A registered result in its source context
Original ledger classification: Formal
Recorded statement: LEAN: SEAM.EQUIV.01 COMPOSITION CHAIN (2026-06-22). Lean 4 formalisation (TfptCarrier/SeamEquivChain.lean) of the v308 closing chain: the four nodes GapPositive -> InvertibleSRE -> HolomorphicC8 -> SeamIsE8 assembled as a well-typed…
Statement, assumptions and sources
Paper context: Origin Theory
The exact identifier, original classification and full claim are available below.
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FORM.SEAMEQUIV.01
Original ledger classification: Formal
Original claim text
LEAN: SEAM.EQUIV.01 COMPOSITION CHAIN (2026-06-22). Lean 4 formalisation (TfptCarrier/SeamEquivChain.lean) of the v308 closing chain: the four nodes GapPositive -> InvertibleSRE -> HolomorphicC8 -> SeamIsE8 assembled as a well-typed composition theorem seamEquivChain, with the three cited literature steps (Kitaev free-fermion invertibility; Mueger / Kawahigashi-Longo-Mueger holomorphy; Conway-Sloane E8 uniqueness) declared as named axioms and the carrier recovery gap (the OS step) as the single open input. #print axioms seamEquivChain confirms the residual is EXACTLY those named steps + recovery_gap (no hidden assumption). Plus a decide-proven discriminator: primariesE8=1 != primariesD8=4 (|det Cartan| distinguishes the holomorphic E8 from the same-central-charge rival D8=SO(16)). Built end-to-end (lake build, 3357 jobs) on Lean v4.29.1 + Mathlib. The VALUE is the machine-checked composition + the axiom audit (which pins the keystone residual to the named cited theorems + the one OS input), NOT a from-scratch proof of the cited steps -- so it does NOT close SEAM.EQUIV.01.
Original classification detail
[E] Lean-built: the well-typed composition seamEquivChain + the axiom audit (residual = the named cited theorems + the one OS input) + the decide-proven discriminator (1 != 4). A formal audit-contract skeleton of the v308 keystone chain; the three literature steps are named axioms (cited, not re-proved), so it MACHINE-PINS the residual but does NOT close SEAM.EQUIV.01.
Dependencies as recorded
SEAM.EQUIV.CHAIN.01; SEAM.EQUIV.01; SEAM.EQUIV.GAP.01
Open the original ledger source, row 423Sections 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.
- Honest statusinput 4 origin theory
- Layer 6 — two independent reproduction pathsVerification safeguards
- Honest statusorigin theory
- OutcomeRed-team audit
- Honest statusOrigin Theory
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- 2026-06-22 (consistency + de-accretion editorial pass: current-state alignment across papers, website and ledger; no new modules)Research changelog; TFPT — Introduction and reading guide
- Honest statusinput 4 origin theory
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
- 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
- 2026-06-24 (The five TOE/QFT closure contracts v398– v402 + a ledger rescope)Research changelog; TFPT — Introduction and reading guide
- 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
- 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)Research changelog; TFPT — Introduction and reading guide
- The hard reduction: the live residual as typed interfacesTFPT — Introduction and reading guide
All 13 linked sections
- Front matter / support
- Front matter / support
- 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
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