A registered result in its source context

SEAM.DETLINE.UNIFICATION.01

Original ledger classification: Open [O] + finite bulk-edge shadow [E] (2+1D/1D QWZ; continuum Bismut-Freed stays Open)

Original claim text

THE DETERMINANT-LINE UNIFICATION HYPOTHESIS [O] (registered 2026-08-27 from the external bird's-eye review; a precise research hypothesis, NOT a result). OBSERVATION: three separately open structures may be projections of ONE geometric object -- (1) the seam extension is described by a Q-system/simple current (SEAM.SIMPLECURRENT.GENERATOR.01), (2) the chiral fermion measure lives on a determinant line (CHIRAL4D.NOMIRROR.01 demand C1), (3) anomalies and CP phases appear as holonomies of that determinant line (the finite Quillen identity is already TWO-SIDED at finite level -- v974/ALPHA.QUILLEN.FACES.01: Berry integral == Poincare-Lelong divisor integral == +1 -- and the continuum Bismut-Freed identification is the named missing step of ALPHA.QUILLEN.EXACT.01). DEMAND (the compatibility theorem): Res_seam det D_4D ~= det D_seam as line bundles WITH connection, AND the holonomy of the bulk determinant line equals the discrete TFPT orientation phase (the classically invisible sgn J orientation bit exhibited at exploration level, round DCXCVII -- experiments only, not promoted). IF such a theorem exists, seam extension, chiral anomaly freedom, the generation index and the discrete CP orientation become different projections of the same object. KILL TESTS: the two determinant lines differ by a nontrivial local factor no counterterm removes; the bulk holonomy disagrees with the discrete orientation phase on a computable family. HONEST BOUNDARY: the continuum Quillen/Bismut-Freed identification is exactly the critical missing step; nothing in the corpus proves any part of the 4D side; the sgn J bit is exploration-level input, cited as MOTIVATION only. EXECUTED UPDATE (2026-08-28, v991): finite bulk-edge determinant-line correspondence on the v367 QWZ collar -- occupied-frame FHS Chern = +1 (curvature 2 pi * (+1)); seam holonomy winding = +1 (diff 6e-16); M=3 control zero both sides; conjugation mutant flips both signs coherently. FIREWALL: 2+1D/1D finite lattice shadow; continuum Bismut-Freed and the 4D chiral-measure unification stay [O]. Python-only / Wolfram mirror deferred. LATE EVENING (2026-08-30, v1014): finite restriction isomorphism Res_Sigma L_bulk isomorphic to L_Sigma verified on the QWZ collar (next finite check after v991); orientation orbit 2 -> 1 only after a U(1) anchor (A0). Continuum Bismut-Freed and the 4D unification stay [O].

Original classification detail

Open: Res_seam det D_4D ~= det D_seam with connection + bulk holonomy == discrete orientation. [E] (v991): finite 2+1D/1D QWZ bulk-edge correspondence (C_bulk = W_seam = +1, M=3 control 0=0, conjugation mutant). Continuum Bismut-Freed stays [O]; no 4D unification. | LATE EVENING (2026-08-30 v1014): finite restriction isomorphism verified; orientation fixes conjugate branch; residual U(1) is the A0 anchor. Continuum stays [O].

Dependencies as recorded

ALPHA.QUILLEN.EXACT.01; ALPHA.QUILLEN.FACES.01; CHIRAL4D.NOMIRROR.01; SEAM.SIMPLECURRENT.GENERATOR.01; TFPT4D.LATTICE.ACTION.01