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Original ledger classification: Applicability ledger [E]/[C]: a hypothesis-by-hypothesis audit of MMST/NPW26/Adamo finds 11 of 12 hypotheses are TFPT-internal computed facts and exactly 1 is external -- the continuum existence of the chiral massless scaling limit; covariance is an Adamo consequence (defuses v215), not an input. SEAM.EQUIV.01's external dependence is pinned to ONE analytic fact; stays [O]

Recorded statement: The applicability ledger (2026-06-30) -- a hypothesis-by-hypothesis audit of the THREE external theorems the seam keystone cites (MMST scaling limit, NPW26 (LTO-RP), Adamo-Giorgetti-Tanimoto covariance), isolating the SINGLE…

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Paper context: Research contracts

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SEAM.EQUIV.APPLICABILITY.01

Original claim text

The applicability ledger (2026-06-30) -- a hypothesis-by-hypothesis audit of the THREE external theorems the seam keystone cites (MMST scaling limit, NPW26 (LTO-RP), Adamo-Giorgetti-Tanimoto covariance), isolating the SINGLE genuinely-imported analytic fact. Answers the reviewer worry that the cited theorems may carry hidden hypotheses, by classifying every hypothesis as either a TFPT-internal computed fact (with its establishing vN) or a genuinely external analytic assumption. [E] MMST HYPOTHESES: D=16 Majoranas (=2^{g_car-1}), c=8 (=g_car+N_fam), rank E8=8, range rank<=c<=D reads 8<=8<=16 (in range, saturating rank=c=8), gapped (6 ln(3/2)>0), quasi-free CAR -- all internal computed facts. [E] NPW26 HYPOTHESES: (LTO-RP)=u_Theta=J, gap, Z2 reflection, mu4 clock, [rho,K]=0 internal (v424/v426/v440); the seam is invertible |det Cartan E8|=1 + beta=1 KMS, OUTSIDE NPW26's topological/trace bucket (worked |det|=4) -- NPW26 used as a TEMPLATE, its theorem not directly imported. [E] ADAMO-GIORGETTI-TANIMOTO (arXiv:2508.07109): DHR reps of nets extending loop-group/Virasoro are AUTOMATICALLY positive-energy + diff-covariant; the seam net extends (D5)_1 x (A3)_1 (v154), so geometric covariance is a CONSEQUENCE -- the 'BW presupposes covariance' circularity (v215) is defused; covariance downgraded ASSUMPTION->[E]. [E] THE SINGLE IMPORTED FACT: of 12 audited hypotheses, 11 are TFPT-internal computed facts and exactly 1 is external -- the continuum EXISTENCE of the chiral massless scaling limit (MMST/v336, Lean FORM.SEAM.MMST.01). [C]/[O] VERDICT: the keystone's external dependence is pinned to ONE analytic fact; covariance is an Adamo consequence, not an input; SEAM.EQUIV.01 stays [O] -- that one fact is the honest closure ceiling.

Original classification detail

Numerical

Dependencies as recorded

SEAM.EQUIV.01; SEAM.MMST.INCLASS.01; SEAM.EQUIV.LTORP.01; SEAM.EQUIV.LTORP.KMS.01; v424; v426; v440; v336; v154; v215

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Research contracts
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Sections that explicitly cite this claim

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Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
2026-06-30 (six convergent attacks on the one SEAM.EQUIV.01 continuum residual — intrinsic Bisognano–Wichmann, a Lieb–Robinson continuum motor, the [formula in source] -homotopy, an applicability audit, uniform rigidity, and falsifiable kill tests; none closes the keystone, together they reduce it to a single analytic fact and make the claim falsifiable)Research changelog; TFPT — Introduction and reading guide

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Research Contract 1 — [formula in source]tfpt research contracts
Front matter / supportResearch contracts
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

Registered verification modules

v441_seam_applicability_ledger.pyRegistered verification module · frontier
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SEAM.EQUIV.APPLICABILITY.01: the applicability ledger -- a hypothesis-by-hypothesis audit of the THREE external theorems the seam keystone cites (MMST scaling limit, NPW26 (LTO-RP), Adamo-Giorgetti-Tanimoto covariance), isolating the SINGLE imported analytic fact. [E] MMST HYPOTHESES: D=16 Majoranas (=2^{g_car-1}), c=8 (=g_car+N_fam), rank E8=8, range rank≤c≤D (8≤8≤16), gapped, quasi-free CAR -- all internal computed facts. [E] NPW26: (LTO-RP)=u_Θ=J, gap, Z2 reflection, mu4 clock, [ρ,K]=0 internal; the seam invertible |det Cartan E8|=1 + β=1 KMS is OUTSIDE NPW26's bucket (|det|=4) -- a TEMPLATE not a direct import. [E] ADAMO (arXiv:2508.07109): covariance is a CONSEQUENCE (defuses the v215 circularity, downgrades cov. ASSUMPTION→[E]). [E] of 12 hypotheses, 11 internal [E] and exactly 1 external -- the continuum EXISTENCE of the chiral massless scaling limit. [C]/[O] external dependence pinned to ONE analytic fact; SEAM.EQUIV.01 stays [O]. Python-only (dets Wolfram-mirrored via v89/v281/v422).

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