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

Abstract A Short Orientation to the Identity-Persistence Program is a program guide to a formal research corpus on the structural conditions under which bounded evaluators can make coherent, reproducible judgments about identity, persistence, admissibility, and verification under declared regimes. The program begins from the question of what must already be fixed before a claim of sameness through change can be meaningfully evaluated. Its foundational layer establishes structural floors for identity persistence, admissibility under transformation, and sufficient regime specification, together with finite and compact-metric capacity, coding, enforcement, and verification results and a quotient-relative ceiling on what bounded evidence can identify. Above that floor, the corpus develops a structural theory of declared regimes: demand-relative normal forms, regime equivalence and refinement, recurrence classification, symmetry-compatible reduction, nested regime composition, reconstructibility and mechanization theory, finite condensation dynamics, and a retirement and erasure branch completed through trajectory-level quotient structure. These results characterize which distinctions must persist, which may be safely compressed or forgotten, how downstream demands constrain upstream representations, and which structures are canonical only relative to declared questions. Version 50 incorporates the publication-frozen Declaration Boundary v1.1. Once licensed distinctions determine an information quotient, derivable consequences are those available through that quotient. For a desired consequence that cannot be so derived, the theory identifies the exact obstruction and the canonical minimum informational refinement required to remove it. On finite carriers, a specialization of the Gate’s Minimum Repair Alphabet theorem additionally determines the minimum finite informational width any sufficient realization must possess. This closes the informational question without collapsing it into realization or authority: mathematics can determine what distinction is missing and how much discriminating capacity is required, but not thereby produce a permitted realization or an actor entitled to supply it. The Orientation proves no new theorem. It records the corpus dependency structure, reading paths, claim statuses, ownership boundaries, closed results, explicit open problems, and relationships between the foundational, structural, and engineering layers. Claims remain regime-relative and are not promoted into final ontology.