C0 → Physics: A Persistence-First Computational Ontology with Constructor-Theoretic Vacuum Support, Gauge Closure, and Emergent Gravity

This manuscript develops a persistence-first ontological framework beginning from a single primitive constraint: C0: A beginning cannot presuppose the conditions required for its own specification. From this primitive, the work derives a persistence kernel: Omega = (I, A, E, chi, Epsilon) where: I = identity preservationA = admissible continuationsE = elimination structurechi = constraint densityEpsilon = expressive capacity Together, these form the minimal substrate for durable lawful systems. The central result is the Vacuum Theorem: V = the Omega-state that minimizes chi(Omega) In plain language: vacuum is interpreted not as absence, but as the minimum admissible anti-collapse support required for persistent excitation and lawful evolution. The framework is then extended through Constructor Theory and superinformation constraints, CPTP-style quantum channel analogues, locality and emergent geometry, gauge redundancy and anomaly cancellation, conditional Standard Model closure, scalar-tensor chi-gravity, near-Lambda-CDM cosmology, executable persistence-kernel simulations, and observer/self-model emergence. The manuscript carefully distinguishes rigorously derived results, formal analogues, effective constructions, conditional closures, and unresolved hinges. The work does not claim a completed Theory of Everything. Instead, it proposes a coherent research program in which known physics appears as the stable faithful representation of admissible persistence under recursive constraint.