What Licenses Sameness Through Change? A Short Orientation to the Identity-Persistence Program Toward a Structural Theory of Regime Specification

Abstract

Abstract This orientation introduces the Identity-Persistence Program, a research program investigating the structural conditions under which bounded independent evaluators can license, reproduce, and verify persistence and admissibility judgments under declared regimes. Rather than treating persistence as an ontological primitive, the program asks the logically prior question: what must be specified before different evaluators can legitimately determine whether something remains the same through change? The corpus develops a dependency architecture in which sufficient regime specification precedes identity, admissibility, invariants, observables, probability, certification, and verification. A bounded evaluator is not assumed to possess a final generator, uniquely correct identity rule, or complete constraint field. Instead, evaluation proceeds relative to declared symbolic conditions specifying the tracked object, admissible transformations, required invariants, evidential grain, authority, and verdict rule. At declared scope, the program establishes three principal structural boundaries: a specification floor identifying the roles required for reproducible verdicts; an attainable interior within the proved finite and compact-metric classes where persistence can be represented and enforced exactly; and an identification ceiling showing that finite admissible evidence cannot distinguish more finely than the declared quotient, while an adequate channel attains that quotient exactly within the finite deterministic, basis-presented class. The guide also distinguishes this identification limit from the separate Entitlement Cut, which constrains a different transition in consequential autonomous systems and is not a corollary of the ceiling. The post-v23 structural-analysis layer substantially extends the original map. Finite interaction at declared partitions and coordinate-level refinement are abstractly complete at their source papers' declared strengths; joint omission is abstractly complete while awaiting corpus instantiation; unrestricted external representation is closed; and the floor-relative intrinsic-image problem has been reduced to a universal recognition scaffold whose corpus realization remains declaration-gated. Throughout, the guide distinguishes abstract closure, corpus-native computation, independent proof verification, genuinely open successor mathematics, architectural interpretation, and engineering implementation. This paper contributes no new mathematical theorem. Its contribution is organizational and epistemic: it presents the dependency architecture of the corpus, records the exact status of each layer, explains the significance of the proved finite interior, and provides reading paths for mathematicians, philosophers, engineers, AI researchers, biologists, and new readers. Every result is carried only at its declared scope, and machine corroboration is explicitly distinguished from independent proof verification.