Carrier, Interface, and Closure: A Claim-Controlled Reconstruction of the Unified Fields Research Program

This research status paper reconstructs the Carrier–Field–Residual–Gate–Closure program against standard literature in analytic number theory, Frobenius integrability, effective descent, dissipative field theory, and Hamiltonian computation. It presents the exact Archimedean interface F_Z + F_P = A_Gamma, local Euler–Pascal and Rouché closure gates, gauge-covariant phase-flow integrability, typed effective descent, and finite-dimensional spectral-kernel preservation. Every claim is confined to the theorem, assumptions, domain, and verification gate explicitly stated for it. Proved results, conditional implications, exact reductions, computed evidence, and open obligations retain distinct status labels, and no conclusion is extended beyond its declared scope. The record includes two independent technical notes: the Observable Memory Potential and Certified Correction Bounds Theorem, and the CI-01–CI-18 character-level compliance register.