Original 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
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
DYN.MARKOV.EMBED.01
THE MARKOV EMBEDDING CONTRACT (registered 2026-08-27; 'three meanings of dynamics' split, step (a)->(b)). FINITE KERNEL HALF [E] (v971, sympy-exact): for the v221 seam transfer kernel T (spectrum exactly {1, 64/729, 1/729}) the principal logarithm Q = log T is an EXACT classical Markov generator -- e^Q = T by exact spectral calculus; row sums symbolically zero; off-diagonals exactly {ln(9/8), 2 ln 3, 2 ln 3} = {0.117783, 2.197225, 2.197225} > 0 (the reviewer's independently verified numbers), diagonals -ln(81/8), -ln(81/8), -4 ln 3; uniformization certificate Q + (4 ln 3) I >= 0 entrywise (diagonals ln 8, ln 8, 0, exact) => e^{tQ} positivity-preserving doubly stochastic for ALL t >= 0, T embeddable, every root T^{1/n} stochastic; spec(Q) = -spec(H_mod) = {0, -6 ln(3/2), -6 ln 3} (gap = Delta = 6 ln(3/2)); detailed balance w.r.t. the uniform state. NEGATIVE CONTROL: second eigenvalue -1/10 gives det = -1/200 < 0 -- provably NOT embeddable (det e^Q = e^{tr Q} > 0 always); embeddability is not generic, the RP/OS spectral positivity (CONTRACT.F.01 axiom 3) is the enabling fact. WHAT STAYS [O]: the same embedding statement at FIELD level (reconstructed net / quasi-local algebra, uniform in system size). FIREWALL: e^{tQ} is irreversible statistical dynamics (H-theorem), NOT unitary evolution -- step (b)->(c) is the separate contract DYN.UNITARY.DILATION.01; the shared F_transfer relaxation shape is a universal CONTRACTION CLASS, not one physical clock (v723/v724/v777). Python-only per GATE.WOLFRAM.02 (matrix-log/spectral identities; the exact rationals 64/729, 1/729 already mirrored).
Recorded status: Contract [E] (finite kernel embedding, sympy-exact; v971) + [O] (field level)
Dependencies, status detail and source
Canonical status: [E] the finite kernel half: Q = log T is an exact Markov generator (row sums 0, off-diagonals ln(9/8), 2ln3, 2ln3 > 0, uniformization positivity for all t >= 0); [O] the field-level embedding
Dependencies: v221 (kernel); v957 (T = e^{-H_mod}); CONTRACT.F.01 (axiom 3 positivity); v723/v724/v777 (external clocks)
Scripts: v971_markov_embedding_generator.py
Location: tfpt_research_contracts
Original CSV, line 741Original ledger status
TRANSFER.HIDDEN.CIRCULATION.01
THE HIDDEN CIRCULATION CONTRACT, executed half (registered 2026-08-27; external-review round, companion of the DYN.MARKOV.EMBED.01/DYN.UNITARY.DILATION.01 split). [E] (v976, sympy/Fraction-exact): (1) the Birkhoff fibre of the seam single step B (exact sixth root of the v221 kernel; B = (1/2)I + (1/18)P12 + (2/9)P13 + (2/9)P23 bit-exact) is EXACTLY a one-parameter line w_t, t in [0, 1/18], because the decomposition map on R[S3] has the 1-dim kernel (even - odd); the hidden parameter is the sign-character Fourier coefficient w_t-hat(sgn) = 6t; populations are exactly t-free and no fibre member is chiral (w(C123) = w(C132) forced -- the typed obstruction for any chirality reading). (2) THE DISCRIMINATOR: one-step coherence dynamics is the weighted left regular S3 representation with spectrum {1, 6t, 2/3 x2, 1/3 x2} exactly; the triangle loop current A is an exact eigen-observable Psi_t(A) = 6t A (population-blind; one step + one current readout measures t, no ancilla; one-step tomography rank 6 determines all six weights). (3) CONTRAST-QUBIT CHOI LAW: spec(Choi^{T2}) = {-3t/2, 1/6+3t/2, 1/3+3t/2, 1/2-3t/2} symbolically; CRITICALITY lambda_min = (1 - lambda2 - lambda3 - 6t)/4 with lambda2 + lambda3 = 2/3 + 1/3 = 1 EXACTLY: t = 0 sits precisely ON the entanglement-breaking boundary (mutated spectra {2/3,1/2}/{1/2,1/3} miss by -1/12/+1/12 -- criticality not generic); the squared channel is PPT on the whole range (endpoint minima 1/9, 1/12). (4) FULL-LEVEL NPT PERSISTENCE: lambda_min(Choi(Psi_t^n)^{T2}) = -(1/3)(2/3)^n, t-independent (exact eigenvalue for n in {1,2,6}; float minimum n = 1..8) -- the 3-level family is never EB at tested n (pinned by the invariant coherent state (1,1,1)/sqrt3). (5) THE NO-GO for DYN.UNITARY.DILATION.01: the deployed Kraus dilation K_ij = sqrt(T_ij)|i><j| is measure-and-prepare (one step kills every coherence, fully symbolic), its Choi is diagonal => entanglement breaking => quantum capacity 0; C_0(T) = 0 exactly (T entrywise > 0); the Kraus channel is NOT in the Birkhoff fibre. (6) BINARY MESSAGE (KKT, 50 digits): p* = (1/2, 1/2, 0) exactly capacity-achieving for BOTH T and B; C(T) = 0.00835801913781 bit, C(B) = [13 log2(13/7) - log2 7]/18 = 0.4890415237 bit, ratio 1.709%. [C] literature-typed: PPT<=>separable in 2x2 (Peres-Horodecki), separable Choi <=> EB (Horodecki-Shor-Ruskai quant-ph/0302031), EB index (Lami-Giovannetti 1411.2517) => qubit n_EB = 1 (t = 0) / 2 (t > 0). [C] VALUE COINCIDENCE (observation, NOT a theorem): the t = 0 weights (9,1,4,4)/18 = (3^2,1^2,2^2,2^2)/18 hit the v652 c = 0 defect-ladder values 2*Delta = g^2/18 including w(I) = 1/2 = 2*Delta(gt=3); multiplicity matches only at g = 2; the forcing functor (CFT defect dimension -> Birkhoff weight) is the OPEN half, named TRANSFER.DEFECT.BIRKHOFF.01. OPEN: the physical selection of a fibre point t; any 4D/flavor reading. Python-only per GATE.WOLFRAM.02 (channel/Choi/Birkhoff algebra; the exact seam rationals already mirrored).
Recorded status: Identity [E] (executed half: fibre line, discriminator, criticality, EB no-go, KKT) + literature [C]; fibre-point selection open
Dependencies, status detail and source
Canonical status: [E] the Birkhoff fibre of B is the sign-character line t in [0,1/18]; loop-current discriminator Psi_t(A) = 6t A; qubit Choi law -3t/2 with EB criticality 2/3 + 1/3 = 1; full-level NPT -(1/3)(2/3)^n; the deployed Kraus dilation is EB (Q = 0, C_0 = 0); binary-message KKT certificates; [C] defect-Birkhoff value coincidence (forcing functor OPEN as TRANSFER.DEFECT.BIRKHOFF.01)
Dependencies: DYN.UNITARY.DILATION.01; DYN.MARKOV.EMBED.01; QEC.SEAM.01; v221_seam_qecc.py; v652_orbifold_arf.py
Scripts: v976_seam_lift_birkhoff.py
Location: tfpt_research_contracts
Original CSV, line 743Original ledger status
TRANSFER.COHERENT.WILSON.01
THE COHERENT WILSON CONTRACT, executed half (registered 2026-08-27; external-review round, companion of TRANSFER.HIDDEN.CIRCULATION.01). [E] (v977, sympy-exact): (1) UNISTOCHASTICITY: the seam single step B equals |U_ij|^2 entrywise for an exact U in SU(3); the angles are forced by B (sin^2 th13 = 2/9, sin^2 th12 = 1/14, sin^2 th23 = 2/7), cos delta = -4/sqrt(65) is uniquely solved, so the complete lift set up to rephasing is the two-branch family {U, U*} with e^{i delta} = (-4 +- 7i)/sqrt(65). (2) THE WILSON DATA ARE CLASSICAL UP TO ONE SIGN: J = 1/27 exact, Re of every plaquette fixed by B through unitarity (Re Q_{12;12} = -5/324, J^2 = 1/729 from B alone) -- the classically invisible datum is the Z2 orientation bit sgn J (U* lifts the same B with J = -1/27); minimal observable = the plaquette interference readout Im(U11 U22 U12* U21*). (3) THE 5-12-13 CODE: Q_{12;12} = (-5+12i)/324, normalized (-5+12i)/13 with 5^2 + 12^2 = 13^2 (atoms 5 = g_car, 12 = dim g_SM, 13 = Delta_Q = N(3+2i)); all nine plaquettes close on four Gaussian phase types with norms exclusively {10, 13, 130, 169} = {2*5, 13, 2*5*13, 13^2}; every plaquette has Im = +-1/27; the four fundamental plaquettes generate all nine via exact B-weighted composition. (4) THE CENTER BRIDGE: disc chi_A = 65 = det(A-I)^2 + (det A/2)^2 = 4^2 + 7^2 for the v530 atom matrix A = [[8,2],[5,3]], and e^{i delta} = (-det(A-I) +- i det A/2)/sqrt(disc chi_A) equals the transport-lift phase EXACTLY; -4+7i = (1+2i)(2+3i) with Gaussian norms 5, 13 (the v738 tower primes); NEGATIVE controls: the v530 siblings A_K (disc 48 vs identity 13) and A_Q (disc 13 vs 13/4) FAIL the identity -- the bridge selects the atom quotient A. (5) POWER LAW + RATIONALITY SELECTION: J_n^2 = (1-b)^2(1+2b-3a^2)/108 (a = (2/3)^n, b = (1/3)^n), every B^n unistochastic with its own U_n (U_6 built, |U_6|^2 = T exact); |J_6| = 0.0951088904 = 0.9884006 J_max; the uniform limit lifts to the Fourier matrix F3 at J_max = 1/(6 sqrt 3) exactly; J_n is RATIONAL ONLY at n = 1 (the deployed step hits 3(1+2b-3a^2) = 1 exactly, so J = 1/27) -- the Gaussian-Pythagorean code selects the single step. (6) NO FIXED MICROSTEP: B^2 != |U^2|^2 exact, and the Dirichlet recurrence witness n* = 967909 has min diag |U^{n*}|^2 = 0.999999 while B^{n*} is uniform to 5.6e-17 -- no single closed unitary generates the relaxing sequence; repeated steps require dephasing between steps, the six-step macro-gate U_6 is NOT U_1^6 (the coherent sharpening of the k5 clock-vs-walk verdict). (7) SELECTIVITY (hard kill passed): the obstruction certificate J^2 = -1/64 < 0 fires on the classic non-unistochastic control; mutated spectra give irrational J; census over 238 valid family points: 4 rational-J, EXACTLY ONE full 5-12-13 code point = the deployed (2/3, 1/3) (0.42% << the preregistered 10% kill). (8) PMNS NEAR-MISS stays NEGATIVE: branch phase 240.2551 deg near the deployed 240 deg (4pi/3, v270) but J_tr = -1/27 = -0.037037 != J_PMNS = -0.02965 and all three angles differ -- NO PMNS derivation. [C] literature: coherification by a reversible unitary iff unistochastic (Dunkl-Zyczkowski 0909.0116; Korzekwa et al. 1710.04228); a unitary lift carries quantum capacity log2 3. OPEN: the physical selection of sgn J; the A -> angles intertwiner (the bridge fixes the PHASE from A-invariants, the ANGLES come from B alone); any CP/time-orientation reading. Python-only per GATE.WOLFRAM.02 (SU(3)/plaquette/center-bridge symbolic algebra with nested radicals).
Recorded status: Identity [E] (executed half: unistochastic lift, Wilson code, center bridge, selectivity census) + literature [C]; branch selection and intertwiner open
Dependencies, status detail and source
Canonical status: [E] B unistochastic with exact SU(3) lift {U, U*}, J = +-1/27; 5-12-13 plaquette code (norms {10,13,130,169}); center bridge disc chi_A = 65 = det(A-I)^2 + (det A/2)^2 with sibling negatives; rationality selection (J_n rational only at n = 1); census unique full-code point = deployed (2/3, 1/3); no fixed microstep (Dirichlet witness); [C] coherification literature; PMNS near-miss stays negative; sgn J and the intertwiner OPEN
Dependencies: TRANSFER.HIDDEN.CIRCULATION.01; DYN.UNITARY.DILATION.01; v530_center_quotient_compiler.py; v738_hecke_mod_ramified.py; v270_pmns_jarlskog_assembly.py
Scripts: v977_transfer_unistochastic_wilson.py
Location: tfpt_research_contracts
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