A registered result in its source context
Original ledger classification: Identity [I] (BFK/Kac algebra exact) + [A] (the theorem proper stays open)
Recorded statement: THE BFK SPLIT (the Calderon-transfer step of SEAM.EHMODEL.01/v150 ANSWERED; SEAM.THEOREM.01 narrows again, stays open): (1) DOUBLING => C_N = C_D [I] - reflecting a wedge across its edges gives the cone of doubled angle with exact odd/even…
Statement, assumptions and sources
Paper context: Origin Theory
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SEAM.EHMODEL.02
Original ledger classification: Identity [I] (BFK/Kac algebra exact) + [A] (the theorem proper stays open)
Original claim text
THE BFK SPLIT (the Calderon-transfer step of SEAM.EHMODEL.01/v150 ANSWERED; SEAM.THEOREM.01 narrows again, stays open): (1) DOUBLING => C_N = C_D [I] - reflecting a wedge across its edges gives the cone of doubled angle with exact odd/even (D/N) spectral split, so C_N(theta) = C_cone(2 theta) - C_D(theta) = (pi^2 - theta^2)/(24 pi theta) = C_D(theta): the Kac corner constant is boundary-condition INDEPENDENT (the D/N difference lives in the perimeter term); (2) BFK SPLIT [I]: by Burghelea-Friedlander-Kappeler, det(bulk) = det(D-half)^2 x det(DtN) x (local edge factors), so the conical deficit of the two-sided Calderon/DtN jump determinant is C_cone(gamma) - 2 C_D(gamma/2) = C_N - C_D = 0 IDENTICALLY - the nonlocal Calderon kernel is conically CLEAN, it carries no curvature term of its own; (3) CONSEQUENCE [I]: log Z_boundary = -(1/2) log det(bulk) (BFK consistency), so the gapped conical variation of the seam-reduced effective action is the v150 EH form verbatim (coefficient ln m/(12 pi), cutoff-independent), with ALL of it localised in the LOCAL half-space determinants - the 'Calderon version' demands no new derivation; (4) target equation unchanged [I, audit]: k = c3/2 <=> ln m = 3/4 = q(A3). HONEST SCOPE [P]: 2d gapped model; remaining for SEAM.THEOREM.01: the q(A3) normalisation + the standing premise that the RP seam kernel is this BFK Calderon datum
Original classification detail
Identity [I]: Calderon kernel conically clean; EH content = local half determinants; residue = q(A3) normalisation + premise
Dependencies as recorded
SEAM.EHMODEL.01; SEAM.THEOREM.01; v59; v150
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- Origin Theory
Sections that explicitly cite this claim
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- The seam and the horizon: the precise statementorigin theory
- The seam and the horizon: the precise statementinput 4 origin theory
- The seam and the horizon: the precise statementinput 4 origin theory
- 2026-06-12 (fourth round: the Calder\'on transfer answered — the BFK split, v151)Research changelog; TFPT — Introduction and reading guide
- The seam and the horizon: the precise statementOrigin Theory
Navigation through a shared verification script
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- 2026-07-02 ( v471 — the Seam–Horizon replica chain exercised numerically on the discretized collar: the kernel-identification premise of SEAM.THEOREM.01 discharged at the finite/model level; residual retypes to the continuum MMST leg [formula in source] the anchor; gate stays . Plus: the GW ringdown-echo channel hardened — 10 loudest events incl.\ GW250114, redshift-corrected templates, stacked search and a 12-variant signature battery, all null)Research changelog; TFPT — Introduction and reading guide
- The whole integer skeleton from one pair [formula in source]input 4 origin theory
- The EM closure: [formula in source] as an explicit fixed point (made explicit here)tfpt 1 architecture e8
- The whole integer skeleton from one pair [formula in source]input 4 origin theory
- The EM closure: [formula in source] as an explicit fixed point (made explicit here)tfpt 1 architecture e8
- 2026-06-13 (the seam-side identification reduced to one shared premise, v155)Research changelog; TFPT — Introduction and reading guide
- The whole integer skeleton from one pair [formula in source]Origin Theory
- The EM closure: [formula in source] as an explicit fixed point (made explicit here)Architecture, E8 and the electromagnetic fixed point
All 14 linked sections
- Research Contract 2 — [formula in source]
- Front matter / support
- Front matter / support
- 2026-07-14 (IV) ( v485 — the merged analytic target's computable side COMPLETED: the diagonal self-energy is renormalised to ZERO exactly at the KMS seam scale, the mark contact calculus resums in closed form (BFK route), and the [formula in source] / [formula in source] multiplicities are ONE state set under two response weights — the residual collapses onto the SEAM.EQUIV.01 face alone; no gate closes, no marker moves)
- Research Contract 2 — [formula in source]
- The whole integer skeleton from one pair [formula in source]
Registered verification modules
- v151_bfk_split.pyRegistered verification module · registry
Read the description recorded in the module registry
BFK split (R3): Kac corner constant is boundary-condition independent (C_N = C_D, via doubling) ⇒ the conical deficit of the Calderón/DtN jump determinant VANISHES identically — the seam-reduced action inherits the v150 EH form via BFK; the EH content sits in the local half determinants; residue = q(A₃) normalisation + kernel premise
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