Skip to main content

A registered result in its source context

Original ledger classification: SEAM.EQUIV.01 reduced to the single S3 lattice-realisation input; MMST in-class verified for the collar [E]/[C]/[O]

Recorded statement: 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…

Statement, assumptions and sources

Paper context: tfpt research contracts

The exact identifier, original classification and full claim are available below.

The source wording and classification below are preserved as recorded. A paper link, shared script or authored topic relation does not upgrade the claim or report a new proof run. Read later reviewed findings separately.

Read the exact registered claim and its dependencies

SEAM.MMST.INCLASS.01

Original ledger classification: SEAM.EQUIV.01 reduced to the single S3 lattice-realisation input; MMST in-class verified for the collar [E]/[C]/[O]

Original claim text

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.

Original classification detail

[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 as recorded

SEAM.EQUIV.01; v336; v356; v351; v302; v155; v160; v297; v301

Open the original ledger source, row 79

Location recorded in the ledger

These document locations are recorded directly on the ledger row. They are document level navigation, rather than a newly inferred section citation.

Sections that explicitly cite this claim

A literal claim identifier is present in these paper sections. The section and its premises determine what the citation supports.

Navigation through a shared verification script

These sections cite a script associated with the claim. This is a source navigation join, rather than an explicit citation of the claim or a theorem equivalence.

All 10 linked sections

Registered verification modules

  • v366_mmst_seam_collar.pyRegistered verification module · core
    Read the description recorded in the module registry

    Direction 7: 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. Osborne-Stottmeister (arXiv:2107.13834, CMP 398 (2023) 219; legacy internal token MMST, on the MMST/Morinelli-Morsella-Stottmeister-Tanimoto OAR framework): free lattice fermions (CAR quasi-free) -> chiral-CFT massless scaling limit with correct c, range rank<=c<=D. [E] class arithmetic: D=dim S^+=2^(g_car-1)=16 Majoranas, c=g_car+N_fam=8, rank E8=8 => rank<=c<=D is 8<=8<=16 (in MMST range). [E] gapped (Delta=6 ln(3/2)>0, derived v302). [C] quasi-free CAR class (v155/v160). [E] chirality c_-=D/2=8 != 0 (non-gappable anomalous edge, v356 S4). [C] the MMST scaling-limit theorem applies (in-class & gapped & chiral & in-range) => chiral CFT c=8 (v336). [E] target pinned to (E8)_1 by c=8 + the order-4 mu4 clock (det K=1 vs SO(16) det K=4, v351). [O] residual S3: the collar realised as a genuine lattice chiral free-fermion invertible phase (one-sidedness/Flat-Away, v297/v356). Verifies MMST in-class; ADVANCES SEAM.EQUIV.01, does NOT close it.

A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.

Search later reviewed research for this identifierRead the coverage boundaries