A registered result in its source context
Original ledger classification: Formal [F] (Lean theorem, all-orders closure)
Recorded statement: FLAT-METRIC ALL-ORDERS CLOSURE FORMALISED IN LEAN (2026-06-18): TfptCarrier/SeamDeckClosure.lean (theorems diagonal_commutesClock, flat_all_orders_clock) machine-proves the v276 all-orders step -- any SPECTRAL FUNCTION g of the…
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Paper context: E8 audit and bootstrap
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FORM.QGEO.04
Original ledger classification: Formal [F] (Lean theorem, all-orders closure)
Original claim text
FLAT-METRIC ALL-ORDERS CLOSURE FORMALISED IN LEAN (2026-06-18): TfptCarrier/SeamDeckClosure.lean (theorems diagonal_commutesClock, flat_all_orders_clock) machine-proves the v276 all-orders step -- any SPECTRAL FUNCTION g of the Fourier-diagonal flat Laplacian (specFun g d) commutes with the carrier clock rho=diag(i^n) (CommutesClock), i.e. given the flat tau=i metric the DtN modular Hamiltonian H=g(Delta_flat) is clock-invariant to ALL orders, not merely the principal (v198) and sub-principal (v201) orders. Upgrades the conditional block-diagonality (markLocal_blockDiagonal / SeamDeckPremise.clock_invariant) to the full operator. Only the standard axioms {propext, Classical.choice, Quot.sound}, no sorry; full lake build green (3356 jobs), listed in AxiomCheck.lean. The premise (the seam IS flat) stays the [O] QGEO.SYM.01 input. QA NOTE (2026-08-08, round 36, v878_ledger_integrity.py): claim_id RENAMED FORM.QGEO.03 -> FORM.QGEO.04 -- the id FORM.QGEO.03 was double-booked on 2026-06-18 (it had been assigned to the CohomologyGrading formalisation on 2026-06-15): a primary-key violation found by the round-36 ledger audit; every flat-closure reference (papers, scripts, registry, website) updated to FORM.QGEO.04; the CohomologyGrading row keeps FORM.QGEO.03. The claim content is UNCHANGED.
Original classification detail
Formal [F]: the v276 flat-metric all-orders commutator closure is a Lean theorem (SeamDeckClosure.flat_all_orders_clock), standard axioms only, no sorry, full build green.
Dependencies as recorded
FORM.QGEO.01; FORM.QGEO.02; QGEO.SYM.03
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- Research contracts
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- Research Contract 1 — [formula in source]Research contracts
- =150 2026-08-01 (XVIII) (the duality-and-forms round lands ( v602 promoted): the J-adjoint exchanges the two parabolic types exactly ( [formula in source] compiler pair); the dictionary completes in the J-projector language (the corpus anchor formula [formula in source] holds verbatim on the curve); Weil positivity holds exactly (the Riemann bilinear relations on the [formula in source] -sheet); the canonical bilinear form [formula in source] is symmetric with [formula in source] ; the v600 integer core is Lean-certified ( FORM.QGEO.04); the contracts paper gains the [formula in source] -cover model paragraph)Research changelog; TFPT — Introduction and reading guide
- 2026-06-18 (the Gr\"al: QGEO.SYM.01 as one precise lemma [formula in source] the all-orders step Lean-formalised, v279/ FORM.QGEO.04)Research changelog; TFPT — Introduction and reading guide
- Research Contract 1 — [formula in source]tfpt research contracts
- Group-theoretic audits (optional)input 5 tfpt 3 e8 audit bootstrap
- Research Contract 2 — [formula in source]tfpt research contracts
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- Group-theoretic audits (optional)E8 audit and bootstrap
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