A registered result in its source context
Original ledger classification: (E8)_1 modular data [E]/[C]: the character chi=E4/eta^8 is S-invariant (one primary), T-multiplies by e^{-2pi i/3} (=e^{-2pi i c/24}, c=8) and has leading power q^{-1/3} (c=8=0 mod 8, holomorphic) -- the full torus modular signature of the seam (E8)_1 net; SEAM.EQUIV.01 stays [O]
Recorded statement: The (E8)_1 torus MODULAR DATA (2026-06-30) -- one primary, S-invariant, T-phase e^{-2pi i/3}, the holomorphic c=8 signature, extending v156's character q-expansion to the modular transformation data. A holomorphic (single-primary) RCFT…
Statement, assumptions and sources
Paper context: Research contracts
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SEAM.EQUIV.E8.MODULAR.01
Original ledger classification: (E8)_1 modular data [E]/[C]: the character chi=E4/eta^8 is S-invariant (one primary), T-multiplies by e^{-2pi i/3} (=e^{-2pi i c/24}, c=8) and has leading power q^{-1/3} (c=8=0 mod 8, holomorphic) -- the full torus modular signature of the seam (E8)_1 net; SEAM.EQUIV.01 stays [O]
Original claim text
The (E8)_1 torus MODULAR DATA (2026-06-30) -- one primary, S-invariant, T-phase e^{-2pi i/3}, the holomorphic c=8 signature, extending v156's character q-expansion to the modular transformation data. A holomorphic (single-primary) RCFT must have its torus character transform as a weight-0 modular form: S-invariant and T-multiplied by e^{-2 pi i c/24}. [E] S-INVARIANCE: chi(-1/tau)=chi(tau) for chi=E4/eta^8 (weight 0), to ~1e-30 at generic tau -- ONE primary, the S-matrix is [1]. [E] T-PHASE: chi(tau+1)/chi(tau)=e^{-2 pi i/3}=e^{-2 pi i c/24} (c=8), to ~1e-30 -- the central charge in the modular T eigenvalue. [E] LEADING POWER => c=8: chi*q^{1/3}->1, so the leading power is q^{-c/24}=q^{-1/3} => c=8=g_car+N_fam. [E] HOLOMORPHIC CONSTRAINT: c=8=0 mod 8 -- the minimal holomorphic chiral central charge, the even unimodular rank-8 lattice E8. [C]/[O] the (E8)_1 modular data (one primary, S-invariant, T-phase e^{-2pi i/3}, c=8) is the torus signature of the seam boundary net; with the edge readings (v444/v447/v450/v451) the (E8)_1 identity is pinned on the torus AND the edge; SEAM.EQUIV.01 stays [O] -- the cited continuum existence theorem (v336) is the residual.
Original classification detail
Identity
Dependencies as recorded
SEAM.EQUIV.01; SEAM.EQUIV.EDGE.CHERN.01; v156; v444; v281; v336
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- Research contracts
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- 2026-06-30 ( v449– v453 + Lean + Wolfram — the edge CFT named end-to-end: uniform-in- [formula in source] convergence, three independent reads of [formula in source] , the Ising operator tower, the [formula in source] modular data, and [formula in source] -symmetry derived from the four marks)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
- OutcomeRed-team audit
- Front matter / supportResearch contracts
- Research Contract 1 — [formula in source]tfpt research contracts
Registered verification modules
- v452_seam_e8_modular.pyRegistered verification module · frontier
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SEAM.EQUIV.E8.MODULAR.01: the (E8)_1 torus modular data -- one primary, S-invariant, T-phase e^{-2pi i/3}, the holomorphic c=8 signature (extends v156's q-expansion). [E] S-INVARIANCE: chi(-1/tau)=chi(tau) for chi=E4/eta^8 (weight 0), to ~1e-30 -- ONE primary, S-matrix=[1]. [E] T-PHASE: chi(tau+1)/chi(tau)=e^{-2pi i/3}=e^{-2pi i c/24} (c=8), to ~1e-30. [E] LEADING POWER => c=8: chi*q^{1/3}->1 so the leading power is q^{-c/24}=q^{-1/3} => c=8=g_car+N_fam. [E] HOLOMORPHIC CONSTRAINT: c=8=0 mod 8 (even unimodular rank-8 lattice E8). [C]/[O] the (E8)_1 modular data is the torus signature of the seam net; with the edge readings (v444/v447/v450/v451) (E8)_1 is pinned on torus AND edge; SEAM.EQUIV.01 stays [O]. Wolfram-mirrored.
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