A registered result in its source context
Original ledger classification: Exact [E] finite lemma (integer/Fraction arithmetic; Lean companion module; Python-only per GATE.WOLFRAM.02).
Recorded statement: The projective Hamming incidence lemma on V = L/(1+i)L -- the symplectic F2^4 of the unimodular hermitian E8 lattice, and the v737 resolution (one module, 36 checks, ~5 s; discovery probe projective_hamming_incidence_probe.py 36/36,…
Statement, assumptions and sources
Paper context: input 5 tfpt 3 e8 audit bootstrap
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E8.PROJHAMMING.01
Original ledger classification: Exact [E] finite lemma (integer/Fraction arithmetic; Lean companion module; Python-only per GATE.WOLFRAM.02).
Original claim text
The projective Hamming incidence lemma on V = L/(1+i)L -- the symplectic F2^4 of the unimodular hermitian E8 lattice, and the v737 resolution (one module, 36 checks, ~5 s; discovery probe projective_hamming_incidence_probe.py 36/36, verdict PROJ-HAMMING-EXACT). THE LEMMA FROM THE CONCRETE LATTICE: h = H/4 is Z[i]-valued with hermitian Gram determinant 1 (the UNIMODULAR hermitian E8 lattice over Z[i]); doubly-even => hbar alternating, well-defined on V, NONDEGENERATE: (V, hbar) is symplectic over F2 with explicit Darboux basis. THE CORE IDENTITY: |H_y| = 7 for all 15 points, pair intersections 3 for all 105 pairs; B B^T = 4 I + 3 J EXACT with characteristic polynomial (x-7)(x-2)^9(x+2)^5 -- the eigenvalue multiplicities (1, 9, 5) are the SYMPLECTIC signature (honest P7.2 finding: B B^T = 4I + 3J alone holds for ANY nondegenerate form; the symplectic content is the projective part -- diagonal 1, tr B = 15, multiplicities). THE CHANNEL: K = B/7 with K^2 = (4/49) I + (45/49) Pi0 exactly (K itself honestly NOT psd). NS/R AS GEOMETRY: chi_NSR = hbar(., y0) for the UNIQUE sigma-fixed point y0 = FSUM (the anchor bit); 112 NS + 128 R, +8 Cartan: 248 = 120 + 128 (SO(16)). THE v737 RESOLUTION: the seam-48 distribution 0:96/1:64/2:64/3:16 is DERIVED exactly (48 x 5 = 16 x the 3 x 5 label table), AND the 5 x 48 coordinatization EXISTS via exactly ONE ubar-invariant spread of the 56 -- the v737 kill is EXPLAINED (wrong blocks), not revised. Two honest corrections to the review derivation documented (P6.5d, P7.2). Companion Lean module TfptCarrier/ProjectiveHamming.lean (32 theorems, kernel decide/norm_num only, lake build green). No marker move, NO RH claim.
Original classification detail
PROJ-HAMMING-EXACT: (V, hbar) is the symplectic F2^4 of the unimodular hermitian E8 lattice; B B^T = 4I + 3J exact, eigenvalues 7^1 (+2)^9 (-2)^5, K^2 = (4/49) I + (45/49) Pi0; NS/R = hbar(., FSUM) = the anchor bit; 248 = 120 + 128; the v737 distribution derived and the 5 x 48 coordinatization exists via exactly one ubar-invariant spread (kill explained, not revised); no RH statement.
Dependencies as recorded
E8.GAUSSCODE.01; E8.ORBITPACKET.01; E8.SEAM48.01; v689; v634; v722; v736; v737; v738
Open the original ledger source, row 677Location recorded in the ledger
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- Architecture, E8 and the electromagnetic fixed point
- Standard Model and flavor structure
- E8 audit and bootstrap
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- Group-theoretic audits (optional)input 5 tfpt 3 e8 audit bootstrap
- Group-theoretic audits (optional)input 5 tfpt 3 e8 audit bootstrap
- Front matter / supportE8 audit and bootstrap
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- How to read this documenttfpt 1 architecture e8
- How to read this documentArchitecture, E8 and the electromagnetic fixed point
- The Sheet Diamond and the Winding Line: masses and transport from one surfacetfpt 2 standard model
- Front matter / supportStandard Model and flavor structure
- Front matter / supportE8 audit and bootstrap
- How to read this documenttfpt 1 architecture e8
- Research Contract 2 — [formula in source]tfpt research contracts
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
Registered verification modules
- v752_projective_hamming_incidence.pyRegistered verification module · core
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E8.PROJHAMMING.01: das projektive Hamming-Inzidenzlemma auf V = L/(1+i)L — der symplektische F2^4 des unimodularen hermiteschen E8-Gitters, und die v737-Auflösung — **PROJ-HAMMING-EXACT: h = H/4 ist Z[i]-wertig mit hermitescher Gram-Determinante 1 (Z[i]-UNIMODULAR); h̄ alternierend (doubly-even), nicht-entartet ⇒ (V, h̄) symplektisch mit expliziter Darboux-Basis; |H_y| = 7, Paarschnitte 3; B Bᵀ = 4I + 3J EXAKT, char. Polynom (x−7)(x−2)⁹(x+2)⁵ — die Multiplizitäten (1, 9, 5) sind die SYMPLEKTIK-Signatur; K² = (4/49) I + (45/49) Π₀ exakt (K selbst ehrlich nicht psd); NS/R-χ = h̄(·, y0) für den EINDEUTIGEN σ-fixen Punkt y0 = FSUM (das Anker-Bit), 112 + 128 = 240, +8 Cartan: 248 = 120 + 128; DIE v737-AUFLÖSUNG: Verteilung 0:96/1:64/2:64/3:16 exakt abgeleitet (16 × 3×5-Label-Tafel) UND die 5×48-Koordinatisierung existiert via genau EINEN ū-invarianten Spread (Kill erklärt, nicht revidiert)**; zwei ehrliche Korrekturen an der Review-Herleitung dokumentiert; Lean-Begleitmodul ProjectiveHamming.lean (32 Theoreme) (36 Checks, ~5 s)
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