A registered result in its source context
Original ledger classification: Lattice Virasoro/current algebra c=8 [E]/[C]: Casimir c_Dirac=1.000 (1/2 per Majorana), lattice U(1) current Kac-Moody level 1 (<J_n J_-n>=n exact), Sugawara c=dim G/(1+h^v)=8 for BOTH SO(16)_1 120/15 and (E8)_1 248/31; 16*(1/2)=8=g_car+N_fam; SEAM.EQUIV.01 stays [O]
Recorded statement: The lattice level-1 current algebra with Sugawara c=8 (2026-06-30, G2 of the post-F next steps) -- testing the cited MMST 'Koo-Saleur lattice generators -> continuum Virasoro with the correct c' fact on our own free-fermion edge. v450/v451…
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Paper context: Research contracts
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SEAM.EQUIV.EDGE.VIRASORO.01
Original ledger classification: Lattice Virasoro/current algebra c=8 [E]/[C]: Casimir c_Dirac=1.000 (1/2 per Majorana), lattice U(1) current Kac-Moody level 1 (<J_n J_-n>=n exact), Sugawara c=dim G/(1+h^v)=8 for BOTH SO(16)_1 120/15 and (E8)_1 248/31; 16*(1/2)=8=g_car+N_fam; SEAM.EQUIV.01 stays [O]
Original claim text
The lattice level-1 current algebra with Sugawara c=8 (2026-06-30, G2 of the post-F next steps) -- testing the cited MMST 'Koo-Saleur lattice generators -> continuum Virasoro with the correct c' fact on our own free-fermion edge. v450/v451 read c=1/2 and {1/16,1/2}; this tests the ALGEBRA carries the correct central extension. [E] CASIMIR: the critical complex free-fermion ring E_0(L)=e_inf L - pi v c/(6L) (Affleck-Cardy) fits c_Dirac=1.000 => c per Majorana 1/2 (L=64..1024, parameter-free). [E] KAC-MOODY LEVEL: the lattice U(1) current J_n has <0|J_n J_-n|0>=n EXACTLY (n=1..8) -- the level-1 affine central extension closes; a gapped (dimerised) control gives a vanishing non-linear term. [E] SUGAWARA EXACT: c=dim G/(1+h^v)=8 for BOTH SO(16)_1 (120/15) and (E8)_1 (248/31) -- Wolfram-mirrored. [C] ASSEMBLY: 16 Majoranas x 1/2 = 8 = the level-1 Sugawara c; the edge IS a c_-=8 level-1 current-algebra CFT. SEAM.EQUIV.01 stays [O] (the continuum existence theorem v336 is the cited backbone).
Original classification detail
Numerical
Dependencies as recorded
SEAM.EQUIV.01; SEAM.EQUIV.EDGE.CARDY.01; SEAM.EQUIV.EDGE.ENTANGLEMENT.01; SEAM.MMST.INCLASS.01; v450; v451; v336
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- Research contracts
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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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- Der positive Fermi-Patch: ein kontrollierter AnfangTFPT Universalraum Sitzungsdokumentation 2026-09-20 v2
- Der positive Fermi-Patch: ein kontrollierter AnfangTFPT Universalraum Sitzungsdokumentation 2026-09-20
- Research Contract 1 — [formula in source]tfpt research contracts
- Front matter / supportResearch contracts
- Front matter / supportResearch contracts
- Research Contract 1 — [formula in source]tfpt research contracts
Registered verification modules
- v454_seam_edge_virasoro.pyRegistered verification module · frontier
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SEAM.EQUIV.EDGE.VIRASORO.01: the lattice realises the level-1 current algebra whose Sugawara central charge is EXACTLY 8 (G2) -- testing the cited MMST 'Koo-Saleur -> Virasoro with the correct c' fact on our own free-fermion edge. [E] CASIMIR c: E_0(L)=e_inf*L - pi*v*c/(6L) (Affleck-Cardy) gives c_Dirac=1.000 -> 1/2 per Majorana (parameter-free, L=64..1024). [E] KAC-MOODY LEVEL: the lattice U(1) current has <0|J_n J_-n|0>=n exactly (n=1..8) -- the affine level-1 central extension closes; a gapped control gives a vanishing non-linear term. [E] SUGAWARA EXACT: c=dim G/(1+h^v)=8 for BOTH SO(16)_1 (120/15) and (E8)_1 (248/31). [C] 16 Majoranas => c_-=8=g_car+N_fam. [C]/[O] SEAM.EQUIV.01 stays [O]. Mixed numerical (Casimir, Kac-Moody) + exact (Sugawara, Wolfram-mirrored).
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