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Original ledger classification: Exact [E] machinery; the preregistered break fires -- honest structural negative, correlation typed decorative (Python-only per GATE.WOLFRAM.02).

Recorded statement: The preregistered Fano -> discriminant(-7) bridge -- the three-cycle half is real, the parity half dies arithmetically: the seven-correlation is typed decorative for good (one module, 26 checks, ~1 s, ONE preregistered [FAIL] line C2.d =…

Statement, assumptions and sources

Paper context: input 5 tfpt 3 e8 audit bootstrap

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QGEO.FANODISC7.01

Original ledger classification: Exact [E] machinery; the preregistered break fires -- honest structural negative, correlation typed decorative (Python-only per GATE.WOLFRAM.02).

Original claim text

The preregistered Fano -> discriminant(-7) bridge -- the three-cycle half is real, the parity half dies arithmetically: the seven-correlation is typed decorative for good (one module, 26 checks, ~1 s, ONE preregistered [FAIL] line C2.d = the COND2 break; discovery probe fano_disc7_bridge_probe.py, verdict FANO-DISC7-DECORATIVE). THE FOUR-CONDITION TEST breaks exactly at condition 2: the NS/R parity bit has NO arithmetic carrier in O_{-7} -- 2 SPLITS in Q(sqrt(-7)) (-7 == 1 mod 8, O tensor Z2 = Z2 x Z2), so every 2-adic ideal quotient has 2-rank <= 2 < 3 (complete census of all norm-8/16 ideals): the code F2-structures are arithmetically UNREALIZABLE; candidates 2a (norm parity does not factor through the ramified fiber) and 2b (chi_7 pullback nonconstant) die too. THE REAL HALF (COND1, exact): equivariant lifts EXIST for both canonical difference-set Fano models (3 each), the canonical order-3 action is x -> 2x (the difference-set multiplier, 2 = the transfer step), and every lift sends the unique sigma-bar fixed point of the NS Fano plane to 0 = red(alpha_0) = the C corner (norm 14 = dim G2) -- forced. Controls fire (x -> 3x zero lifts; broken incidence zero lifts; the ideal 7-set refuses the 3-cycle). No marker move, NO RH claim.

Original classification detail

FANO-DISC7-DECORATIVE: preregistered four-condition test, break exactly at condition 2 -- 2 splits in Q(sqrt(-7)) => 2-rank <= 2 < 3, the code F2-structures are arithmetically unrealizable; the three-cycle half is real (Fano sigma-bar = x2 multiplier, C corner = fixed point); the seven-correlation is permanently typed decorative; no RH statement.

Dependencies as recorded

E8.PROJHAMMING.01; PRIME.HECKEMODRAM.01; QGEO.CAR.01; v533; v571; v632; v722; v738

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Registered verification modules

  • v757_fano_disc7_bridge.pyRegistered verification module · core
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    QGEO.FANODISC7.01: die preregistrierte Fano→Diskriminante(−7)-Brücke — die Dreizyklus-Hälfte real, die Paritäts-Hälfte stirbt arithmetisch — **FANO-DISC7-DECORATIVE (Bruch exakt bei Bedingung 2): das NS/R-Paritäts-Bit hat KEINEN arithmetischen Träger in O_{−7} — 2 SPALTET in Q(√−7) (−7 ≡ 1 mod 8, O ⊗ Z₂ = Z₂ × Z₂), jeder 2-adische Idealquotient hat 2-Rang ≤ 2 < 3 (vollständiger Zensus aller Norm-8/16-Ideale): die Code-F₂-Strukturen sind arithmetisch UNREALISIERBAR; DIE REALE HÄLFTE (COND1, exakt): äquivariante Lifts existieren für beide kanonischen Differenzmengen-Fano-Modelle, die kanonische Ordnung-3-Wirkung ist x → 2x (der Differenzmengen-Multiplikator, 2 = der Transfer-Schritt), jeder Lift schickt den eindeutigen σ̄-Fixpunkt auf 0 = red(α₀) = die C-Ecke (Norm 14 = dim G2)**; die Sieben-Korrelation dauerhaft als DEKORATIV getypt; Kontrollen feuern; der eine [FAIL] = der preregistrierte COND2-Bruch (26 Checks, ~1 s)

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