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Original ledger classification: Exact identity-grade theorem [Identity]: the anchor law characterizes the doily among ALL 35 lines (exclusivity census 15 + 10 + 10); no marker move

Recorded statement: 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…

Statement, assumptions and sources

Paper context: Architecture, E8 and the electromagnetic fixed point

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DOILY.ANCHOR.CLASSIFY.01

Original ledger classification: Exact identity-grade theorem [Identity]: the anchor law characterizes the doily among ALL 35 lines (exclusivity census 15 + 10 + 10); no marker move

Original claim text

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.

Original classification detail

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 as recorded

CFIN.QSTAR.NORMALFORM.01; MESSAGE.LADDER.01; v832; v844; v857

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Location recorded in the ledger

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Registered verification modules

  • v880_finite_anchor_theorems.pyRegistered verification module · core
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    CFIN.QSTAR.NORMALFORM.01 + DOILY.ANCHOR.CLASSIFY.01 + DOILY.HODGE.FACTOR.01 + P2.QUADRATIC.EXHAUSTION.01: **die vier endlichen Anker-Sätze (26/26, FINITE-ANCHOR-CLOSED)** — die geschlossene, zensus-freie Normalform q*(x) = Σ_{i<j}x_ix_j + Σx_i = C(|x|+1,2) mod 2 (gewichts-rein; Selektor auf dem Linearteil erzwungen); die EXKLUSIVE Anker-Klassifikation der PG(3,2)-Linien (alle 15 Doily-Linien tragen {2,1,1} = a = (1,1,2), Linien-Vieta (4,5,2); 10 Sekanten = falscher Anker (1,2,2), 10 externe); die Doily als Multiplikationstafel Λ²E×Λ²E→Λ⁴E des Fünf-Slot-Carriers (Wedge ≠ 0 GENAU auf Doily-Linien); Ein-Schritt-Exhaustion erzwingt g = 5 ([E]-Satz, Calderón-Prämisse bleibt [O] — P2 verengt, nicht eliminiert). Alle Kontrollen feuern.

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