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A registered result in its source context

Original ledger classification: Exact algebraic theorem [Identity] with the [O]/[C] physical premise EXPLICITLY typed and NOT claimed: P2 unchanged

Recorded statement: v880 (part 4) -- QUADRATIC ONE-STEP EXHAUSTION FORCES g_car = 5 ([E] theorem / [O] premise split): the demand Lambda^2 E ^ Lambda^2 E = Lambda^{g-1} E (one quadratic composition step exhausts the top nontrivial half-spinor sector) holds…

Statement, assumptions and sources

Paper context: Architecture, E8 and the electromagnetic fixed point

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P2.QUADRATIC.EXHAUSTION.01

Original ledger classification: Exact algebraic theorem [Identity] with the [O]/[C] physical premise EXPLICITLY typed and NOT claimed: P2 unchanged

Original claim text

v880 (part 4) -- QUADRATIC ONE-STEP EXHAUSTION FORCES g_car = 5 ([E] theorem / [O] premise split): the demand Lambda^2 E ^ Lambda^2 E = Lambda^{g-1} E (one quadratic composition step exhausts the top nontrivial half-spinor sector) holds for EXACTLY one odd g in {3, 5, 7, 9, 11}, namely g = 5 (exact rank 5 = dim Lambda^4; S+ = 1 + 10 + 5 = 16); even control g = 4 breaks the half-spinor demand. THE THEOREM IS [E]; the PHYSICAL premise (the Calderon boundary kernel satisfies one-step quadratic exhaustion) is [O]/[C] -- P2 stays narrowed to v799's R1', NOT eliminated; NO marker move (per the review, the open physical premise must not be buried under a green finite module). Probe S4.

Original classification detail

FINITE-ANCHOR-CLOSED (S4): one-step exhaustion <=> g = 5 (unique among odd g); the Calderon premise stays [O] -- the sharpened but open half of P2

Dependencies as recorded

AX.P2.01; NORMALFORM.CFIN.01; v799; v845

Open the original ledger source, row 722

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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