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A registered result in its source context

Original ledger classification: Proven finite statement [E] (Identity, exact over Z/Q via sympy); C7 Gauss-code transform stays OPEN (rem:c7-audit); NO RH claim

Recorded statement: THE SEVEN EXACT E8 READOUT CELLS [E] Identity (round r609, promoted 2026-09-02; module v1018, re-derived, no probe imports). (1) Seifert/Euler: S+S^T=A_E8, charpoly(-S^{-1}S^T)=Phi_30, rank(S-S^T)=8, orientation-independent charpoly…

Statement, assumptions and sources

Paper context: TFPT — Introduction and reading guide

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E8.DIRECTED.READOUT.01

Original ledger classification: Proven finite statement [E] (Identity, exact over Z/Q via sympy); C7 Gauss-code transform stays OPEN (rem:c7-audit); NO RH claim

Original claim text

THE SEVEN EXACT E8 READOUT CELLS [E] Identity (round r609, promoted 2026-09-02; module v1018, re-derived, no probe imports). (1) Seifert/Euler: S+S^T=A_E8, charpoly(-S^{-1}S^T)=Phi_30, rank(S-S^T)=8, orientation-independent charpoly (exponents=totatives of 30; degrees {2,8,12,14,18,20,24,30}, sum(2m_i+1)=248). (2) Hamming H_8 enumerator 1+14 y^4+y^8, 240=16+14*16, S(3,4,8). (3) srg(120,56,28,24) eigenvalues 56/8/-4 with multiplicities 1/35/84. (4) Hecke N(n)=240 sigma_3(n) for n<=10 (theta of E8 = E_4). (5) Delta: A_P(n)/A_P(1)=tau(n) for n<=8 on three axes, degree-2/4/6 vanishing, E_4^3-E_6^2=1728 Delta. (6) (Z/30)^x cong C_2 x C_4 (orders {1,2,2,2,4,4,4,4}, not C_2^3); D_chi(s)=L(s,chi)L(s-3,chi) for n<=200. (7) E6 oplus A2 gluing: index 3, Smith (1^6,3,3), roots 72+6+162, glue classes 78/81/81. C7 Gauss-code transform NOT promoted: stays OPEN (note_e8_gaussian_code.tex rem:c7-audit). NOT evidence for or against the Riemann Hypothesis. NO RH CLAIM.

Original classification detail

[E] Identity: seven exact E8 readout cells (Seifert/Phi_30, Hamming, srg(120,56,28,24), N(n)=240 sigma_3(n), tau, C2 x C4, E6 oplus A2 glue); C7 OPEN (rem:c7-audit); NO RH claim

Dependencies as recorded

v1018

Open the original ledger source, row 771

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  • v1018_e8_directed_readout.pyRegistered verification module · core
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    E8.DIRECTED.READOUT.01 [E] (2026-09-02, Runde r609): sieben exakte E8-Ablese-Zellen (C7 offen) -- neu abgeleitet (keine Proben-Importe): Seifert/Phi_30, Hamming 1+14y^4+y^8, srg(120,56,28,24), N(n)=240 sigma_3(n) n<=10, A_P/A_P(1)=tau(n), (Z/30)^x = C2 x C4, E6 oplus A2 Index 3 Smith (1^6,3,3) Glue 78/81/81. C7 Gauss-Code bleibt offen (rem:c7-audit). KEIN RH-CLAIM. Python-only / Wolfram zurueckgestellt.

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