Original ledger status
DOILY.PLUCKER.GR25.01
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
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