x 15 synthemes, 3-regular in rows AND columns) and the symplectic point incidence B on PG(3,2) (B B^T = 4I + 3J entrywise on all 225 cells, charpoly (x-7)(x-2)^9(x+2)^5 exact, v774 S9 rebuilt) are ONE object: via the K6 duad model D(v) = {q Arf-1 : q(v) = 0} (exactly 16 quadratic refinements by brute force over 2^16, Arf census 6 + 10) the bijection point <-> duad carries N N^T onto B + 2I ENTRYWISE -- duad collinearity = symplectic orthogonality, and the spectrum shift 7/2/-2 -> 9/4/0 makes v774's (-2)-eigenspace v814's kernel. THE RANK THEOREM (exact Fraction/sympy): charpoly(N N^T) = (x-9)(x-4)^9 x^5, so sing(N) = {3^1, 2^9, 0^5}: rank N = 10 = A_Lambda = C(g_car, 2) (the decuple sector), dim ker N = dim ker N^T = 5 = g_car (the five-slot carrier), multiplicity 9 = N_fam^2, top singular value 3 = N_fam, and the SIX ovoid indicators 3*1_{O_q} - 1 (q Arf-1) lie in ker N^T and SPAN it -- the P2 integers are the singular-value data of the Cremona-Richmond incidence. THE RECOVERY VALUE: sing(N/3) = {1, 2/3 x9, 0 x5} exact, 2/3 = (N_fam - 1)/N_fam (the corpus recovery survival, v327); THE EXPONENTIATION IDENTITY: charpoly(((N/3)(N^T/3))^3) = (x-1)(x-64/729)^9 x^5 exact with 64/729 = (2/3)^6 = the deployed lambda_2 of {1, (2/3)^6, (1/3)^6} (v330/v486; the sixth power is the compiler clock, v814); TYPED GAP re-affirmed with NO upgrade: 1/729 is NOT a root of the six-step charpoly -- the deployed (1/3)^6 stays on the clock side (v814 SIXSTEP-CLOCK-ONLY [E], cited, consistent). Controls fire: the circulant and the frozen-seed LCG 3-regular pairings (same row/col sums 3) give rank 13 != 10, kernel 2 != 5 and the wrong charpoly. Exact integer/Fraction/sympy arithmetic; no floats, no fit; the only RNG is the frozen-seed LCG of control C2 (v775 C2 precedent). No marker moves; the compression is a normal form, not a new claim. Python-only per GATE.WOLFRAM.02.
Recorded status: Exact identity-grade compression [Identity]: both parts exact integer/Fraction/sympy arithmetic certified against the rebuilt lattice objects (h(E8) = 30 derived from the rebuilt root system, not cited); the (1/3)^6 typed gap re-affirmed with NO upgrade (v814 cited); no marker move (Python-only per GATE.WOLFRAM.02)
Dependencies, status detail and source
Canonical status: MESSAGE-LADDER-EXACT + DOILY-PASCAL-RANK-EXACT: M_0..M_4 = (15, 30, 60, 120, 240) = 15 * 2^n with one named structure per rung (address space / h(E8) from the rebuilt root system / Gaussian lines / positive system / root census) and the coda 248 = 15*16 + 8; N N^T = B + 2I entrywise; rank N = 10 = A_Lambda, ker = 5 = g_car, multiplicity 9 = N_fam^2, top 3 = N_fam, recovery 2/3, six-step (2/3)^6 = 64/729 exact; NO (1/3)^6 doily mode (v814, no upgrade); all controls fire
Dependencies: v832; v833; v774; v814; v330; v486; v327; v775
Scripts: v844_message_doily_rank.py
Location: tfpt_1;tfpt_3
Original CSV, line 706