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Original ledger classification: Lattice-VOA route to (E8)_1 [E]/[C]: E8 even unimodular (det 1, holomorphic); 248=8+240 currents, the 240 roots split 112 integer + 128 spinor (248=120+128) -- A_{E8} (Adamo-Giorgetti-Tanimoto) constructs the 128-spinor extension MMST (v458) misses; two complementary routes cover (E8)_1, residual = the single realization input (v456); SEAM.EQUIV.01 stays [O]
Recorded statement: The SECOND, independent route to (E8)_1 -- the lattice-VOA / conformal-net A_Q(E8) construction supplies EXACTLY the 128-spinor extension MMST (v458) leaves open (2026-06-30, G5 of the post-F next steps). Cited: Adamo-Giorgetti-Tanimoto,…
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SEAM.EQUIV.LATTICEVOA.01
Original ledger classification: Lattice-VOA route to (E8)_1 [E]/[C]: E8 even unimodular (det 1, holomorphic); 248=8+240 currents, the 240 roots split 112 integer + 128 spinor (248=120+128) -- A_{E8} (Adamo-Giorgetti-Tanimoto) constructs the 128-spinor extension MMST (v458) misses; two complementary routes cover (E8)_1, residual = the single realization input (v456); SEAM.EQUIV.01 stays [O]
Original claim text
The SECOND, independent route to (E8)_1 -- the lattice-VOA / conformal-net A_Q(E8) construction supplies EXACTLY the 128-spinor extension MMST (v458) leaves open (2026-06-30, G5 of the post-F next steps). Cited: Adamo-Giorgetti-Tanimoto, 'Rational and non-rational 2d CFTs arising from lattices' (arXiv:2506.01008, 2025); OS for unitary lattice VOAs (Adamo-Moriwaki-Tanimoto, arXiv:2407.18222). [E] E8 EVEN UNIMODULAR: det Cartan(E8)=1 and even => A_{E8} HOLOMORPHIC (one sector, the det K=1 the residual demanded). [E] LATTICE CURRENTS 248=8+240: 8 Cartan + 240 roots = the full (E8)_1 weight-1 space, constructed from the lattice (not bilinears). [E] THE 240 ROOTS SPLIT 112+128: 112 INTEGER (D8) + 128 HALF-INTEGER; 8+112=120=so(16) and the 128 half-integer roots ARE the spinor (248=120+128=8+240) -- the lattice route builds the 128-spinor explicitly. [C] AGT THEOREM: A_Q of an even lattice IS a 2d conformal net; the holomorphic SO(16)_1->(E8)_1 extension is CONSTRUCTED, not assumed. [C]/[O] TWO complementary routes now cover (E8)_1 (MMST fermions v458 + lattice net A_{E8}); the residual reduces to the single realization input 'the collar's scaling limit = A_{E8}' (tied to P1 by v456). SEAM.EQUIV.01 stays [O].
Original classification detail
Identity
Dependencies as recorded
SEAM.EQUIV.01; SEAM.S3.MODULAR.01; SEAM.S3.FROM-P1.01; v458; v456; v281; v336
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- 2026-06-30 ( v454– v459 + Lean + Wolfram — the post-F ``G-block'': the lattice Sugawara current algebra, a uniform-in- [formula in source] Tomita–Takesaki tower, chirality forced by [formula in source] , an [formula in source] character kill test, the exact MMST citation audit and the complementary lattice-VOA route)Research changelog; TFPT — Introduction and reading guide
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
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- 2026-06-30 ( v463/ v464 + Lean + Wolfram — the [formula in source] holomorphic-uniqueness pin and the one-particle realisation rigidity: the SEAM.EQUIV.01 residual reduced to entirely certification on both halves)Research changelog; TFPT — Introduction and reading guide
- Die direkte KonstruktionTFPT Gesamtsynthese 2026-09-28
- Originale Herleitungs- und AusschlussorteTFPT Gesamtsynthese 2026-09-28
- Research Contract 1 — [formula in source]tfpt research contracts
- Front matter / supportResearch contracts
- 2026-06-30 ( v461/ v462 + Lean axiom merge — the strict-locality obstruction made explicit, the 128-spinor extension exhibited at character level, and the SEAM.EQUIV.01 residual reduced to ONE realisation axiom [formula in source] ONE combined cited theorem)Research changelog; TFPT — Introduction and reading guide
- Front matter / supportResearch contracts
- 2026-07-02 ( v469/ v470 — the closure-route round on the two named targets: the SEAM.EQUIV.01 extension leg re-founded on 1995–2001 peer-reviewed crossed-product theorems [formula in source] the realisation axiom reduced to invariant level; the [formula in source] level [formula in source] the computed bulk Chern invariant [formula in source] the seam [formula in source] -normalisation [formula in source] the embedding index [formula in source] ; both targets stay )Research changelog; TFPT — Introduction and reading guide
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Registered verification modules
- v459_seam_lattice_voa_route.pyRegistered verification module · frontier
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SEAM.EQUIV.LATTICEVOA.01: the SECOND, independent route to (E8)_1 -- the lattice net A_Q(E8) (Adamo-Giorgetti-Tanimoto arXiv:2506.01008 + OS arXiv:2407.18222) supplies the 128-spinor extension MMST (v458) leaves open (G5). [E] E8 EVEN UNIMODULAR: det Cartan=1, all 240 roots norm 2 -- A_{E8} is a holomorphic net (det K=1). [E] LATTICE CURRENTS 248=8+240: weight-1 = 8 Cartan + 240 roots. [E] THE 240 ROOTS SPLIT 112+128=SPINOR: 8+112=120=so(16), the 128 half-integer roots ARE the spinor (248=120+128=8+240). [C] AGT: A_Q of an even lattice IS a 2d conformal net, so the SO(16)_1->(E8)_1 extension is constructed, not assumed. [C]/[O] two complementary routes cover (E8)_1; residual = the one realization input (collar=A_{E8}), tied to P1 by v456; SEAM.EQUIV.01 stays [O]. Exact (Wolfram-mirrored) + structural.
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