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The seam realization contract

Original ledger classification: Contract [E] (typing + firewall + taxonomy) + [O] (the named theorem)

Recorded statement: THE SEAM EQUIVALENCE CONTRACT (2026-06-18): concentrates the whole open structure on ONE named arrow (does NOT prove it). THE NAMED THEOREM: the raw reflection-positive seam state (gap, chirality, carrier clock) reconstructs canonically…

Statement, assumptions and sources

Paper context: TFPT — Introduction and reading guide

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.

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SEAM.EQUIV.01

Original ledger classification: Contract [E] (typing + firewall + taxonomy) + [O] (the named theorem)

Original claim text

THE SEAM EQUIVALENCE CONTRACT (2026-06-18): concentrates the whole open structure on ONE named arrow (does NOT prove it). THE NAMED THEOREM: the raw reflection-positive seam state (gap, chirality, carrier clock) reconstructs canonically the SAME state as the holomorphic (E8)_1 boundary net at the tau=i pillowcase, respecting the DtN, KMS modular flow, mu4 deck, Q-system extension, det K=1 and the (E8)_1 character (short: the raw seam is (E8)_1 at tau=i). [E] four objects (RawRPSeam, FlatTauIPillowcaseDtN, HolomorphicE8Net, SREKitaevE8Phase). [E] six arrows: 2 closed (Route i: FlatDtN->omega o rho=omega, v276/v280/v284; Route ii: SRE->HolomorphicE8Net, v235/v277/v281), 1 conditional (FlatDtN<->HolomorphicE8Net at tau=i, v282), 2 open premises (RawRPSeam->FlatDtN and RawRPSeam->SRE, the SAME lemma per v284/v285), 1 Gral (RawRPSeam->HolomorphicE8Net = SEAM.EQUIV.01). [E] IMPORT FIREWALL (anti-circularity): no Route-i module (v276/v280/v284) imports any Route-ii module (v277/v281/v285) or vice versa, verified by scanning the sources -- the routes converge ONLY through this contract, killing the 'E8 smuggled into the geometry and pulled back out' attack. [E] exact-label taxonomy {Formal Exact (Lean), Numerical Exact (reproducible experiment), Conditional Exact (standard theorem under a stated premise), Open Selection (theory-selection premise)}. [O] the one open arrow: free Gaussian RP bulk => holomorphic single-sector boundary net. Writes seam_equivalence.json. NOT closed by this: v_geo (metrology primitive), F_transfer (downstream), QG.AMB.01 (nonperturbative ambient measure). ROUTE SPLIT (2026-07-22; ID restructuring after the external review, NO status change in substance): the target statement now carries two named routes -- SEAM.EQUIV.MMST.01 (the conditional scaling-limit route: closed modulo cited existence theorems) and SEAM.EQUIV.TWISTOR.01 (the open Costello-Li construction). PARENT LOGIC (the claim text of this row): closed if MMST.01 OR TWISTOR.01 closes; currently: MMST conditional-closed modulo cited theorems, TWISTOR open => parent stays [O] as an unconditional claim. UPDATED 2026-08-27 (v973): the route narrowing -- the MMST route's cited-theorem coverage is carved into COVERED (bilinear half) vs NOT-COVERED (the named N1-N4 list, headed by the mu4/GSO net extension), the twistor route's declared measure is unique on the computable sector up to exactly ONE named flat direction, and the two routes provably share the executable OS skeleton 5/5 with all divergences control-typed (NEW row SEAM.EQUIV.SKELETON.01 [E]) -- the open structure of the parent is now concentrated on the SAME named extension question from both sides (N1/N4 on the MMST side, the global quantisation + OS bridge on the twistor side), with the executable levels verified to agree. Parent logic unchanged: closed if MMST.01 OR TWISTOR.01 closes; both stay [O]; parent stays [O].

Original classification detail

[E] the four-object/six-arrow typing + the import firewall (routes non-circular) + the exact-label taxonomy + the single-open-arrow certificate; [O] the named Seam Equivalence Theorem stays open. A contract concentrating the open structure on one arrow; does NOT prove it. Route split 2026-07-22: closed if SEAM.EQUIV.MMST.01 OR SEAM.EQUIV.TWISTOR.01 closes; currently MMST conditional-closed modulo cited theorems, TWISTOR open => parent stays [O] as an unconditional claim.

Dependencies as recorded

QGEO.SYM.01; QGEO.OBLIG.01; QGAMB.UNIFY.01; QGEO.ROUTEI.01; QGAMB.ROUTEII.01; SEAM.EQUIV.MMST.01; SEAM.EQUIV.TWISTOR.01

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Registered verification modules

  • v286_seam_equivalence_contract.pyRegistered verification module · frontier
    Read the description recorded in the module registry

    SEAM.EQUIV.01 — the Seam Equivalence contract: concentrates the whole open structure on ONE named arrow (does NOT prove it). Theorem: the raw RP seam state reconstructs canonically the holomorphic (E8)₁ boundary net at the τ=i pillowcase ('the raw seam is (E8)₁ at τ=i'). [E] four objects (RawRPSeam, FlatTauIPillowcaseDtN, HolomorphicE8Net, SREKitaevE8Phase); [E] six arrows — 2 closed (Route i v276/v280/v284, Route ii v281/v277/v235), 1 conditional (v282), 2 open premises (the same lemma, v284/v285), 1 Gral; [E] IMPORT FIREWALL: no Route-i module imports any Route-ii module or vice versa, so the routes converge only through SEAM.EQUIV.01 (kills the 'E8 into the geometry and back' circularity); [E] exact-label taxonomy (Formal/Numerical/Conditional Exact, Open Selection); [O] the one open arrow 'free Gaussian RP bulk ⇒ holomorphic single-sector boundary'. Writes seam_equivalence.json.

A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.

Interlocking clocksCosmologyCarrier, families and E8 closureGravityMetrologySeam, origin and declared inputsProcess and compilationQuantum and boundary structureExternal project: Prime FrontSpacetimeUniversalraumTests and predictionsSearch later reviewed research for this identifierRead the coverage boundaries