A registered result in its source context
Original ledger classification: c=8 holomorphic-uniqueness pin [E]/[C]: c=8 has three level-1 candidates (A8/80, D8/120, E8/248) so c=8 is not sufficient; holomorphy forces the character E4/eta^8 => dim V_1=248 => E8 uniquely; Dong-Mason/Schellekens give holomorphic c=8 VOA unique = V_{E8}, so the identification half of SEAM.EQUIV.01 is [C] (classification-forced); SEAM.EQUIV.01 stays [O]
Recorded statement: The c=8 HOLOMORPHIC-UNIQUENESS pin (2026-06-30, B of the A+B 'actually close it' round) -- the positive lever making the IDENTIFICATION half of SEAM.EQUIV.01 classification-forced rather than assumed. v458/v459 close the continuum…
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Paper context: Research contracts
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SEAM.EQUIV.UNIQ.01
Original ledger classification: c=8 holomorphic-uniqueness pin [E]/[C]: c=8 has three level-1 candidates (A8/80, D8/120, E8/248) so c=8 is not sufficient; holomorphy forces the character E4/eta^8 => dim V_1=248 => E8 uniquely; Dong-Mason/Schellekens give holomorphic c=8 VOA unique = V_{E8}, so the identification half of SEAM.EQUIV.01 is [C] (classification-forced); SEAM.EQUIV.01 stays [O]
Original claim text
The c=8 HOLOMORPHIC-UNIQUENESS pin (2026-06-30, B of the A+B 'actually close it' round) -- the positive lever making the IDENTIFICATION half of SEAM.EQUIV.01 classification-forced rather than assumed. v458/v459 close the continuum EXISTENCE; this pins WHY the limit must be (E8)_1 and not a same-c rival. [E] c=8 NOT UNIQUE AT LEVEL 1: c=dim g/(1+h^v)=8 has THREE simple solutions A8 (dim 80), D8=so(16) (dim 120), E8 (dim 248) -- c=8 is necessary but NOT sufficient (the v457 det K=4 SO(16) rival is a genuine gleich-c competitor). [E] HOLOMORPHY FORCES dim V_1=248: a single-sector c=8 chiral CFT has an SL(2,Z)-covariant character; the only weight-0 form with leading q^{-1/3} and integer coeffs is j^{1/3}=E4/eta^8, q^1 coeff 248 (1-dim candidate space, vacuum a_0=1) -- forced. [E] dim 248 + level-1 c=8 => E8 uniquely (only E8 has dim 248; 248/(1+30)=8); A8/D8 excluded. [E] tower {1,248,4124,34752,213126}=E4/eta^8; E4/eta^8=j^{1/3} (numeric <1e-25). [C] Dong-Mason/Schellekens: the holomorphic VOA at c=8 is UNIQUE = V_{E8}; the even unimodular rank-8 lattice is unique = E8 (Mordell-Witt). So 'c=8 holomorphic limit = (E8)_1' is classification-forced; with v458/v459 the continuum/identification HALF of SEAM.EQUIV.01 is [C], leaving the realisation R1 (v464). SEAM.EQUIV.01 stays [O].
Original classification detail
Identity
Dependencies as recorded
SEAM.EQUIV.01; SEAM.EQUIV.MMST.AUDIT.01; SEAM.EQUIV.LATTICEVOA.01; SEAM.EQUIV.KILLTEST.01; v457; v458; v459
Open the original ledger source, row 526Location recorded in the ledger
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- Research contracts
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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
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
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- Research Contract 1 — [formula in source]tfpt research contracts
- Front matter / supportResearch contracts
- 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
- Research Contract 1 — [formula in source]tfpt research contracts
Registered verification modules
- v463_seam_c8_holomorphic_uniqueness.pyRegistered verification module · frontier
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SEAM.EQUIV.UNIQ.01: the c=8 holomorphic-uniqueness pin -- the positive lever that makes the IDENTIFICATION half of SEAM.EQUIV.01 classification-forced (B of the A+B round). [E] c=8 NOT UNIQUE AT LEVEL 1: c=dim/(1+h^v)=8 has THREE simple solutions -- A8 (80), D8=so(16) (120), E8 (248); c=8 is necessary but NOT sufficient. [E] HOLOMORPHY FORCES dim V_1=248: the only weight-0 form with leading q^{-1/3} and integer coeffs is j^{1/3}=E4/eta^8, q^1 coeff 248. [E] dim 248 + level-1 c=8 => E8 uniquely (248/(1+30)=8); A8/D8 excluded. [E] tower {1,248,4124,34752,213126}=E4/eta^8; E4/eta^8=j^{1/3}. [C] Dong-Mason/Schellekens: holomorphic c=8 VOA unique = V_{E8}; so the identification half of SEAM.EQUIV.01 is [C], leaving the realisation R1 (v464). SEAM.EQUIV.01 stays [O]. Exact (sympy q-series + Lie scan; mpmath) Wolfram-mirrored.
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