Original ledger status
SEAM.MMST.INCLASS.01
SEAM.MMST.INCLASS.01
Direction 7 (2026-06-23): the seam collar is IN MMST's free-lattice-fermion scaling-limit class, so the chiral scaling limit is a chiral CFT of central charge 8 pinned to (E8)_1 -- reducing SEAM.EQUIV.01 to the single S3 lattice-realisation input. the cited theorem (Osborne-Stottmeister, arXiv:2107.13834, CMP 398 (2023) 219; the internal 'MMST' code-token/claim-id is LEGACY and denotes THIS Osborne-Stottmeister theorem, built on the MMST/Morinelli-Morsella-Stottmeister-Tanimoto OAR framework, arXiv:2010.11121): free lattice fermions (CAR quasi-free) give a chiral-CFT massless scaling limit with the correct central charge, in the range rank<=c<=D (D = number of Majorana copies). [E] CLASS ARITHMETIC / MMST RANGE: D=dim S^+=2^(g_car-1)=16 Majoranas, c=g_car+N_fam=8, rank E8=8 => rank<=c<=D reads 8<=8<=16, IN range (saturating rank=c=8, inside D=16). [E] GAPPED (derived, not assumed): Delta=6 ln(3/2)>0 (v302). [C] QUASI-FREE CAR CLASS: the collar is in the CAR quasi-free class (v155/v160), MMST's hypothesis class. [E] CHIRALITY: c_-=D/2=8=g_car+N_fam!=0 (a non-gappable anomalous edge by inflow, v356 S4). [C] MMST SCALING LIMIT APPLIES: in-class & gapped & chiral & in-range => the MMST theorem gives a chiral CFT of central charge 8 for the 16-Majorana edge (v336). [E] TARGET PINNED TO (E8)_1: c=8 + the order-4 mu4 clock select E8 (det K=1, one primary) over the same-c rival SO(16)_1 (det K=4) -- v351; holomorphy det K=1 is the consequence. [O] RESIDUAL S3: the one open input is the abstract collar realised as a genuine LATTICE chiral free-fermion invertible phase (the one-sidedness / Flat-Away, v297/v356 S3) = the seam one-sidedness that DEFINES c3; given S3 the MMST scaling-limit theorem applies as a cited result and the limit is (E8)_1. Verifies MMST in-class; ADVANCES SEAM.EQUIV.01, does NOT close it.
Recorded status: SEAM.EQUIV.01 reduced to the single S3 lattice-realisation input; MMST in-class verified for the collar [E]/[C]/[O]
Dependencies, status detail and source
Canonical status: [E] class arithmetic 8<=8<=16 + derived gap + chirality c_-=8 + (E8)_1 pinning; [C] the CAR-class typing + the MMST scaling-limit theorem (cited); [O] the S3 lattice realisation. Verifies MMST in-class; ADVANCES SEAM.EQUIV.01, does not close it.
Dependencies: SEAM.EQUIV.01; v336; v356; v351; v302; v155; v160; v297; v301
Scripts: v366_mmst_seam_collar.py
Location: tfpt_research_contracts
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