The Epistemic Map of Identity Persistence_ Regime Specification, Identity, Admissibility, Capacity, and Verification

Abstract This architecture paper maps the Identity–Persistence Program after the identity forcing theorem, finite identity coding theorem, admissibility forcing theorem, and runtime verification layer. It argues that identity and admissibility are not a vertical chain but sibling structural roles within a regime specification: identity names what persistence concerns, admissibility names which transformations preserve it, and together they determine an admissible transition object A within a declared regime. Capacity, coding, and verification then operate downstream of A. The paper does not introduce a new forcing theorem or claim to solve epistemology. Its contribution is to make explicit the dependency structure already implicit across the corpus: structural forcing results are closed within their stated scopes; finite declared regimes and the homeomorphic compact-metric category are closed within their respective theorem classes; stochastic, nonstationary, hybrid, and broader general-topological extensions remain open; and the recurring uncharacterized object is the sufficient regime specification. The result is an architectural dependency map for symbolic persistence: a bounded computational grammar for epistemic operations requiring identity, admissibility, transition, verdict, replay, and verification under declared conditions.