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Original ledger classification: Entanglement c_-=8 [E]/[C]: the Calabrese-Cardy law gives c_Dirac=1=2*(1/2) for the critical free-fermion chain (vs a saturating gapped control), so c_Majorana=1/2 and c_-=16*(1/2)=8=g_car+N_fam -- a third independent reading of the edge central charge after v444/v447; SEAM.EQUIV.01 stays [O]
Recorded statement: A THIRD independent reading of the edge central charge c_-=8 (2026-06-30) -- the Calabrese-Cardy entanglement scaling, after v444 (correlator) and v447 (topology). For a critical 1D free-fermion chain the Calabrese-Cardy law…
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SEAM.EQUIV.EDGE.ENTANGLEMENT.01
Original ledger classification: Entanglement c_-=8 [E]/[C]: the Calabrese-Cardy law gives c_Dirac=1=2*(1/2) for the critical free-fermion chain (vs a saturating gapped control), so c_Majorana=1/2 and c_-=16*(1/2)=8=g_car+N_fam -- a third independent reading of the edge central charge after v444/v447; SEAM.EQUIV.01 stays [O]
Original claim text
A THIRD independent reading of the edge central charge c_-=8 (2026-06-30) -- the Calabrese-Cardy entanglement scaling, after v444 (correlator) and v447 (topology). For a critical 1D free-fermion chain the Calabrese-Cardy law S(ell)=(c/3)ln[(L/pi)sin(pi ell/L)]+const fixes the central charge. [E] CALABRESE-CARDY LAW: the block entanglement entropy of the critical XX (Dirac) chain has a flat log slope -> c_Dirac=1.000 (fit ell=20..200, L=400) -- the universal scaling-limit signature. [E] c PER MAJORANA = 1/2: c_Dirac=1=2*c_Majorana (Dirac = two Majoranas), so c_Majorana=1/2 -- the chiral CFT of one p+ip edge mode (v444). [E] GAPPED NEG CONTROL: a dimerised (gapped) chain has saturating, ell-independent entanglement (c=0) -- the log growth is the CRITICAL edge CFT, not a lattice artefact. [C] EDGE CENTRAL CHARGE: c_- = N_Maj*c_Majorana = 16*(1/2) = 8 = g_car+N_fam, from entanglement -- the SAME c_-=8 as v444 (correlator) and v447 (topology), from a third independent observable. [C]/[O] three observables agree; SEAM.EQUIV.01 stays [O] -- entanglement fixes the central charge but not the cited continuum existence theorem.
Original classification detail
Numerical
Dependencies as recorded
SEAM.EQUIV.01; SEAM.EQUIV.CONTINUUM.EDGE.01; SEAM.EQUIV.EDGE.CHERN.01; v444; v447
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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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- 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
- 2026-07-13 ( v478 — first computable steps on the two remaining legs of the entropic-action bridge: the state-side modular data flows to the CHM/Bisognano–Wichmann geometric form (Calabrese–Cardy [formula in source] , CHM parabola, even bands exactly zero) — the bridge's modular side meets TFPT's Einstein-derivation input; and the measure condition reduced to one exact KMS time [formula in source] with the [formula in source] near-miss explicitly declined; both legs stay , no status moves)Research changelog; TFPT — Introduction and reading guide
- Research Contract 1 — [formula in source]tfpt research contracts
- OutcomeRed-team audit
- 2026-07-20 (IV) (evidence scorecard: five new typed rows — the [formula in source] running prediction of record, the [formula in source] -distortion [formula in source] branch discriminator, and three parked analog beds (bosonic-E8 thermal Hall, E8 mass-ladder recovery, Efimov DSI tuning); experiments level only — no verification module, no gate closes, no marker moves)Research changelog; TFPT — Introduction and reading guide
- Front matter / supportResearch contracts
- Front matter / supportResearch contracts
- 2026-07-21 (XI) ( v501 — WP5d- [formula in source] of CELEST.SEAM.01 ``the two-interval index from the lattice'' promoted as CELEST.WP5D.01: the KLM Haag-duality discriminator measured entropically on the seam edge — the [formula in source] -layer carrier saturates the [formula in source] offset at machine precision, [formula in source] the v490 census, and the condensation arithmetic [formula in source] closes with [formula in source] ; the preregistered KILL (`` [formula in source] -offset [formula in source] after condensation'') does NOT fire; contract now ``WP1–WP5d executed; WP5e the single remaining milestone''; Wolfram extension [formula in source] (verified engine run); SEAM.EQUIV.01 stays , no marker moves)Research changelog; TFPT — Introduction and reading guide
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Registered verification modules
- v450_seam_edge_entanglement.pyRegistered verification module · frontier
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SEAM.EQUIV.EDGE.ENTANGLEMENT.01: a THIRD independent reading of the edge c_-=8 -- the Calabrese-Cardy entanglement scaling c=1/2 per Majorana (after v444 correlator, v447 topology). [E] CALABRESE-CARDY LAW: the block entanglement entropy of the critical XX (Dirac) chain fits S=(c/3)ln[(L/pi)sin(pi l/L)]+const with c_Dirac=1.000 -- the universal scaling-limit signature. [E] c PER MAJORANA = 1/2: c_Dirac=1=2*c_Majorana (Dirac=two Majoranas), so c_Majorana=1/2. [E] GAPPED NEG CONTROL: a dimerised chain has saturating (c=0) entanglement. [C] c_-=N_Maj*c_Majorana=16*(1/2)=8=g_car+N_fam, the SAME c_-=8 as v444/v447 from a third observable. [C]/[O] three observables agree; SEAM.EQUIV.01 stays [O]. Python-only (numpy).
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