2026/06/10 by Piotr Ogonowski · 1 voice
Physics and Astronomy · #physics.gen-ph
arxiv published 2026/06/10 · arxiv updated 2026/06/25
A filtered local reconstruction scheme is formulated for codimension-three Codazzi defects in four-dimensional Lorentzian branches. The closure defect of the self-reconstruction loop is organized as a lexicographic residual whose entries fix, in order, the projective link, Gauss-local charges, Toeplitz support, determinant carrier, finite shadow, torsor response, and Schur completion. For a worldline defect with resolved link \mathbbCP1Γ, the scalar two-jet leaves two principal non-scalar types, V1 and V2. Faithful reconstruction of these Gauss-local charges, together with \mathbbCP1 Toeplitz visibility, selects the separated support E3⊕ E2; reduced finite visibility fixes the degree-one line. After this carrier has been selected, the split top-form condition gives the familiar S(U(3)× U(2))/\mathbb Z6 global form and the standard one-generation exterior package, with the usual hypercharge normalization and anomaly checks. This determinant package is used as the structural comparison layer for the reconstructed carrier. The remaining construction keeps the full \mathbb Z6 finite shadow, realizes its projective-color projection as a boundary torsor, and organizes the locked low sector by a B-L-filtered Schur-Kuranishi completion. Yukawa, neutrino, mixing, running, and contact coefficients are thereby treated as completed-branch data rather than as inputs to the carrier selection. A scale-free charged-lepton balance residual is recorded as a Schur-layer diagnostic; its zero-correction form gives the Koide-type singlet-torsor balance, while the observed deviation is left as a finite Schur-tensor datum.