A registered result in its source context

DOILY.PFAFFIAN.WICK.01

Original ledger classification: Closed finite theorems [E] + one honest kill (the operative-30 reading); the Wick-compiler premise stays [O]; no marker move

Original claim text

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.

Original classification detail

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 as recorded

DOILY.PLUCKER.GR25.01; DOILY.HODGE.FACTOR.01; P2.QUADRATIC.EXHAUSTION.01; v880; v868