Skip to main content

A registered result in its source context

Original ledger classification: Closed finite theorems [E]: four exact statements; the physical vacuum-selection mechanism stays [O]; no marker move

Recorded statement: 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):…

Statement, assumptions and sources

Paper context: Research contracts

The exact identifier, original classification and full claim are available below.

The source wording and classification below are preserved as recorded. A paper link, shared script or authored topic relation does not upgrade the claim or report a new proof run. Read later reviewed findings separately.

Read the exact registered claim and its dependencies

DOILY.PLUCKER.GR25.01

Original ledger classification: Closed finite theorems [E]: four exact statements; the physical vacuum-selection mechanism stays [O]; no marker move

Original claim text

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.

Original classification detail

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 as recorded

CFIN.QSTAR.NORMALFORM.01; DOILY.ANCHOR.CLASSIFY.01; DOILY.HODGE.FACTOR.01; v880; v845; v844

Open the original ledger source, row 723

Location recorded in the ledger

These document locations are recorded directly on the ledger row. They are document level navigation, rather than a newly inferred section citation.

Sections that explicitly cite this claim

A literal claim identifier is present in these paper sections. The section and its premises determine what the citation supports.

Navigation through a shared verification script

These sections cite a script associated with the claim. This is a source navigation join, rather than an explicit citation of the claim or a theorem equivalence.

Registered verification modules

  • v888_finite_pfaffian_signature.pyRegistered verification module · core
    Read the description recorded in the module registry

    DOILY.S6.IRREP.01 + DOILY.PLUCKER.GR25.01 + CFIN.ANCHOR.HADAMARD.01 + CFIN.S6.VACUUM.01 + CFIN.AUT.FLAVOR.C6.01 + CFIN.K6.MOTIF.01 + DOILY.PFAFFIAN.WICK.01 + P2.SELFHOSTING.PAIRING.01 + ANCHOR.MOD30.CLOCK.01: **die komplette endliche Pfaffian/K₆-Signatur (27/27 + 19/19 + 42/42, exakte Ganzzahl/sympy)** — Specht-Kanäle (1, 0, 2/3) exakt; die 15 Doily-Linien SIND die 15 Plücker-Monome von Gr(2,5) mit perfektem Vorzeichen-Match; (16,6,2,10)-Hadamard-Anker; S₆→S₅-Vakuumselektion (Orbits [1,5,10] mengengleich (Λ⁰,Λ⁴,Λ²)); DER FLAVOR-HEXAGON IST DIE Aut(C_fin)-BAHN (g² = σ exakt, (2/3)⁶ = Recovery, 0/600 Nicht-Automorphismen faktorisieren); K₆-Motiv (35 = 15 Matchings + 20 Dreiecke); die fermionischen Pfaffian-Vorzeichen GAUGE-MATCHED via kanonischem χ(i) = (−1)^{i+1} (dreifach identifiziert); SELFHOSTING: C(g+1,2) = g‼ ⟹ g = 5 einzig nichttrivial, N_fam = 3 ([E]-Satz, Wick-Prämisse [O]); Mod-30-Uhr CLOCK-DISTINGUISHED ({5,10,15,30}, lcm 30); äußere-Automorphismus-Signatur exakt.

A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.

Search later reviewed research for this identifierRead the coverage boundaries