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

Three companion case studies on the Hamada mechanism, causal fermion systems, and loop quantum cosmology suggest a common structural question: when has an asymmetry formulaearned the descendant language it uses? This note formulates a gate-and-kernel answer. In a firstdescendant regime where linear evolution is meaningful, the observable asymmetry is written asa gated transport law. The transport identity itself is standard variation of parameters; the useful claim is the decom-position around it. Gates are built from calibrated witness maps for ordering, geometry, currentbasis, thermal support, EFT control, and, when needed, transport-state admissibility. Thethresholds are inherited from the control inequalities of the chosen reduction rather than fittedto the desired baryon yield, which makes the framework prospective as well as retrospective.A baryon-channel support diagnostic then yields a three-category classification of publishedformulas. The kernel representation is placed inside a five-layer architecture linking emergencecriteria, background realization, primitive source and transfer, descendant transport, and finalreadout. Tests include the Hamada/CFS/LQC triad, standard thermal leptogenesis, and a harderresonant-leptogenesis stress test in which witness maps select between a diagonal Boltzmannreduction and a density-matrix description. The result is a reusable audit and model-buildingscaffold for asymmetry generation on emergent backgrounds.