A registered result in its source context
Original ledger classification: Seam State Rigidity contract+evidence [E]/[O] (Paper A: the G_net keystone as one named theorem -- RP-definability hinge + band-limited mu4-character core swept N=4..64 + holomorphy=>(E8)_1; the one residual = full-L^2 / intrinsic BW). NOT a closure of SEAM.EQUIV.01
Recorded statement: THE SEAM STATE RIGIDITY THEOREM AS ONE NAMED TARGET (2026-06-24, Paper A / the G_net closure contract): consolidates the scattered state-invariance reductions (v177/v198/v199/v308/v309/v335) into a single citable theorem and HARDENS the…
Statement, assumptions and sources
Paper context: tfpt research contracts
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SEAM.RIGIDITY.01
Original ledger classification: Seam State Rigidity contract+evidence [E]/[O] (Paper A: the G_net keystone as one named theorem -- RP-definability hinge + band-limited mu4-character core swept N=4..64 + holomorphy=>(E8)_1; the one residual = full-L^2 / intrinsic BW). NOT a closure of SEAM.EQUIV.01
Original claim text
THE SEAM STATE RIGIDITY THEOREM AS ONE NAMED TARGET (2026-06-24, Paper A / the G_net closure contract): consolidates the scattered state-invariance reductions (v177/v198/v199/v308/v309/v335) into a single citable theorem and HARDENS the finite-block evidence to a multi-mode sweep. Does NOT close SEAM.EQUIV.01 (the continuum scaling-limit existence stays the cited MMST/Adamo step, v336/v392). [E] RP-DEFINABILITY HINGE: OS reconstruction gives a canonical transfer operator T=e^{-H} from the RP state + reflection alone (v54) on a quasi-free state (v155), so Lambda_Sigma is RP-definable WITHOUT importing the mu4 normal form (non-circular). [E] GROUND-STATE REDUCTION: for a quasi-free RP state C=1/2(1+sgn H_1), so omega o rho=omega <=> [rho,H_1]=0 <=> H_1 block-diagonal in the four mu4-character classes. [E] BAND-LIMITED CORE (the hardening): [rho,|k|]=0 exactly and a character-block-diagonal sub-principal symbol commutes with rho while a single off-character entry breaks it, swept N=4..64 (beyond the 3-dim H^1 of v177/v199). [E] HOLOMORPHY=>(E8)_1: c=g_car+N_fam=8, |det Cartan(E8)|=1 (one primary) vs |det Cartan(D8)|=4, index 4=|mu4|, gap 6 ln(3/2)>0 -- the unique even-unimodular rank-8 lattice net (v83/v154/v308). [O] THE ONE RESIDUAL: [rho,Lambda_Sigma]=0 on the FULL L^2 <=> intrinsic Bisognano-Wichmann modular geometricity, the same [O] as v199/v309, now stated as the single theorem residual.
Original classification detail
[E] the RP-definability hinge (OS canonical transfer + quasi-free) + the band-limited character-block-diagonal core swept N=4..64 (hardens v177/v199 beyond H^1) + the holomorphy=>(E8)_1 arithmetic (det Cartan 1 vs 4, c=8, index 4); [O] the full-L^2 / intrinsic-Bisognano-Wichmann step (G_net's irreducible analytic residual). A contract+evidence consolidation (genre of v275/v343/v384/v392); NOT a closure of SEAM.EQUIV.01 (continuum=cited MMST v336); no new number.
Dependencies as recorded
SEAM.EQUIV.01; v54; v155; v177; v198; v199; v308; v309; v335; v83; v154; v336
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- Research contracts
Sections that explicitly cite this claim
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- 2026-06-30 ( v445 — the rigidity FORCING converse: commuting with the order- [formula in source] clock is exactly [formula in source] -block-diagonality, upgrading the rigidity step from ``permit'' to ``force'')Research changelog; TFPT — Introduction and reading guide
- Research Contract 1 — [formula in source]tfpt research contracts
- 2026-06-24 (The five TOE/QFT closure contracts v398– v402 + a ledger rescope)Research changelog; TFPT — Introduction and reading guide
- Front matter / supportResearch contracts
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- Research Contract 1 — [formula in source]tfpt research contracts
Navigation through a shared verification script
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- 2026-06-24 (The [formula in source] dual keystone + the flavor residuals it homes: v405– v407)Research changelog; TFPT — Introduction and reading guide
- Front matter / supportResearch contracts
- 2026-06-30 (six convergent attacks on the one SEAM.EQUIV.01 continuum residual — intrinsic Bisognano–Wichmann, a Lieb–Robinson continuum motor, the [formula in source] -homotopy, an applicability audit, uniform rigidity, and falsifiable kill tests; none closes the keystone, together they reduce it to a single analytic fact and make the claim falsifiable)Research changelog; TFPT — Introduction and reading guide
Registered verification modules
- v398_seam_state_rigidity.pyRegistered verification module · registry
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Seam State Rigidity Theorem (Paper A / G_net): RP-definability hinge (OS transfer + quasi-free) + band-limited mu4-character core swept N=4..64 + holomorphy=>(E8)_1; [O] full-L^2 / intrinsic BW
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