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Original ledger classification: Formal [F] (Lean kernel; closed modulo the cited MMST/Adamo theorems)

Recorded statement: LEAN 4 FORMALISATION of the S3 / SEAM.EQUIV.01 continuum leg (the MMST scaling-limit theorem applied to the seam collar), 2026-06-23 -- new module TfptCarrier/SeamScalingLimit.lean, lake build OK (target TfptCarrier.SeamScalingLimit,…

Statement, assumptions and sources

Paper context: TFPT — Introduction and reading guide

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FORM.SEAM.MMST.01

Original ledger classification: Formal [F] (Lean kernel; closed modulo the cited MMST/Adamo theorems)

Original claim text

LEAN 4 FORMALISATION of the S3 / SEAM.EQUIV.01 continuum leg (the MMST scaling-limit theorem applied to the seam collar), 2026-06-23 -- new module TfptCarrier/SeamScalingLimit.lean, lake build OK (target TfptCarrier.SeamScalingLimit, 230ms), #print axioms CLEAN. It formalises the status 'CLOSED MODULO A CITED THEOREM': (1) [F] the MMST applicability HYPOTHESES for the collar are PROVABLE arithmetic facts by kernel decide (NO axioms) -- D=16 Majoranas, rank=c=8, the range rank<=c<=D i.e. 8<=8<=16 (mmst_range), chiral c_-=D/2=8!=0 (chiral), and the holomorphy discriminator det K=1 vs the same-c rival SO(16) det K=4 (holomorphic_discriminator); (2) [C] the seam scaling-limit theorem (Osborne-Stottmeister, arXiv:2107.13834, CMP 398 (2023) 219; legacy internal token 'MMST', built on the MMST/Morinelli-Morsella-Stottmeister-Tanimoto OAR framework arXiv:2010.11121) and the Adamo-Moriwaki-Tanimoto OS/holomorphy selector (2024) are declared as NAMED cited axioms (mmst_scaling_limit, adamo_holomorphic_e8); (3) the conclusion SeamIsE8 = (E8)_1 follows by the well-typed composition seamScalingLimit, and #print axioms pins the residual to EXACTLY those two cited theorems + the one carrier-forced gap (collar_gapped) -- no hidden assumption, no sorry. Mirrors the S3 closure stack v376/v377/v378/v379 (which pin the TARGET c=8 / (E8)_1 character / torus GSD=1 / RP numerically). So S3 is closed modulo the two published theorems; every TFPT-internal hypothesis is machine-checked.

Original classification detail

Formal [F]: the S3 continuum leg machine-formalised as 'closed modulo cited theorems' -- the collar's MMST hypotheses kernel-proved (decide, no axioms), the MMST/Adamo theorems named axioms, the composition's #print axioms clean. The honest closure ceiling for SEAM.EQUIV.01.

Dependencies as recorded

SEAM.EQUIV.01; v336; v366; v376; v377; v378; v379; FORM.GLUE.01

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