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

Abstract

This orientation guide introduces the Identity-Persistence Program, a research program investigating the structural conditions under which bounded independent evaluators can independently reproduce persistence and admissibility judgments under declared regimes. Rather than treating persistence, verification, probability, or inference as primitive, the program asks the logically prior question: what must already be specified before independent evaluators can legitimately determine whether something has remained the same through change?

The corpus develops a dependency architecture in which declared regime specification precedes identity, admissibility, observables, probability, and verification. This ordering does not replace mathematics, logic, probability, or statistical inference. Instead, it identifies the structural conditions under which those disciplines become jointly verdict-producing by requiring the objects over which they reason to be explicitly declared before computation begins.

At declared scope, the program establishes a specification floor describing the structural roles required for reproducible persistence judgments, an attainable interior within the proved finite and compact-metric classes, and an identification ceiling showing that finite admissible evidence identifies objects only up to the declared quotient. It further distinguishes forcing theorems, structural analysis, architectural dependencies, interpretive consequences, engineering implementations, and open mathematical questions through explicit claim-status discipline.

This guide contributes no new mathematical results. Its contribution is organizational: it presents the dependency architecture of the corpus, summarizes the established results at their declared scope, records the current research frontier—including specification algebra, recoverability, equivalence, refinement, machine reasoning, stochastic extensions, and empirical validation—and provides reading paths for mathematicians, engineers, philosophers, AI researchers, and new readers. Throughout, every claim is carried only at its proved scope, applying to the program itself the same discipline of licensed inference that it studies.