A registered result in its source context
Original ledger classification: Reduction/certificate [E]/[O] (composition)
Recorded statement: SEAM.EQUIV.01 COMPOSITION CERTIFICATE (2026-06-21, TOE attack point 1): assembles the v297 literature stack into ONE well-typed logical chain gap>0 -> invertible/SRE (Kitaev) -> holomorphic c=8 (Mueger/KLM) -> (E8)_1 (Conway-Sloane),…
Statement, assumptions and sources
Paper context: Research contracts
The exact identifier, original classification and full claim are available below.
The source wording and classification below are preserved as recorded. A paper link, shared script or authored topic relation does not upgrade the claim or report a new proof run. Read later reviewed findings separately.
Read the exact registered claim and its dependencies
SEAM.EQUIV.CHAIN.01
Original ledger classification: Reduction/certificate [E]/[O] (composition)
Original claim text
SEAM.EQUIV.01 COMPOSITION CERTIFICATE (2026-06-21, TOE attack point 1): assembles the v297 literature stack into ONE well-typed logical chain gap>0 -> invertible/SRE (Kitaev) -> holomorphic c=8 (Mueger/KLM) -> (E8)_1 (Conway-Sloane), out(i)=in(i+1). [E] arithmetic discriminators exact (sympy): |det Cartan(E8)|=1 (one anyon/primary/invertible/holomorphic) vs |det Cartan(D8=SO(16))|=4 (the same-c rival, NON-holomorphic, excluded); carrier |det D5|*|det A3|=4*4=16 => anyon-condensation tower 16->4->1; c=g_car+N_fam=8. [E] the input gap is the DERIVED recovery gap 6 ln(3/2)>0 with the v76 margin>0. [O] the only undischarged TFPT-internal premise is the cited OS step (OS-reconstructed bulk gap = transfer gap). An assembly/reduction certificate (like v261/v297) + a Lean target; does NOT machine-prove SEAM.EQUIV.01 end-to-end.
Original classification detail
[E] the exact Cartan-det discriminators + the well-typed four-link composition + the derived-gap input; [O] the cited OS step + the end-to-end machine proof (Lean target). Pins the keystone's open content to one named step; NOT a closure of SEAM.EQUIV.01.
Dependencies as recorded
SEAM.EQUIV.01; SEAM.EQUIV.GAP.01; v297; v301; v302
Open the original ledger source, row 406Location recorded in the ledger
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- Research contracts
Sections that explicitly cite this claim
A literal claim identifier is present in these paper sections. The section and its premises determine what the citation supports.
- 2026-06-21 (TOE-roadmap solver round: the SEAM.EQUIV.01 keystone certificate, the modular bedrock, the carrier [formula in source] SM closure, the gap-decoupled measure, and the sharpened hypergraph substrate: v308– v312)Research changelog; TFPT — Introduction and reading guide
Navigation through a shared verification script
These sections cite a script associated with the claim. This is a source navigation join, rather than an explicit citation of the claim or a theorem equivalence.
- 2026-06-22 (Wolfram mirror of the arithmetic arc [formula in source] three sharpening steps: the CP-lock made quantitative, the Bisognano–Wichmann keystone, the minimal hypergraph fibre: v322, v323, v324)Research changelog; TFPT — Introduction and reading guide
- The closure ledger: what is done, and what genuinely remainsTFPT — Introduction and reading guide
- Honest statusinput 4 origin theory
- 2026-06-22 (keystone unification + status reframe: ONE open theorem, ONE decoupled foreign problem: v335, FORM.QGEO.BW.01 qgeoSymIsCorollary)Research changelog; TFPT — Introduction and reading guide
- Research Contract 1 — [formula in source]tfpt research contracts
- Honest statusorigin theory
- 2026-06-24 (The five TOE/QFT closure contracts v398– v402 + a ledger rescope)Research changelog; TFPT — Introduction and reading guide
- OutcomeRed-team audit
All 19 linked sections
- 2026-06-22 (frontier round: the OS step discharged at the many-body level, the ambient measure built on the gap-decoupled sector, and the carrier Cartan determinants grounded in Lean: v329, v330, FORM.CARTAN.DET.01)
- The hard reduction: the live residual as typed interfaces
- Honest status
- Front matter / support
- Front matter / support
- Front matter / support
- Honest status
- 2026-06-22 (Lean: the SEAM.EQUIV.01 composition chain formalised — the keystone residual machine-pinned to the named cited steps: FORM.SEAMEQUIV.01)
- Research Contract 1 — [formula in source]
- 2026-06-25 (The (LTO-RP) reduction of the keystone SEAM.EQUIV.01: v424)
- 2026-06-22 (next-steps round: the keystone collapsed to one shared premise (Lean [formula in source] one citable theorem), the [formula in source] solver suite, the cusp weight derived from a minimal rewrite, and the [formula in source] pressure point: FORM.QGEO.BW.01, v325, v326, v327, v328)
Registered verification modules
- v308_seam_equiv_chain.pyRegistered verification module · frontier
Read the description recorded in the module registry
TOE attack 1 -- the SEAM.EQUIV.01 keystone as a composition certificate: the v297 stack as ONE well-typed chain gap>0 -> invertible (Kitaev) -> holomorphic c=8 (Mueger/KLM) -> (E8)_1 (Conway-Sloane), with exact discriminators |det Cartan(E8)|=1 vs |det Cartan(D8)|=4, carrier tower 4*4=16->4->1, c=g_car+N_fam=8; the input gap = the derived recovery gap 6 ln(3/2)>0. The only undischarged premise is the cited OS step -- an assembly/reduction certificate (Lean target), NOT a closure
A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.