A registered result in its source context
Original ledger classification: Lattice/AQFT selection (exact) [E]/[O]
Recorded statement: SEAM-HOLOMORPHY SELECTION CERTIFICATE (2026-06-17): the entire structural residual of TFPT is ONE condition with THREE provably-equivalent faces, all forcing E8 -- so P2/G_net/Target A/QGEO are ONE gate, not four. THE CONDITION: 'the seam…
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GATE.HOLO.01
Original ledger classification: Lattice/AQFT selection (exact) [E]/[O]
Original claim text
SEAM-HOLOMORPHY SELECTION CERTIFICATE (2026-06-17): the entire structural residual of TFPT is ONE condition with THREE provably-equivalent faces, all forcing E8 -- so P2/G_net/Target A/QGEO are ONE gate, not four. THE CONDITION: 'the seam carries no nontrivial abelian sector.' Faces: (i) AQFT -- the boundary chiral net is HOLOMORPHIC (mu-index 1, single vacuum sector; Target A, v83/v154); (ii) geometry -- the seam link is a HOMOLOGY 3-sphere <=> the binary group Gamma is PERFECT <=> Gamma=2I (v232); (iii) rep theory -- exactly ONE 1-dim irrep (v219). All three are the SAME number: #(1-dim irreps)=|Gamma^ab|=|H_1(S^3/Gamma)|=#(mark-1 affine-Dynkin nodes), which equals 1 ONLY for affine E8 (A_n->n+1, D_n->4, E6->3, E7->2, E8->1). So 2I is the unique nontrivial perfect finite SU(2) subgroup and the Poincare sphere is the unique homology-sphere spherical space form. And holomorphic c=8=g_car+N_fam => the unique even unimodular rank-8 lattice = E8 (Gram even, det 1). THE CLOSING THEOREM (stated, NOT proved): RP + gap + chirality => quasi-free bulk (v160 fixed-point) => invertible bulk => holomorphic boundary net (no abelian sector) => E8; the single residual analytic step is 'free bulk => holomorphic boundary', after which P2/QGEO/G_net all follow. This certifies that the three faces coincide and force E8; it does NOT prove the analytic step.
Original classification detail
[E] #mark-1 = |Gamma^ab| = |H1(link)|; only E8->1 (2I unique perfect, Poincare unique homology sphere); holomorphic c=8 unique E8; the three faces (holomorphy/homology-sphere/one-1dim-irrep) are one E8-selector => Target A/G_net/P2/QGEO are ONE gate; closing theorem 'free bulk => holomorphic boundary' stated [O]
Dependencies as recorded
E8.GLU.01; MCKAY.E8.01; TOPO.E8.01; GATE.METRIC.06
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- Research contracts
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- 2026-06-17 (CP phases as [formula in source] powers — a reduction of red-team Target D)Research changelog; TFPT — Introduction and reading guide
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
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- Front matter / supportResearch contracts
- 2026-06-19 (an infinite-derivative narrowing of the Stelle-ghost attack, the double-pushout figure, and the ``constancy of [formula in source] '' framing of SEAM.EQUIV.01: v304)Research changelog; TFPT — Introduction and reading guide
- Research Contract 1 — [formula in source]tfpt research contracts
- The hard reduction: the live residual as typed interfacesTFPT — Introduction and reading guide
- The [formula in source] compiler: [formula in source] as a closure, not an inputtfpt 1 architecture e8
- The [formula in source] compiler: [formula in source] as a closure, not an inputtfpt 1 architecture e8
- Research Contract 1 — [formula in source]tfpt research contracts
- The [formula in source] compiler: [formula in source] as a closure, not an inputArchitecture, E8 and the electromagnetic fixed point
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Registered verification modules
- v234_seam_holomorphy_selection.pyRegistered verification module · frontier
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The Seam-Holomorphy selection certificate: the entire structural residual is ONE condition with THREE equivalent faces, all forcing E8. THE CONDITION: 'the seam carries no nontrivial abelian sector.' (i) AQFT: the boundary net is holomorphic (mu-index 1); (ii) geometry: the seam link is a homology 3-sphere <=> the binary group is perfect <=> 2I; (iii) rep theory: exactly one 1-dim irrep. #(mark-1 affine-Dynkin nodes) = |Gamma^ab| = |H1(S^3/Gamma)| = #(1-dim irreps): A_n->n+1, D_n->4, E6->3, E7->2, E8->1 -- ONLY E8 gives 1 (2I the unique perfect SU(2) subgroup, Poincare the unique homology-sphere space form). Holomorphic c=8=g_car+N_fam => unique even unimodular rank-8 lattice = E8. The three faces (v83/v154, v232, v219) are the SAME E8-selector, so Target A, G_net, P2 and the Kleinian seam are ONE gate. The closing theorem (stated, [O]): RP+gap+chirality => quasi-free bulk (v160) => invertible bulk => holomorphic boundary => E8; the single residual is 'free bulk => holomorphic boundary'.
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