A Gate-and-Kernel Framework for Baryogenesis on Descendant Backgrounds (Version 1)

Early-universe calculations often begin by writing cosmic time, an effective geometry, andactive sectors as though the background were already settled. This note isolates that priorquestion. It asks when a reduced description has earned the right to use descendant-backgroundlanguage at all. The framework begins at the first establishment regime where a controlledreduced state exists and writes the candidate background in a gated reduced-state representation,dZdτ = Lbg(τ )Z + Gbg(τ )Pbg(τ )Qprec(τ ), Ibg(τb) = e⊤bgZ(τb).The linear identity is only bookkeeping. The substantive content lies in the separation of precursorsubstrate, ordering realization, geometry realization, active-sector bundle, and descendant-background interface state, together with witness-defined audits of ordering support, geometrysupport, patch or homogenization control, sector activation, coarse-graining or classicality, andEFT control. The note yields a three-category reading of background claims: inadmissible,corrective, and confirmatory. Tests are drawn from causal-fermion-systems spacetime, effectiveloop quantum cosmology, and standard post-inflation FRW. The effective LQC case also illustratesthe key stage split: a line can pass descendant-background establishment and still fail later onceasymmetry-specific EFT or thermal language is introduced. The result is a standalone modulefor deciding when background language is licensed.