A registered result in its source context
Original ledger classification: Formal [F] (Lean kernel; the standard-pair relations kernel-proved axiom-free, the Borchers step + continuum input named axioms)
Recorded statement: LEAN 4 FORMALISATION of the Borchers/Wiesbrock standard-pair algebra (2026-06-30; the kernel-hardening of v438/SEAM.EQUIV.BW.HSMI.01) -- new module TfptCarrier/SeamStandardPair.lean, lake build OK, #print axioms CLEAN. It kernel-checks the…
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Paper context: tfpt research contracts
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FORM.SEAM.BW.HSMI.01
Original ledger classification: Formal [F] (Lean kernel; the standard-pair relations kernel-proved axiom-free, the Borchers step + continuum input named axioms)
Original claim text
LEAN 4 FORMALISATION of the Borchers/Wiesbrock standard-pair algebra (2026-06-30; the kernel-hardening of v438/SEAM.EQUIV.BW.HSMI.01) -- new module TfptCarrier/SeamStandardPair.lean, lake build OK, #print axioms CLEAN. It kernel-checks the four standard-pair RELATIONS on the centred 5-mode ladder over Z: [F] boost-translation commutator [K,P]=P (boost_translation_comm), [F] reflection involution J^2=1 (reflection_involution), [F] reflection reverses the boost JKJ=-K (reflection_reverses_boost), [F] reflection flips the translation JPJ=P_+ (reflection_flips_translation), bundled as standard_pair_relations -- ALL by kernel decide (axioms propext/Classical.choice/Quot.sound only, NO domain axiom); plus [F] boost_traceless tr K=0 (the structural reason a reflection CAN reverse the boost). The cited Borchers/Wiesbrock theorem (standard pair => +half-sided modular inclusion => geometric modular flow) and the one continuum input (assembling the finite ladder + positive-energy rep into a CONTINUUM standard pair, the same wall as MMST/NPW26) are declared as NAMED axioms (borchers_wiesbrock, seam_continuum_standard_pair); the composition geometricModularFlowFromStandardPair pins face (ii) of SEAM.EQUIV.01 to EXACTLY those two -- intrinsic Bisognano-Wichmann, no rotation-covariance presupposed. So the standard-pair RELATIONS are machine-checked; only the cited Borchers step + the continuum existence are assumed -- no sorry, no hidden assumption. Mirrors v438 (which verifies the same relations + sl(2,R) positivity numerically).
Original classification detail
Formal
Dependencies as recorded
SEAM.EQUIV.BW.HSMI.01; SEAM.EQUIV.01; FORM.SEAM.MMST.01; v438
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- Research contracts
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- Research Contract 1 — [formula in source]tfpt research contracts
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- Research Contract 1 — [formula in source]tfpt research contracts
- 2026-06-30 (Lean kernel-hardening of two of the seven SEAM.EQUIV.01 routes — the Borchers/Wiesbrock standard-pair relations and the applicability-ledger count, machine-verified with clean axioms; rigor without new mathematics)Research changelog; TFPT — Introduction and reading guide
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