Finite Standard-Model Carrier from Timelike Codazzi Defects

Abstract

The inverse problem of whether protected data carried by a local Lorentzian defect can determine a finite internal gauge-and-matter carrier before microscopic dynamics are chosen is considered. For a codimension-three timelike Codazzi defect, a marking-preserving reconstruction fixes a five-dimensional complex carrier $V=C\oplus W$ with ${\dim }_{\mathbb{C}}(C,W)=(3,2)$, the global gauge form $S(U(3)\times U(2))$, a chiral $16$-dimensional exterior packet with $k_Y=5/3$, and a norm-seven family structure. The chiral packet has the standard algebraic $SU(5)$-Spin$(10)$ envelope without assuming grand unification. Within a declared regularized-domain class, one constrained microscopic realization is constructed. Its distinguished branch ends at a single intrinsic terminal where the strict charge minimum and the first simple invariant-sector fixed-charge degeneracy coincide; soft-coupled readouts acquire a rank-one critical-response pole. On the rank-two exact-five moment stratum, four native matrix moments reconstruct a five-dimensional cyclic operator up to hidden unitary. The resulting scale-free observables lie on a one-dimensional solution manifold with a discrete conjugate orientation. With $W/Z$ used to set its longitudinal coordinate, direct CKM and reactor/solar data are consistent with the same manifold, while first-row CKM normalization remains a separate transverse structural test. Existence within the stated class is established, not uniqueness. A blind determination of the longitudinal coordinate still requires the unresolved centered-response incidence; physical transport remains an independent microscopic gate.