A registered result in its source context
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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- Research contracts
Sections that explicitly cite this claim
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- Externalization Contract — SEAM.EQUIV.01 (the seam scaling-limit theorem, packaged for external specialists)tfpt research contracts
- The closure ledger: what is done, and what genuinely remainsTFPT — Introduction and reading guide
- Honest statusinput 4 origin theory
- Front matter / supportResearch contracts
- The unique attractor: a gapped transport selects ONE fixed pointorigin theory
- The unique attractor: a gapped transport selects ONE fixed pointinput 4 origin theory
- Research Contract — CELEST.SEAM.01 (the celestial and twistor continuum route)tfpt research contracts
- 2026-06-23 (Status propagation: the v365– v380 [formula in source] FORM.SEAM.MMST.01 status carried into the remaining papers, the README and the Zenodo description)Research changelog; TFPT — Introduction and reading guide
All 40 linked sections
- Layer 6 — two independent reproduction paths
- Research Contract 1 — [formula in source]
- Honest status
- Research Contract — CELEST.SEAM.01 (the celestial and twistor continuum route)
- What this means for the theory-of-everything question
- Outcome
- The celestial and twistor continuum route
- The hard reduction: the live residual as typed interfaces
- Honest status
- Front matter / support
- (4) Constructive QFT closure of the admissible physical sector /
- The unique attractor: a gapped transport selects ONE fixed point
- Front matter / support
- Research Contract — CELEST.SEAM.01 (the celestial and twistor continuum route)
- Front matter / support
- Honest status
- Front matter / support
- The [formula in source] compiler: [formula in source] as a closure, not an input
- The celestial and twistor continuum route
- The [formula in source] compiler: [formula in source] as a closure, not an input
- Research Contract 1 — [formula in source]
- The compact status formula: three honest layers
- Front matter / support
- 2026-06-23 (Lean: the S3 continuum leg formalised as ``closed modulo a cited theorem'' — FORM.SEAM.MMST.01)
- Front matter / support
- The [formula in source] compiler: [formula in source] as a closure, not an input
- (4) Constructive QFT closure of the admissible physical sector /
- Full quantum gravity — induced from the boundary kernel
- Externalization Contract — SEAM.EQUIV.01 (the seam scaling-limit theorem, packaged for external specialists)
- The unique attractor: a gapped transport selects ONE fixed point
- In plain words
- Externalization Contract — SEAM.EQUIV.01 (the seam scaling-limit theorem, packaged for external specialists)
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