Original ledger status
NORMALFORM.CFIN.01
v845 -- NORMALFORM.CFIN.01: the finite compiler normal form C_fin = (V, hbar, q*, sigma, iota) assembled as ONE machine-checked object from the Gaussian quotient, with the code-to-matter kill built in as a checked NEGATIVE and the remaining P2 bridge typed -- the round's central corpus compression, ONE module from one probe (28/28 checks, declared SPEC v2, verdict NORMAL-FORM-ASSEMBLED; discovery probe finite_compiler_normal_form_probe.py, 2026-08-07, re-run identically at promotion, promoted VERBATIM with no downscoping, ~4 s). THE OBJECT, read off the lattice and not postulated: V = L/(1+i)L rebuilt from the Gaussian Construction-A E8 (the unique mu4/sigma-invariant placement C*, 2 of 30; census 240 = 15 x 16, zero class EMPTY); hbar = the descended symplectic form with a FOUND family/anchor basis (F1, F2, F3, A) of Gram J - I, equal to the bit form on ALL 256 label pairs; sigma = the descended order-3 deck (sigma^3 = id, symplectic, EXACTLY 3 fixed nonzero classes {A, F_Sigma, F_Sigma + A}, the other 12 in exactly 4 free 3-orbits -- the family cycle); q* = the distinguished quadratic refinement (EXACTLY 16 refinements by brute force over 2^16, Arf census 6 + 10; the frozen selector sigma-invariant 4 -> q(A) = 1: 2 -> q(F_Sigma) = 0: 1 picks a UNIQUE q*, Arf type 1, sigma-preserved); iota = the parity lift onto the even five-slot code C_even(5) (bijective; beta = iota.iota == hbar on all 256 cells; q_wt = wt(iota)/2 mod 2 IS q*; sigma acts on the FIVE carrier slots as the 3+2 split -- message register and carrier register intertwined). DERIVED COUNTING from the one object: |Sp(4,2)| = 720 by full 65536-matrix census; |Stab(q*)| = 120 acting FAITHFULLY as S5 on the five, orbits [1, 5, 10]; 16 = 1 + 5 + 10 and 15 = 5 + 10; the PASCAL READING (iota-weight census (1, 10, 5) = (C(5,0), C(5,2), C(5,4))); the PROJECTIVE READING (PG(3,2): 15 points, 35 lines, 15 isotropic = the doily; the 5bar is an OVOID meeting every isotropic line exactly once); the BUDGET against the actual lattice objects: 240 = 16 x (5+10), 60 lines = 4 x 15, 30 = 2 x (5+10) = h(E8) (MESSAGE.LADDER.01 rung 1), rank 8 (HNF index 16), 248 = 16 x (5+10) + 8. THE MANDATORY NEGATIVE (built in, v775 re-anchored): the exact counting bound -- every D5(+)A3 c E8 has 128 spinor-side roots, so at most floor(128/16) = 8 all-spinor classes and >= 7 of the 15 classes ALWAYS contain adjoint-side roots (the 15 mailboxes canNOT be 15 pure matter multiplets); the concrete doubled-model census SATURATES both bounds (8 spinor-pure + 7 adjoint-side, ZERO both-type classes -- the J-quotient respects the D8 grading); the WEIGHT-level kill at the canonical split D = (0,2,4,6,7): each spinor-pure class restricts to 8 DISTINCT half-spinor weight pairs, never 1 -- v775 ROOTCLASS-MIXED [E] re-verified, NOT overturned. WHAT THE NORMAL FORM DOES NOT REMOVE (P2 typed, no upgrade): all 30 placements are Type II [8,4] doubly-even self-dual codes (enumerator 1 + 14 z^4 + z^8) -- the v799 TYPEII-FORCED echo; C_fin does NOT derive the three seam axioms A1-A3, the OPE-linearity scope note, or the v776 selection of ONE copy -- P2 (g_car = 5 = the iota slot count) is NARROWED to the v799 residual R1' ([C] class), not eliminated. Controls fire: the non-alternating dot form admits 0 refinements; the trivial deck leaves 4 selector candidates (q* NOT unique without the family 3-cycle); the wrong lift breaks C_even membership and beta == hbar. SPEC v2 declared (v836 precedent; the v1 wording of S7(b) mis-typed the v775 bound as 'mixed classes'; the factual census is the clean 8 + 7 split along the D8 grading; no numeric result changed). Exact integer/sympy; no floats, no RNG, no fit. Python-only per GATE.WOLFRAM.02.
Recorded status: Exact identity-grade normal form [Identity] with the built-in checked NEGATIVE (v775 ROOTCLASS-MIXED re-anchored via the 128-spinor counting bound + the saturated 8 + 7 census) and the typed P2 bridge: C_fin does NOT derive A1-A3 / the linearity scope / the v776 uniqueness selection -- P2 NARROWED to the v799 residual R1' ([C]), NOT eliminated; SPEC v2 declared (v836 precedent, no numeric result changed); no marker move (Python-only per GATE.WOLFRAM.02)
Dependencies, status detail and source
Canonical status: NORMAL-FORM-ASSEMBLED: C_fin = (V, hbar, q*, sigma, iota) read off the Gaussian quotient -- selector-unique q*, faithful S5 stabilizer (|Sp(4,2)| = 720, Stab = 120, orbits [1,5,10]), Pascal (1,10,5), ovoid projective reading, budget 240 = 16*15 / 248 = 16*15 + 8 against the actual census; the code-to-matter reading stays DEAD (bounds saturated 8 + 7, weight kill 8 pairs never 1); P2 narrowed to v799 R1' ([C]), not eliminated; all controls fire
Dependencies: AX.P2.01; v752; v774; v775; v799; v776; v833; MESSAGE.LADDER.01
Scripts: v845_cfin_normal_form.py
Location: tfpt_1;tfpt_3;tfpt_research_contracts
Original CSV, line 707Original ledger status
CFIN.UNIQUE.01
CFIN.UNIQUE.01: finite compiler uniqueness, one orbit and C6 automorphisms; cofinal Weil mirror moved to Prime Front. Original module ID retained; original complete mixed record is preserved in extraction provenance.
Recorded status: Exact identity-grade uniqueness theorem [Identity] for the finite compiler object: exhaustive finite verification over F_2^4 (no floats, no RNG, no fit; orbit-stabilizer exact); the strict terminal-object reading FAILS honestly and is typed (unique up to NON-unique isomorphism, a one-object groupoid); P2 stays NARROWED to the v799 residual R1' (why THIS normal form), NOT eliminated; no marker move (Python-only per GATE.WOLFRAM.02)
Dependencies, status detail and source
Canonical status: CFIN-UNIQUE: admissible tuple census at omega = hbar = 14400, G-orbits = 1 (orbit-stabilizer 14400 x 6 = 86400 = |Sp(4,2) x S_5| exact); Aut(C_fin) ~= C6 (element orders [1,2,3,3,6,6], faithful into Sp(4,2), the S_5 slot permutation determined by the symplectic part); the Gaussian diagram fixes the carrier triple up to the 18-element centralizer torsor, q* selector-unique, 120 iota-completions in one orbit; strict terminal reading FAILS (typed either way); controls fire (dot form 0 refinements; wrong Arf class: empty iota set; no sigma: canonicity dies 16 -> 8 -> 4 != 1)
Dependencies: AX.P2.01; NORMALFORM.CFIN.01; MESSAGE.LADDER.01; v774; v833; v844; v845
Scripts: v849_cfin_unique_cofinal_lean.py
Location: tfpt_1;tfpt_3;tfpt_research_contracts
Original CSV, line 708Original ledger status
ARF.VACUUM.SYNDROME.01
v852 -- ARF.VACUUM.SYNDROME.01 + OVOID.DECODER.01: the Arf-vacuum syndrome theorem and the integral five-mode decoder -- the corpus's flat counts, orbit splits, Hecke matches and code enumerators compress into ONE two-bit syndrome table on the Hamming code, and the doily recovery channel gains an explicit integral inverse with the S6 standard representation identified, ONE module from two probes (24/24 + 23/23 checks, zero fails, verdicts ARF-VACUUM-SYNDROME-EXACT and OVOID-DECODER-EXACT; discovery probes affine_arf_vacuum_probe.py and doily_ovoid_decoder_probe.py, 2026-08-07, re-run identically at promotion, embedded BYTE-EXACT and executed verbatim, exact integer/Fraction/sympy arithmetic, <1 s). PART A, THE ARF-VACUUM SYNDROME: (a) THE ARF BIT THEOREM -- for every affine flat t+U of (F_2^4, hb) the Arf bit a(t+U) = sum_{x in t+U} q*(x) mod 2 equals the direction bit hb(u,v) of the underlying plane U for ALL 140 flats (position independence: all 4 cosets agree; the direction bit is well-defined on all 35 planes); (b) THE TWO-BIT SYNDROME CENSUS -- (s_vac, s_Arf) = (origin bit, direction bit) splits the 140 flats EXACTLY into 15/20/45/60 (doily lines / non-isotropic lines / isotropic off-planes / non-isotropic off-planes), reproducing v821's 35 = 15 + 20 and v834's 105 = 45 + 60 as rows of ONE table; (c) THE LOCAL HECKE THEOREM -- at EVERY nonzero point x: 3 isotropic + 4 non-isotropic directions through x with the isotropic ones in bijection with the points of x^perp/<x>, and the 28 off-origin flats through x split 12 + 16 with A_3 + B_3 = 28 = sigma_3(3) and A_3 - B_3 = -4 = a_3 (the eta-product Hecke eigenvalue, v820/v535 rebuilt LOCALLY at all 15 points; 28 - (-4) = 32 = 2^5 the pi_cusp denominator, v785); (d) THE CODE PENCIL -- H = ker X = [15,11,3] (weight-3 words == the 35 lines, weight-4 == the 105 off-origin flats, SET EQUALITIES), H^perp = the simplex code, and the CANONICITY LEMMA: all 16 refinements differ from q* by simplex words, hence induce ONE Arf functional on H; below H sit D = [15,10,4] (v819's enumerator EXACT), C_iso and C_non = [15,10,3] (weight-3 words == the 15 doily lines resp. the 20 non-isotropic lines), all pairwise intersections == K = [15,9,4], all pairwise sums == H, and the syndrome map H -> F_2^2 is surjective with four fibers of 512; (e) RM(2,4) RESTORED -- puncturing RM(2,4) = [16,11,4] at the vacuum coordinate gives H, shortening gives D, and c -> (p.c, c) is a bijection H -> RM(2,4): THE VACUUM BIT IS THE PARITY BIT, and on the 140 flat words the restored coordinate == s_vac exactly. Controls fire: the dot form admits 0 refinements and an ill-defined direction bit; an Arf-0 refinement leaves the table invariant but breaks the labeling (zero set 10 != 6, not an ovoid); a frozen-LCG column permutation preserves [15,11,3] but destroys the line labeling (31/35 weight-3 supports not lines). PART B, THE OVOID DECODER: the Cremona-Richmond incidence N (15 duads x 15 synthemes) and the six ovoid vectors v_a = 3*1_{O_a} - 1 satisfy (a) N^T v_a = 0 for ALL six a (every syntheme covers each letter exactly once -- the kernel facts from perfect matchings), any five of the six are independent, sum_a v_a = 0; (b) the Gram V^T V = 36I - 6J ENTRYWISE; (c) SNF(N) = diag(1^10, 0^5) EXACT over Z -- rank 10 = C(g_car, 2), kernel 5 = g_car, NO TORSION, with a det-+-1 10x10 minor exhibited; (d) the Moore-Penrose closed form N+ = N^T/4 - J/36 verified against all four Penrose axioms in exact Q; (e) the carrier projector P5 = I/2 - B/4 + J/12 == (1/36) sum_a v_a v_a^T entrywise, P5^2 = P5 = P5^T, P5 N = 0, tr P5 = 5 = g_car, N N+ = I - P5 (the visible-part projector); (f) THE MOD-2 SHADOW: v_a mod 2 == q_a entrywise and ker_F2(N^T) == A_q = [15,5,6] (weight enumerator 1 + 10z^6 + 15z^8 + 6z^10) -- THE THREE-RING CORRESPONDENCE: the same kernel is (R) the ovoid span, (Z) torsion-free rank 5, (F_2) the code A_q; (g) THE DECODER DEMO: mhat = (1/4)N y - (1/36)J y == (I - P5) m EXACTLY on the predeclared 6-vector test set (kernel modes invisible, im(N) modes fully visible) -- the recovery channel of DOILY.PASCAL.RANK.01 now has an explicit integral inverse, not just a spectrum; (h) THE S6 IDENTIFICATION: N is S6-equivariant and tr(P5 Pi(pi)) == fix(pi) - 1 for representatives of ALL 11 conjugacy classes -- ker N^T IS the 5-dimensional standard representation: the five-slot carrier is the sixth-root-free shadow of six ovoid modes with one relation. Control fires: a frozen-LCG wrong pairing (same row/col sums 3) breaks SNF (torsion 3 appears), the F_2 kernel (4 != 32) and the ovoid kernel property. The P2 integers remain the singular-value data of the doily; no marker moves -- the compression is a normal form plus an inverse, not a new claim. NO RH claim. Python-only per GATE.WOLFRAM.02.
Recorded status: Exact identity-grade compression [Identity]: both parts exhaustive finite algebra (F_2 / Z / Q; SNF, Penrose axioms, S6 class characters exact; SET equalities, not counts); the corpus surfaces v819/v820/v821/v834/v535/v785 compressed into ONE two-bit syndrome table and the v774/v814 doily channel into ONE integral decoder; controls fire (dot form, Arf-0 labeling break, frozen-LCG permutation/pairing); no marker move (Python-only per GATE.WOLFRAM.02)
Dependencies, status detail and source
Canonical status: ARF-VACUUM-SYNDROME-EXACT + OVOID-DECODER-EXACT: a(t+U) = hb(u,v) on all 140 flats; census 15/20/45/60; the local Hecke theorem 12/16 -> 28/-4 at all 15 points with x^perp/<x> semantics; pencil [15,11,3] > {[15,10,4], 2 x [15,10,3]} > [15,9,4] with the canonicity lemma (one Arf functional on H) and the vacuum bit = the RM(2,4) parity bit; N^T v_a = 0, Gram 36I - 6J, SNF diag(1^10, 0^5) torsion-free (det +-1 minor exhibited), N+ = N^T/4 - J/36 (four Penrose axioms exact in Q), P5 = I/2 - B/4 + J/12 (tr 5 = g_car), decoder exact on the predeclared set, ker = the S6 standard representation (11/11 classes), three rings (R ovoid span / Z torsion-free / F2 code A_q = [15,5,6] via v_a mod 2 = q_a)
Dependencies: NORMALFORM.CFIN.01; MESSAGE.LADDER.01; v774; v819; v820; v821; v834; v844; v845
Scripts: v852_arf_vacuum_ovoid.py
Location: tfpt_1;tfpt_3
Original CSV, line 709Original ledger status
ARF.BENT.CSS.01
ARF.BENT.CSS.01: exact bent phase and CSS code identities; Mangoldt incidence experiment moved to Prime Front. Original module ID retained; original complete mixed record is preserved in extraction provenance.
Recorded status: Exact identity-grade compression [Identity] with the operator-level relation bridge typed HONESTLY as classical incidence algebra (mu*log = Lambda in matrix clothes -- the value is the packaging + the four-comb discipline transport at operator level, NOT new mathematics); the -4 triple point is ONE machine-checked integer (Hecke = Gauss = Walsh = a_3); the bent/character MUB partner of v800 REPORTED with no upgrade; controls fire; no marker move (Python-only per GATE.WOLFRAM.02)
Dependencies, status detail and source
Canonical status: ARF-BENT-CSS-EXACT + MANGOLDT-COMMUTATOR-EXACT: s_q-hat = -4 s_q on all 16 (W^2 = 16I, perfect autocorrelation 16 delta); (16,6,2) difference set {0} u 5bar; A_q = C_iso^perp = [15,5,6] with the 31-word structural census; [[15,5,3]] -> [[16,4,4]] (the 60 minimal words = the 60 isotropic planes, the s_Arf = 0 rows of the v852 table; vacuum transformation typed: slot +1, logical qubit -1, distance 3 -> 4); the -4 triple point Hecke = Gauss = Walsh = a_3 (v785: 32 = 28 - (-4)); the 16 bent translates a second Gram-16I frame mutually unbiased vs the characters (+-4; reported, no upgrade); L = -M[D,Z] = -[D, log Z] = T(Lambda) exact three ways (BCH truncates; log Z rational), L^k = ordered chains (nilpotency floor(log2 N) + 1), the four-comb discipline at operator level (Epstein leak [6,14,21,...] exact, first unramified 21 = 3x7, repaired by a_A + a_B = 1 * chi_{-20}; ideal-level Dedekind Lambda_K with norm aggregation (1 + chi4) Lambda), the carrier bridge (the deployed mu-pairing IS row one of L; rows are shifts; L^2 - [D,L] = T(mu*log^2) -- the Selberg hierarchy)
Dependencies: ARF.VACUUM.SYNDROME.01; PRIME.RELATION.MULT.01; v535; v774; v785; v800; v819; v820; v852
Scripts: v853_bent_css_mangoldt.py
Location: tfpt_1;tfpt_3
Original CSV, line 710Original ledger status
E8.SIMPLEX.FOURIER.01
v857 -- E8.SIMPLEX.FOURIER.01 + FLAVOR.WINDING.QUADRATIC.01: the E8 audits, part I -- the Gaussian census IS a Fourier law and v817's per-prime measurement is the prime restriction of a CHARACTER THEOREM (mh2(n) = -1/15 as an integer identity at EVERY odd n <= 16500), and the tfpt_2 winding line collapses to ONE rank-one determinant quadratic q_wind = t^2 - g_car t + |Z2| with the triple lock s = 6 and the reality threshold typed, ONE module from two probes (26/26 + 20/20 checks, zero fails, verdicts SIMPLEX-FOURIER-EXACT + INTERTWINER-IDENTIFIED and WINDING-QUADRATIC-EXACT; discovery probes simplex_fourier_probe.py and flavor_winding_quadratic_probe.py, 2026-08-08, re-run identically at promotion, embedded BYTE-EXACT and executed verbatim, exact integer/Fraction/sympy arithmetic, ~2 s). PART A, THE FOURIER LAW (audit package A): the Construction-A rebuild is warded (30 placements, 2 invariant under pi_J and pi_sigma; 240 roots, all norm 4, all in L; the quotient V = L/(1+i)L = F_2^4 with class addition well-defined on all 256 pairs and every class 2-torsion), the census r = (0; 16^15) (zero class EMPTY, v833/v844) has the EXACT Walsh transform rhat = (240; -16 x15) with the inversion sum rule, i.e. the normalized spectrum {1, (-1/15)^15}: the uniform-nonzero channel P = (J - I)/15 entrywise in Fractions (doubly stochastic; eigenaction exact on all 16 characters; two-step P^2 = (I + 14J)/225 with contraction 1/225); THE FIVE-LINE THEOREM measured at every level: (i) RAMIFICATION -- Theta_0(n) = 0 for EVERY odd n <= 16 with the one-line proof (x = (1+i)y forces even level) and Theta_0(2m) = 240 sigma_3(m); (ii) EQUIDISTRIBUTION -- Theta_v(n) is ONE value over the 15 nonzero classes at every level n <= 16 (the Sp(4,2) footprint); (iii) hence Thetahat_u(odd n) = -Theta_L(n)/15; (iv) THE INTERTWINER IDENTITY -- the v817 packet numerator (Th0-Th1+Th2-Th3)(n) EQUALS the code Walsh transform Thetahat_u(n) for every nonzero u at EVERY level n <= 16, odd AND even (both ladders read [-16, 112, -448, 1136, -2016, 3136, -5504, 9328] at n = 1..8; the Eisenstein normal form 15 Theta_D8 = 7 Theta_L + 8 Theta_0 across machineries); (v) THE VALUE THEOREM -- 15 (Th0-Th1+Th2-Th3)(n) = -240 sigma_3(n) for EVERY odd n <= 16500, hence mh2(odd n) = -1/15 IDENTICALLY, covering all 1911 odd primes <= 16500: v817's per-prime measurement is a character theorem of the code, one Walsh transform away from the deployed census with NO new input. THE HONEST TYPE (measured, kept): the identification is SPECTRAL (numerator q-series equal) -- the packet 5|3-parity grading (52, 60, 128) and the code grading (15 x 16) do NOT refine each other (the S6.3 cross table: 4 + 3 + 8 mixed classes); the spinor halving Th1 = Th3 stays numerical fiat (typed); 52 = 40 + 12 = |R(D5)| + |R(A3)| is the seam reading. Controls fire (occupied zero class, one class at 15, wrong quotient dim F_2^3 -- each breaks the law at a stated integer), invariances hold (24 explicit isometries of (L, J) preserve census and spectrum; the OTHER invariant placement C** gives the identical law). PART B, THE WINDING QUADRATIC (audit package for tfpt_2, section I.5): against the deployed residue matrix (det R = 8 = h(D5), tr R = 9, PrinMin2 = (5,3,2), SNF (1,1,8), anchor R e1 = (1,1,2), cofactor seam normal adj(R) row 1 = (5,-9,6) with n.1 = 2 = |Z2|), THE MINI-THEOREM: chi_{R_s} - chi_R = -s q_wind with q_wind = e1^T adj(tI - R) 1 = t^2 - 5t + 2 = t^2 - g_car t + |Z2| EXACT in sympy -- the whole winding line is one rank-one matrix-determinant lemma; the keybox coefficients (9+s, 10+5s, 8+2s), the per-winding det increment d(det R_s)/ds = q_wind(0) = 2 = |Z2| and the minor law PrinMin2(R_s) = (5, 3(s+1), 2(s+1)) (carrier minor 5 s-INVARIANT) are all readouts of the single quadratic; q_wind is irreducible over Q (disc 17 nonsquare) and the two base points are s-invariant (rem(chi_{R_s}, q_wind) = -12t, s-free); THE TRIPLE LOCK: trace (tr R_s = 15), determinant (det R_s = 20) and Coxeter lift ((R_s^T a)_1 = 30) each solve to s = 6 ALONE, intersection {6} = {|R+(A3)|}, and at s = 6: chi_L = t^3 - 15t^2 + 40t - 20 with (15, 40, 20) = (dim A3, |R(D5)|, |R(A4)|), 3 real positive roots; THE LOCUS (exact Sturm/resultant): Delta(s) = disc_t chi_{R_s} = 17s^4 - 18s^3 + 709s^2 + 588s - 7996 (irreducible), Delta(6) = 39200 = 2^5 5^2 7^2 = 2 x 140^2 > 0 -- s = 6 is NOT a collision point; the reality threshold is the unique Delta-root in (2, 3), s* ~ 2.8250 (matching the deployed ~2.83; Sturm real-eigenvalue counts jump 1 -> 3 between s = 2 and s = 3); the integer-window census types s = 6 as the ONLY 2xsquare hit in s = -2..12 (measured, typed -- and q_wind(6) = 8 = det R reported as a measured coincidence). Controls fire: the sibling directions 1 e2^T and 1 e3^T change the quadratic AND break the lock (intersections EMPTY; 1 e3^T even reducible), the sibling ROW transport e1 1^T keeps -g_car t but LOSES |Z2| (locks pairwise disjoint 6/12/24), and the sibling minor branch {1,3,4} is unreachable on the whole winding line (integer scan s = -100..100 empty; the carrier minor 5 invariant) -- the triple (1, -5, 2) is direction-specific. Both parts are exact-arithmetic corpus compressions and audits of DEPLOYED claims (v817, v833, v844, v4/v94 keyboxes) -- normal forms and identities, no new physical claim, no marker moves. NO RH claim. Python-only per GATE.WOLFRAM.02. [2026-08-08 round-LXXIX note (v875): THE CENSUS IS NOW A THEOREM -- E8.SHELL.GLOBAL.01 proves Thetahat_u/Theta_L = -1/15 for ALL odd shells (Sp(4,2) transitivity of the G31 class action + (1+i) doubling + Theta_L = 240 sigma_3), replacing the n <= 16500 finite-census argument behind the value theorem; the census range is retained as the exact ward and the character-theorem reading of this row is unchanged; the consequence chain is kernel-checked in FORM.E8.SHELL.GLOBAL.01 (TfptCarrier/GaussianShells.lean).]
Recorded status: Exact corpus compression [typed evidence line: 26/26 + 20/20 checks, zero fails, exact integer/Fraction/sympy arithmetic throughout; the identification typed SPECTRAL-only (the packet and code gradings do not refine each other); the spinor halving stays numerical fiat; q_wind(6) = 8 = det R typed a measured coincidence; the integer-window 2xsquare census measured, not narrated]; audits of DEPLOYED claims (v817/v833/v844, tfpt_2 I.5 keyboxes) -- normal forms and identities, no new physical claim; NO RH claim; no marker move (Python-only per GATE.WOLFRAM.02)
Dependencies, status detail and source
Canonical status: SIMPLEX-FOURIER-EXACT + INTERTWINER-IDENTIFIED + WINDING-QUADRATIC-EXACT: rhat = (240; -16 x15), P = (J-I)/15 with spec {1, (-1/15)^15}, two-step 1/225 exact; ramification + equidistribution at every level <= 16; packet numerator == code Walsh at every level (both [-16, 112, -448, 1136, ...]); mh2(odd n) = -1/15 for every odd n <= 16500 (integer identity, 1911 primes); q_wind = t^2 - 5t + 2 exact by the adjugate lemma; triple lock s = 6; Delta(6) = 39200 = 2 x 140^2, sole 2xsquare hit; s* ~ 2.8250 the unique Delta-root in (2,3); 7 controls fire, 2 invariances hold
Dependencies: CFIN.UNIQUE.01; MESSAGE.LADDER.01; ARF.BENT.CSS.01; v4; v94; v817; v833; v844
Scripts: v857_simplex_fourier_winding.py
Location: tfpt_1;tfpt_2;tfpt_3;tfpt_research_contracts
Original CSV, line 711Original ledger status
E8.G31.CLOCK_ALPHABET.01
v858 -- E8.G31.CLOCK_ALPHABET.01: the E8 audits, part II -- the compiler clock alphabet is a NORMAL FORM of G31: Deg(G31)/4 = {2, 3, 5, 6} = {|Z2|, N_fam, g_car, |R+(A3)|} with the audit identity (sum d/4)(sum (d-1)/4) = 16 x 15 = 240 REALIZED on the roots, (8, 12, 20, 24) the UNIQUE integer quadruple with product 46080 and sum 64, the 607-group rank-4 kill scan typed (G31 the SOLE full-battery passer; weak-triple and raw-sum-64 impostors named), and the W(D5) x W(A3) fence re-killed with COMPUTED centers 4 vs 1, ONE module from one probe (19/19 checks, zero fails, verdict CLOCK-ALPHABET-SELECTIVE; discovery probe g31_clock_alphabet_probe.py, 2026-08-08, re-run identically at promotion, embedded BYTE-EXACT and executed verbatim, ~4 s). THE REBUILD (warded against v634): 240 doubled-integer E8 roots, J free of order 4 with EXACTLY 60 Gaussian lines, 60 order-2 reflections (one per line, all distinct), BFS closure |G| = 46080 = 8 x 12 x 20 x 24 = prod Deg(G31), every element complex-linear (commutes with J), the base certified by an exact adjugate identity (det = -512), and the EXACT reflection census: 60 elements with rank(M - I) = 2, all order 2, all generators -- ZERO quasi-reflections (v634 TEST2 reproduced; sum (d-1) = 60 anchors the degrees; the Molien uniqueness CITED, not recomputed). THE NORMAL FORM: Deg(G31) = |mu4| x {2, 3, 5, 6} with gcd = 4 = |mu4|, lcm = 120 = |R+(E8)|, lcm/gcd = 30 = h(E8); sum d/4 = 16 (the class size) and sum (d-1)/4 = 15 (the classes) with 16 x 15 = 240 = |R(E8)| -- and the 60/4 = 15 line is REALIZED on the roots (the 15 classes at 4 lines per class, the same 15 x 16 census as the package-A code side); the alphabet {2, 3, 5, 6} = {|Z2|, N_fam, g_car, |R+(A3)|} is EXACTLY the compiler clock alphabet; the Springer footprint is typed (exponents (7, 11, 19, 23) all = 3 mod 4; the d/4-clock realization x^{d/4} in {J, J^3} cited v654). THE ARITHMETIC PIN (measured): the integer-quadruple census with product 46080 and sum 64 returns EXACTLY [(8, 12, 20, 24)]. THE KILL SCAN (the selectivity theorem, 607 groups): the full rank-4 Shephard-Todd catalog (integrity: prod(degrees) = |G| for every entry -- a table second-source check) is run through the seven-gate battery (product, raw sum 64, gcd normalization, alphabet set, lcm, lcm/gcd = 30, audit identity): G31 is the SOLE full-battery passer; the weak-triple (gcd/lcm/30) impostors are typed by name (G(20,10,4), G(20,20,4), G29) and the raw-sum-64 coincidences too (G(8,2,4), G(10,10,4), G30 = W(H4)); the family boundary is verified in range (no G(m,p,4) matches the alphabet for any 2 <= m <= 120, with the typed argument: 3m/g <= 6 forces g >= m/2, then {d/g} contains 1 or 4); THE HONESTY LINE (typed, no kill): degree-only audits cannot separate G31 from the reducible torus Z8 x Z12 x Z20 x Z24 (identical degrees by construction) -- the frozen scope is the irreducible rank-4 list; the controls fire (the perturbed quadruple (8,12,20,28) fails the battery; the wrong normalization gcd 2 breaks the alphabet). THE FENCE (re-killed with a computed one-number invariant): |W(D5)| x |W(A3)| = 1920 x 24 = 46080 = |G31| stays NUMEROLOGY -- the computed |Z(G31)| = 4 with Z = <J> = mu4, versus |Z(W(D5) x W(A3))| = 1 x 1 = 1 (odd-rank D5: -1 not in W(D5); Z(S4) = 1): NOT isomorphic, NOT a decomposition (v634 T1.3/T1.4/T1.5 CITED for the full structural refutation: G = (Z4 o 2^{1+4}).Sp4(2) and W(D5) embeds in NO rank-4 group). The module is an exact-arithmetic corpus compression and a selectivity audit of a DEPLOYED object (v634/v654) -- a normal form plus an armed kill rule, no new physical claim, no marker moves. NO RH claim. Python-only per GATE.WOLFRAM.02. [2026-08-08 round-LXXIX note (v874): THE ALPHABET HAS A DECODER -- E8.WINDING.DECODER.01 proves that the v857 winding quadratic maps the clock alphabet {2,3,5,6} to (-|mu4|,-|mu4|,|Z2|,h(D5)) with the decoder polynomial (y+4)^2(y-2)(y-8) carrying budget coefficients (2, 48, 32, 256) and the exact bridge |mu4| q(|Z2|)/|R(E8)| = -1/15 = the Walsh message eigenvalue; typed AUDIT theorem, not a functor; the 6-vs-7 honesty note of this row carries over verbatim.]
Recorded status: Exact corpus compression + selectivity audit [typed evidence line: 19/19 checks, zero fails; the honesty line kept (degree-only audits cannot separate G31 from the reducible torus Z8 x Z12 x Z20 x Z24 -- frozen scope the irreducible rank-4 Shephard-Todd list); the Molien uniqueness and the full W(D5)-fence structural refutation CITED (v634), not recomputed; X1/X2 controls fire]; a normal form plus an armed kill rule for a deployed object; NO RH claim; no marker move (Python-only per GATE.WOLFRAM.02)
Dependencies, status detail and source
Canonical status: CLOCK-ALPHABET-SELECTIVE: Deg(G31)/4 = {2,3,5,6} = {|Z2|, N_fam, g_car, |R+(A3)|}; gcd 4 = |mu4|, lcm 120 = |R+(E8)|, lcm/gcd 30 = h(E8); (sum d/4)(sum(d-1)/4) = 16 x 15 = 240 realized on the roots (4 lines/class); (8,12,20,24) the unique product-46080/sum-64 quadruple; 607-group scan: G31 sole full-battery passer (weak-triple impostors G(20,10,4)/G(20,20,4)/G29; sum-64 coincidences G(8,2,4)/G(10,10,4)/W(H4)); family boundary m <= 120 empty; fence killed by computed centers 4 vs 1
Dependencies: v634; v654; CFIN.UNIQUE.01
Scripts: v858_g31_clock_alphabet.py
Location: tfpt_1;tfpt_3;tfpt_research_contracts
Original CSV, line 712Original ledger status
FLAVOR.FEEDBACK.NORMALFORM.01
THE FEEDBACK NORMAL FORM OF THE WINDING LINE (2026-08-08 round 36, v874; discovery probe flavor_feedback_probe.py 14/14, verdict FEEDBACK-NORMALFORM-EXACT; exact sympy/integer arithmetic in every decision). THEOREM: with the integral basis P = [2*1 | e3 | R e3] (det P = -4, SNF diag(1,2,2)) the WHOLE winding line R_s = R + s 1 e1^T conjugates EXACTLY (symbolic in s) to M(s) = [[s+4,0,3],[0,0,-2],[4,1,5]]: a gain channel s + |mu4|, the companion block of the v857 winding quadratic q_wind = t^2 - g_car t + |Z2|, and the coupling pair (3,4) with loop product N_fam x |mu4| = 12 = dim g_SM; the conjugated deformation P^{-1}(1 e1^T)P = E11 is a PURE GAIN; hence chi_{R_s}(t) = (t - s - |mu4|) q_wind(t) - 12t identically (equivalently the remainder identity chi_R - (t-4) q_wind = -12t, a pure t-tap at gain offset 4 = |mu4|), and at the locked point s = 6 the coefficients (15, 40, 20) of chi_L are the three gain-10 readouts 10+5, 50+2-12, 10x2. CONTROLS (all fire): directions 1 e2^T (s leaks into the coupling; constant graft +8, offset 8 != 4), 1 e3^T (not integral; mixed remainder), and the sibling row matrix e1 1^T (smeared over all rows; offset 4 coincides -- typed honestly -- but the remainder -11t - 4 has a nonzero constant). THE HONEST TYPING (load-bearing, kernel-checked in FORM.FLAVOR.FEEDBACK.01): the quotient Z^3/PZ^3 = Z2 x Z2 has CARDINALITY 4 = |mu4| but EXPONENT 2 -- the same cardinality as mu4 = Z4, NOT the same group; any mu4 reading would need an extra order-4 witness (none claimed). NO physics claim beyond the audit statement.
Recorded status: Honest promotion of an exact integer theorem [typed evidence line: 14/14 checks, zero fails, verdict FEEDBACK-NORMALFORM-EXACT; all decisions exact sympy; frozen spec SHA f5f40996...]
Dependencies, status detail and source
Canonical status: FEEDBACK-NORMALFORM-EXACT: P^{-1} R_s P = [[s+4,0,3],[0,0,-2],[4,1,5]] exact symbolic in s; chi_{R_s} = (t-s-|mu4|) q_wind - 12t; quotient Z2^2 typed NOT mu4; all sibling controls fire.
Dependencies: E8.SIMPLEX.FOURIER.01; E8.G31.CLOCK_ALPHABET.01; v4; v857; v858
Scripts: v874_feedback_decoder_lean.py
Location: tfpt_2_standard_model;tfpt_3;tfpt_research_contracts
Original CSV, line 713Original ledger status
E8.WINDING.DECODER.01
THE WINDING DECODER OF THE CLOCK ALPHABET (2026-08-08 round 36, v874; discovery probe g31_winding_decoder_probe.py 11/11, verdict WINDING-DECODER-EXACT; exact arithmetic). THEOREM: the v857 winding quadratic q_wind(t) = t^2 - g_car t + |Z2| maps the G31 clock alphabet {2, 3, 5, 6} = {|Z2|, N_fam, g_car, |R+(A3)|} (v858) to the atom quadruple (-|mu4|, -|mu4|, |Z2|, h(D5)) = (-4, -4, 2, 8) -- with q(2) = q(3) FORCED by the palindrome q(5-t) = q(t) (axis g_car/2) and 2 + 3 = 5 = g_car; the decoder polynomial D(y) = prod(y - q(a)) = (y+4)^2 (y-2)(y-8) = y^4 - 2y^3 - 48y^2 - 32y + 256 carries the signed budget coefficients (|Z2|, Omega_adm = N_fam dim S+ = 48, 2^g_car = 32, 2^rank(E8) = 256) with the double root -|mu4| forced by the palindrome pair; and THE FOURIER BRIDGE: |mu4| q(|Z2|)/|R(E8)| = 4 x (-4)/240 = -1/15 is EXACTLY the nonzero-character Walsh eigenvalue of the Gaussian shell census (E8.SIMPLEX.FOURIER.01; now global by E8.SHELL.GLOBAL.01), and -16 = |mu4| q(|Z2|) = rhat(u != 0). CONTROLS (all fire): sibling directions collapse the bridge (q2 -> 1/15, q3 -> 1/15, q_row -> -1/12); alternative alphabets change the decoder ({2,3,5,7}: constant 512 = 2^9 NOT 2^rank(E8); {1,2,3,5} different). HONEST LINES (typed): the -32 y coefficient survives in both alternatives -- per-coefficient selectivity is weak, the selective object is the full vector (-2,-48,-32,+256); the 6-vs-7 tension typed (replacing 6 by 7 loses the y^3/y^2/constant identifications). TYPE: exact AUDIT theorem, NOT a physical functor -- an explicit intertwiner would be needed to make it causal. NO physics claim beyond the audit statement.
Recorded status: Honest promotion of an exact integer theorem [typed evidence line: 11/11 checks, zero fails, verdict WINDING-DECODER-EXACT; frozen spec SHA 6a54768d...]
Dependencies, status detail and source
Canonical status: WINDING-DECODER-EXACT: q({2,3,5,6}) = (-4,-4,2,8); D(y) = (y+4)^2(y-2)(y-8) with budget coefficients (2,48,32,256); |mu4| q(|Z2|)/|R(E8)| = -1/15 == the Walsh message eigenvalue; typed audit-not-functor.
Dependencies: E8.G31.CLOCK_ALPHABET.01; E8.SIMPLEX.FOURIER.01; E8.SHELL.GLOBAL.01; FLAVOR.FEEDBACK.NORMALFORM.01; v857; v858
Scripts: v874_feedback_decoder_lean.py
Location: tfpt_1_architecture_e8;tfpt_3;tfpt_research_contracts
Original CSV, line 714Original ledger status
FORM.FLAVOR.FEEDBACK.01
LEAN 4 FORMALISATION of the feedback normal form (2026-08-08 round 36; TfptCarrier/FlavorFeedback.lean, 16 declarations, 11 theorems) -- AUDIT: PASS, no sorry, no native_decide, no domain axioms (#print axioms = propext, Classical.choice, Quot.sound on every theorem; lake build green 3418 jobs). Kernel-checked over Z with a SYMBOLIC s (no numeric specialization smuggled in): the three action identities R_s b0 = (s+4) b0 + 4 b2, R_s b1 = b2, R_s b2 = 3 b0 - 2 b1 + 5 b2 (the deformation enters ONLY through b0); THE CONJUGATION P F_s = R_s P (the inverse-free house form -- det P = -4 != 0 makes it P^{-1} R_s P = F_s over Q); THE CHARACTERISTIC POLYNOMIAL chi_{R_s}(X) = (X - (s+4))(X^2 - 5X + 2) - 12X in Z[X] via Matrix.charpoly and the 3x3 determinant expansion, with the s = 6 instance chi_L = X^3 - 15X^2 + 40X - 20; and THE LATTICE INDEX facts det P = -4, gcd(entries) = 1, gcd(2x2 minors) = 2 -- the determinantal divisors d1 = 1, d1 d2 = 2, d1 d2 d3 = 4 forcing the invariant factors (1, 2, 2), SNF diag(1,2,2), quotient Z2 (+) Z2. THE HONEST TYPING deliberately NOT a claimed isomorphism: Z2^2 has the CARDINALITY of mu4 but is not mu4 as a group -- the SNF computed in Lean is what makes that distinction kernel-checked rather than blurred. Mirrored numerically in v874 part C.
Recorded status: Formal [F] (Lean kernel; the action identities, the inverse-free conjugation, charpoly in Z[X], the SNF determinantal divisors -- with the Z2^2-not-mu4 typing doc-level)
Dependencies, status detail and source
Canonical status: Formal [F]: the feedback normal form is a Lean theorem family (11 theorems), standard axioms only, no sorry, full build green.
Dependencies: FLAVOR.FEEDBACK.NORMALFORM.01; FORM.QGEO.01
Scripts: lean4-carrier-rigidity/TfptCarrier/FlavorFeedback.lean
Location: tfpt_2_standard_model;tfpt_research_contracts
Original CSV, line 715Original ledger status
E8.SHELL.GLOBAL.01
THE GLOBAL GAUSSIAN SHELL THEOREM (2026-08-08 round 36, v875; discovery probe gaussian_shell_global_probe.py 15/15, verdict SHELL-GLOBAL-THEOREM) -- the census->theorem upgrade: the v857 value law 'Thetahat_u/Theta_L = -1/15 on odd shells' holds for ALL shells, no census cap. THEOREM: on V = L/(1+i)L of the Gaussian E8, for EVERY n >= 1: Theta_v(n) = (Theta_L(n) - Theta_0(n))/15 for all v != 0 (the division exact), Thetahat_u(n) = 16(16 1_{2|n} sigma_3(n/2) - sigma_3(n)) for every nontrivial character u, and at every ODD n: Thetahat_u(n) = -16 sigma_3(n), Thetahat_u(n)/Theta_L(n) = -1/15 EXACTLY. INPUTS (each warded): (i) LEMMA 1 -- every g in G31 is a norm-preserving bijection of L transporting classes ((4M)^T(4M) = 16I; complex linearity (4M)J = J(4M)); the induced group is Sp(4,2) (order 720, generated by the 60 symplectic transvections), TRANSITIVE on the 15 nonzero classes, and IDENTICAL to the shell-module class action (coordination verified on generators); (ii) LEMMA 2 -- (I+J)^T(I+J) = 2I and (1-J)/2 inverts (1+i) on L: Theta_0(2m) = Theta_L(m), Theta_0(odd) = 0 (from 2 = -i(1+i)^2); (iii) LEMMA 3 -- Theta_L(n) = 240 sigma_3(n) (classical Eisenstein E4; verified to n = 24 directly and via the v857 packet glue identity to n = 16500). The n <= 16500 census is RETAINED as the exact ward (matched everywhere, odd AND even). CONTROLS: the non-transitive subgroup <T_1> (11 orbits) admits an explicit invariant NON-uniform census with Walsh multiset {-48 x4, -16 x7, +16 x4} -- transitivity is load-bearing; the even-shell formula differs correctly (7/135 at n = 2: the -1/15 law is the ODD-shell statement only). This REPLACES the finite-census argument behind the v857 value theorem (dated note there); the consequence chain is kernel-checked in FORM.E8.SHELL.GLOBAL.01. NO physics claim beyond the audit statement.
Recorded status: Honest promotion of a proved shell law [typed evidence line: 15/15 checks, zero fails, verdict SHELL-GLOBAL-THEOREM; frozen spec SHA a4b2f6d9...]
Dependencies, status detail and source
Canonical status: SHELL-GLOBAL-THEOREM: Sp(4,2) transitivity + (1+i) doubling + Theta_L = 240 sigma_3 => Thetahat_u/Theta_L = -1/15 at ALL odd shells; census n <= 16500 retained as ward; non-transitive control breaks the law.
Dependencies: E8.SIMPLEX.FOURIER.01; E8.G31.CLOCK_ALPHABET.01; v857; v858; v868
Scripts: v875_shell_global_lean.py
Location: tfpt_1_architecture_e8;tfpt_3;tfpt_research_contracts
Original CSV, line 716Original ledger status
FORM.E8.SHELL.GLOBAL.01
LEAN 4 FORMALISATION of the global shell theorem's consequence chain (2026-08-08 round 36; TfptCarrier/GaussianShells.lean) -- AUDIT: PASS, no sorry, no native_decide, no domain axioms (#print axioms = propext, Classical.choice, Quot.sound on all 7 theorems; lake build green 3418 jobs). THE PATTERN (the house discipline): the ARITHMETIC CONSEQUENCE CHAIN is kernel-checked while the finite/structural inputs stay NAMED hypotheses with verification provenance typed on each field -- the hypothesis bundle ShellSystem carries (H1) equidistribution 15 Theta_v = Theta_L - Theta_0 (provenance: Sp(4,2) transitivity + shell invariance, machine-verified finite-range in v875), (H2) doubling Theta_0(2m) = Theta_L(m), Theta_0(odd) = 0 (exact from 2 = -i(1+i)^2), (H3) Theta_L = 240 sigma_3 for n >= 1 (classical, cited; finite-range verified); the 7 kernel-checked consequences: dvd_diff (the /15 division exact), decomposition, walsh_formula (15 Thetahat_u = 16 Theta_0 - Theta_L; the 16-coset Walsh combinatorics absorbed into the definition, typed), theta_v_odd, walsh_odd (Thetahat_u(2m+1) = -16 sigma_3(2m+1)), walsh_odd_ratio (15 Thetahat_u(2m+1) = -Theta_L(2m+1) -- the -1/15 statement as an integer identity, no division anywhere), walsh_even. sigma_3 is mathlib's ArithmeticFunction.sigma 3 -- nothing bespoke; no modular-forms machinery imported or claimed. Mirrored numerically in v875 part B.
Recorded status: Formal [F] (Lean kernel; the consequence chain from the named ShellSystem hypotheses -- every statement an exact integer identity)
Dependencies, status detail and source
Canonical status: Formal [F]: the shell consequence chain is a Lean theorem family (7 theorems from the named hypothesis bundle), standard axioms only, no sorry, full build green.
Dependencies: E8.SHELL.GLOBAL.01; FORM.QGEO.01
Scripts: lean4-carrier-rigidity/TfptCarrier/GaussianShells.lean
Location: tfpt_1_architecture_e8;tfpt_research_contracts
Original CSV, line 717Original ledger status
GATE.LEDGER.01
THE STATUS-LEDGER INTEGRITY GUARD (2026-08-08 round 36, v878_ledger_integrity.py 10/10; a CI sentinel, no new physics). THE TRIGGER: the round-36 ledger audit found the first PRIMARY-KEY violation -- claim_id FORM.QGEO.03 double-booked (2026-06-15 CohomologyGrading formalisation; 2026-06-18 SeamDeckClosure flat all-orders closure). THE FIX (this round, dated QA note on FORM.QGEO.04): the SeamDeckClosure row RENAMED FORM.QGEO.04; every flat-closure reference updated (tfpt_research_contracts, the two 2026-06-18 changelog mentions, v279/v284/v286 + seam_equivalence.json, make_figures, ResidualChain.tsx, script_registry, run_all); the CohomologyGrading row keeps FORM.QGEO.03; claim contents unchanged. THE GUARD (enforced in the suite from this round): S1 the 10-column schema + claim-id grammar + active flags; S2 claim_id GLOBALLY UNIQUE with the fix pinned; S3 every supersedes target exists, the supersession graph ACYCLIC (Tarjan), no self-supersession; S4 UNIQUE ACTIVE SUPERSESSION TARGETS modulo the frozen remove-only allowlist of the two legitimate 2026-06 joint closures (FLAV.UGATE.01 <- FLAV.RIGID.01+02; GATE.QGEO.01 <- FLAV.QGEO.02+03); S5 the dependencies column typed honestly as a CROSS-REFERENCE field (mutual evidence pointers, not a build DAG): claim-like tokens must resolve or stay within the frozen 37-token legacy list, the mutual-reference cycle census frozen REMOVE-ONLY (<= 13 SCCs, subset of the frozen 265 ids -- the audit_baseline.json precedent), no self-dependency; acyclicity thereby enforced as NO NEW CYCLES. Python-only (stdlib).
Recorded status: Identity [I] (CSV integrity sentinel; frozen baselines remove-only)
Dependencies, status detail and source
Canonical status: Ledger integrity enforced: unique claim_id (active + global), acyclic supersession with existing targets, unique active supersession targets modulo the frozen 2-pair allowlist, dependency cross-reference census frozen remove-only.
Dependencies: FORM.QGEO.01; FORM.QGEO.02; FORM.QGEO.04
Scripts: v878_ledger_integrity.py
Location: tfpt_research_contracts
Original CSV, line 718Original ledger status
CFIN.QSTAR.NORMALFORM.01
v880 (part 1) -- the closed census-free normal form of the distinguished quadratic refinement: q*(x) = sum_{i<j} x_i x_j + sum_i x_i = C(|x|+1, 2) mod 2, WEIGHT-ONLY with value table (0,1,1,0,0); the 16 refinements of the bit form ARE the 16 linear shifts of the polar quadric and the frozen v845 selector acts on the linear part as c1=c2=c3 (4) -> c4=1 (2) -> c1=1 (1), FORCING c = (1,1,1,1) -- the 2^16 search is replaced by a theorem; zeros = {0} u the five ovoid messages (weights 3, 4); sigma splits 5 = 1+1+3 and 10 = 1+3+3+3 (9 = N_fam^2 family cycles). Probe qstar_doily_anchor_probe.py S1 (26/26 total, FINITE-ANCHOR-CLOSED).
Recorded status: Exact identity-grade theorem [Identity]: closed boolean normal form, census-free derivation; no marker move (Python-only per GATE.WOLFRAM.02)
Dependencies, status detail and source
Canonical status: FINITE-ANCHOR-CLOSED (S1): q* = polar quadric + forced linear part (1,1,1,1); weight-only (0,1,1,0,0); sigma splits 5 = 1+1+3, 10 = 1+3+3+3
Dependencies: NORMALFORM.CFIN.01; v845; v774
Scripts: v880_finite_anchor_theorems.py
Location: tfpt_1;tfpt_3
Original CSV, line 719Original ledger status
DOILY.ANCHOR.CLASSIFY.01
v880 (part 2) -- the EXCLUSIVE anchor classification of PG(3,2) lines: EVERY of the 15 doily (isotropic) lines carries the local weight multiset {2 - q*} = {2,1,1} = the anchor a = (1,1,2) (per-line charpoly (t-2)(t-1)^2, elementary symmetric (4,5,2) with e2 = g_car, e3 = |Z2|), and NO other line does: the 20 non-isotropic lines split EXACTLY as 10 secants ({0,0,1} = the WRONG anchor (1,2,2), Vieta (5,8,4)) + 10 external lines ({1,1,1}); incidence budget 15 = M_0 and 30 = M_1 = h(E8) (counting only, no bijection claimed). Anchor-Vieta report: p2(a) = 6, chi_L - chi_R = -p2(a)(t^2 - e2 t + e3), M_n = 15(1, e3, e1, e1 e3, e1^2), rank N = C(e2,2) = 10, ker = e2 = 5. Probe S2+S5.
Recorded status: Exact identity-grade theorem [Identity]: the anchor law characterizes the doily among ALL 35 lines (exclusivity census 15 + 10 + 10); no marker move
Dependencies, status detail and source
Canonical status: FINITE-ANCHOR-CLOSED (S2/S5): doily lines = anchor multiset {2,1,1}, Vieta (4,5,2); secants = wrong anchor (1,2,2); external = (1,1,1); ladder and flavor identities in anchor notation
Dependencies: CFIN.QSTAR.NORMALFORM.01; MESSAGE.LADDER.01; v832; v844; v857
Scripts: v880_finite_anchor_theorems.py
Location: tfpt_1;tfpt_3
Original CSV, line 720Original ledger status
DOILY.HODGE.FACTOR.01
v880 (part 3) -- the doily IS the multiplication table Lambda^2 E x Lambda^2 E -> Lambda^4 E of the five-slot carrier: via the v845 parity lift the three iota-supports of every doily line partition {1..5} as {i} u {j,k} u {l,m}; b_jk ^ b_lm = +-f_i EXACT (integer exterior algebra); the map line -> (i; {j,k},{l,m}) is a BIJECTION onto all 5 x 3 = 15 configurations (three perfect matchings per carrier slot); CONVERSE: the wedge is nonzero EXACTLY on doily lines (external lines: all pairwise products vanish; secants carry <= 1 pair point). Probe S3.
Recorded status: Exact identity-grade theorem [Identity]: the incidence geometry IS the Clifford multiplication; no marker move
Dependencies, status detail and source
Canonical status: FINITE-ANCHOR-CLOSED (S3): support partition + exact wedge factorization + bijection 15 = 5 x 3 + converse (nonzero exactly on doily lines)
Dependencies: CFIN.QSTAR.NORMALFORM.01; v845; v774; v854
Scripts: v880_finite_anchor_theorems.py
Location: tfpt_1;tfpt_3
Original CSV, line 721Original ledger status
P2.QUADRATIC.EXHAUSTION.01
v880 (part 4) -- QUADRATIC ONE-STEP EXHAUSTION FORCES g_car = 5 ([E] theorem / [O] premise split): the demand Lambda^2 E ^ Lambda^2 E = Lambda^{g-1} E (one quadratic composition step exhausts the top nontrivial half-spinor sector) holds for EXACTLY one odd g in {3, 5, 7, 9, 11}, namely g = 5 (exact rank 5 = dim Lambda^4; S+ = 1 + 10 + 5 = 16); even control g = 4 breaks the half-spinor demand. THE THEOREM IS [E]; the PHYSICAL premise (the Calderon boundary kernel satisfies one-step quadratic exhaustion) is [O]/[C] -- P2 stays narrowed to v799's R1', NOT eliminated; NO marker move (per the review, the open physical premise must not be buried under a green finite module). Probe S4.
Recorded status: Exact algebraic theorem [Identity] with the [O]/[C] physical premise EXPLICITLY typed and NOT claimed: P2 unchanged
Dependencies, status detail and source
Canonical status: FINITE-ANCHOR-CLOSED (S4): one-step exhaustion <=> g = 5 (unique among odd g); the Calderon premise stays [O] -- the sharpened but open half of P2
Dependencies: AX.P2.01; NORMALFORM.CFIN.01; v799; v845
Scripts: v880_finite_anchor_theorems.py
Location: tfpt_1;tfpt_3;tfpt_research_contracts
Original CSV, line 722Original ledger status
DOILY.PLUCKER.GR25.01
THE GR(2,5) PLUCKER READING + THE S6 SPECHT CHANNELS + THE HADAMARD ANCHOR + THE VACUUM SELECTION (closed 2026-08-09, round CV; promoted round CVIII in v888; probe s6_plucker_hadamard_probe.py 27/27 S6PLUCKER-CLOSED, exact integer/sympy): (1) the 15 doily lines ARE the 15 monomials of the five Plucker quadrics of Gr(2,5) -- bijection 15/15 with PERFECT sign match (every quadric reads (+,-,+) = the v880 Hodge table; converse warded: secants/externals produce no monomial); (2) the S6 duad representation decomposes 15 = 1 + 5 + 9 (Specht S(6) + S(5,1) + S(4,2)) and the normalized doily operator acts by the scalars (1, 0, 2/3) EXACTLY, with 2/3 = e_3/(e_2 - e_3) and 15 = 1 + e_2 + (e_2 - e_3)^2 at the anchor (4, 5, 2); (3) the q* zero set is a (16, 6, 2) Hadamard difference set with the anchor signature (v, k, lambda, v-k) = (2^{e_1}, p_2, e_3, C(e_2, 2)) = (16, 6, 2, 10), bent ward |W| = 4 on all 16 characters; (4) THE VACUUM-SELECTION THEOREM: Sp(4,2) = S6 acts transitively on the 6 Arf-1 refinements; Stab(q*) has order 120 acting faithfully as S_5 on the remaining five; its orbits on the 16 messages are [1, 5, 10] EQUAL AS SETS to (Lambda^0, Lambda^4, Lambda^2) -- the five-slot carrier is the residual symmetry after choosing one of six equivalent vacua. Controls: Arf-0 has census (16,10,6); a secant breaks the bijection; the wrong scalar breaks the channel law. All exact; no marker moves.
Recorded status: Closed finite theorems [E]: four exact statements; the physical vacuum-selection mechanism stays [O]; no marker move
Dependencies, status detail and source
Canonical status: CLOSED [E]: doily = the Plucker monomial incidence of Gr(2,5) with exact signs; Specht channels (1, 0, 2/3); (16,6,2,10) anchor signature; S6 -> S5 vacuum selection
Dependencies: CFIN.QSTAR.NORMALFORM.01; DOILY.ANCHOR.CLASSIFY.01; DOILY.HODGE.FACTOR.01; v880; v845; v844
Scripts: v888_finite_pfaffian_signature.py
Location: tfpt_1;tfpt_research_contracts
Original CSV, line 723Original ledger status
CFIN.AUT.FLAVOR.C6.01
THE FLAVOR HEXAGON IS THE COMPILER AUTOMORPHISM ORBIT (closed 2026-08-09, round CV; promoted round CVIII in v888; probe cfin_aut_flavor_probe.py 19/19 C6FLAVOR-MEASURED + INTERTWINED): Aut(C_fin) recomputed by exhaustive enumeration = C_6; the pinned generator g satisfies g^2 = the deployed family 3-cycle sigma EXACTLY (sharp, not inverse) and g^3 = the W-edge sheet swap (the S_2 factor of Stab_{S5}(W); honest: no sheet involution is deployed on V itself); the induced action on Lambda^2 E has cycle type 1 + 3 + 6 with orbits = the charge-pure Petersen distance shells, and the 6-orbit IS the deployed v808 hexagon transport edge for edge (up to D_6, orientation -1); the recovery value reads as one full automorphism orbit: (|Z_2|/N_fam)^{|Aut(C_fin)|} = (2/3)^6 = 64/729 == the frozen corpus value (exact Fractions, no fit; typed as a consistent NEW READING -- the corpus derivation via p_2 = |R+(A3)| stands). CONTROL (census, not narration): 0 of the 600 symplectic maps preserving hbar but not q* factor consistently as g^2/g^3; a scrambled transport table fails the D_6 match. Exact arithmetic; no marker moves.
Recorded status: Closed finite theorem [E] (the intertwiner exists and is exact; the exponent reading is typed as consistent, not as the unique derivation); no marker move
Dependencies, status detail and source
Canonical status: CLOSED [E]: g^2 = sigma exact; the hexagon = the Aut(C_fin) 6-orbit on Lambda^2 E; (2/3)^6 = the recovery value; 0/600 non-automorphisms factor
Dependencies: v845; v849; v808; v857
Scripts: v888_finite_pfaffian_signature.py
Location: tfpt_1;tfpt_2;tfpt_research_contracts
Original CSV, line 724Original ledger status
DOILY.PFAFFIAN.WICK.01
THE FERMIONIC PFAFFIAN SIGNATURE OF THE FINITE COMPILER (closed 2026-08-09, round CVII; promoted round CVIII in v888; probe k6_pfaffian_selfhosting_probe.py 42/42 K6PFAFFIAN-CLOSED, exact integer/sympy, first frozen run): (1) THE K6 MOTIF THEOREM (CFIN.K6.MOTIF.01): under the corpus duad labeling the 35 lines of PG(3,2) are EXACTLY 15 perfect matchings of K6 (= the doily) + 10 triangles through the vacuum vertex (= the secants, weights {2,2,1} = the wrong anchor) + 10 triangles avoiding it (= the external lines); q*(e) = 0 iff e touches the vacuum -- the referee bit of relations; (2) THE SIGN THEOREM: the fermionic Pfaffian signs sgn(M) of the symbolic 6x6 expansion match the corpus Hodge table under the CANONICAL global character chi(i) = (-1)^{i+1} on the five vacuum edges -- triple-identified as the vacuum-row Laplace sign (Pf(A) = sum_i (-1)^{i+1} a_0i Pf(A_0i-hat) symbolic, each 4x4 minor Pfaffian = the Gr(2,5) Plucker quadric), the Lambda^4/Lambda^5 volume-form conversion (verified on all 15), and the C6 crossing character (Pf(PAP^T) = det(P) Pf(A) symbolic; sgn(pi(M)) = det(pi) c_pi(M) sgn(M) on all 15) -- a global gauge, NOT a line-dependent fudge (the flipped-chi control produces exactly the 3 expected mismatches); (3) THE SELF-HOSTING COUNTING THEOREM (P2.SELFHOSTING.PAIRING.01): C(g+1, 2) = g!! has g = 5 as its ONLY nontrivial solution (g = 1 trivial; separation for g >= 7 symbolic via g^2 - 3 > 0), and (g-2)!! = 3 = N_fam -- the [E] theorem behind the review's self-hosting pair-compiler reading; THE PHYSICAL PREMISE (the boundary grammar IS a self-hosting Wick pair compiler) stays [O] -- P2 narrowed to ONE premise, NOT eliminated, no marker move; (4) ANCHOR.MOD30.CLOCK.01: p_n = 2 + 2^n with p_{n+1} = 2 p_n - 2 has the mod-30 orbit 4 -> 6 -> 10 -> 18 -> 4 (period 4 = |mu_4|); anti-numerology census: the purely period-4 moduli below 100 are exactly {5, 10, 15, 30}, all dividing 30, lcm 30 -- CLOCK-DISTINGUISHED (30 is the maximal/universal clock), with the honest caveat that 5/10/15 already realize period 4; (5) the 6 one-factorizations of K6 (each matching in exactly 2; 30 = 6 x 5 = 2 x 15) carry the exceptional-outer-automorphism signature ((1,1,1,1,2) on vertices vs (2,2,2) on factorizations); NO canonical vertex-factorization bijection (typed). The operative-Coxeter-30 reading is separately DEAD (coxeter_schedule_probe.py 28/28 SCHEDULE-DEAD, sandbox: no root orbit realizes the 15 classes x2 -- best 12/15; the K6 side allows at most 3/15 separation-15 pairings; w^15 = -1 makes the 15-shift automatic; the counting identity 30 = 2 N_fam g_car stands). All controls fire; no marker moves.
Recorded status: Closed finite theorems [E] + one honest kill (the operative-30 reading); the Wick-compiler premise stays [O]; no marker move
Dependencies, status detail and source
Canonical status: CLOSED [E]: fermionic Pfaffian signs gauge-matched via canonical chi = Laplace/volume-form/C6 character; self-hosting forces g = 5 (N_fam = 3); mod-30 clock distinguished; operative-Coxeter-30 dead
Dependencies: DOILY.PLUCKER.GR25.01; DOILY.HODGE.FACTOR.01; P2.QUADRATIC.EXHAUSTION.01; v880; v868
Scripts: v888_finite_pfaffian_signature.py
Location: tfpt_1;tfpt_research_contracts
Original CSV, line 725Original ledger status
SEAM.CFIN.WICKFUNCTOR.01
THE WICK FUNCTOR ARC [O] (constructed/obstructed/resolved 2026-08-09, rounds CVIII-CX; promoted round CXI in v896): (1) THE SIX ROLES EXIST in the deployed seam system (D5 slot pairs + A3 boundary block on the 16-dim one-particle space; so(16) sector law, q* edge grading, C6 intertwining all exact) but the deployed vacuum kernel is channel-diagonal (all 15 duad two-point functions vanish); (2) THE PROVED SCALAR OBSTRUCTION (SEAM.CFIN.WICKMIX.01): the pinned C6 generator's 2-cycle {4,5} reverses one duad orientation, so every C6-covariant antisymmetric scalar channel covariance vanishes there (max 14/15; the orbit law exact; both relaxation witnesses constructed: C3 = <g^2> gives 15/15, the 16-dim block object exists but no equivariant scalarization); (3) THE BLOCK RESOLUTION (SEAM.CFIN.WICKBLOCK.01): the C6-covariant cross-block space has dimension 33; the canonical block covariance is exactly covariant, strictly CAR-positive, carries 15/15 blocks and 15/15 block Wick monomials with the canonical chi sign law (interleaving character symbolically +1); THE DECISIVE FACT: the deployed seam covariance (v113 family rebuilt exactly) has ZERO cross-blocks everywhere (SEAM-DIAGONAL). DEMAND (final form): a physical channel-mixing mechanism (a boundary/transport-twisted state, not the vacuum) realizing the block functor's value level -- then the K6/Pfaffian grammar of v888 would be the measured correlation grammar of the seam. The [O] premise is unmoved; no marker moves. CANDIDATE NOTE (2026-08-09, round CXV): the mixing-mechanism demand now has a CONSTRUCTED CANDIDATE (SEAM.CFIN.KMSMIX.01 / v898: the C6-covariant mixing KMS state passes ALL block-functor gates and the exact Schur elimination of the boundary generates all 10 carrier duads from the bare diagonal state; the frozen 15-signature table is the registered prediction; RP-THETA-OPEN is the named open check); whether the ACTUAL seam realizes it is untouched -- the [O] premise stays unmoved.
Recorded status: Open contract [O] (structure exact, obstruction proved, block candidate constructed; the physical mixing mechanism is the demand)
Dependencies, status detail and source
Canonical status: Open [O]: block functor constructed; the mixing mechanism has a constructed candidate state (v898) -- the physical realization is the demand
Dependencies: DOILY.PFAFFIAN.WICK.01; P2.QUADRATIC.EXHAUSTION.01; v888; v113
Scripts: v896_wick_block_functor.py
Location: tfpt_1;tfpt_research_contracts
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