The Identity Audit_ An Epistemic Test for Identity, Invariance, and Persistence

Abstract The Identity Audit introduces a constraint-based method for evaluating how theories describe persistence under transformation. Rather than proposing a new theory of reality, it formalizes a minimal set of identity and invariance conditions required for coherent claims of system continuity. These conditions are expressed as a compact axiom set (U1–U6) governing representation-invariance, bounded change, compositional consistency, and non-branching recurrence. The paper defines a stepwise audit procedure that maps any theory to: (i) which identity constraints it preserves, (ii) which it weakens or rejects, (iii) how it compensates, and (iv) what structural consequences follow. Worked examples across evolutionary theory, thermodynamics, quantum interpretations, information theory, and stochastic systems demonstrate a consistent pattern: explanatory flexibility is achieved by relaxing identity constraints, introducing probabilistic structure, or shifting the unit of persistence. Two summary appendices provide a cross-theory comparison of axiom relaxation (Appendix D) and ordering of reasoning layers—identity, invariance, observables, probability (Appendix E)—showing how reordering produces predictable structural effects. The central result is not ontological but epistemic: no theory can reject identity constraints and retain full identity persistence without incurring structural loss. The contribution of the paper is to make these tradeoffs explicit, providing a general-purpose audit for reasoning about persistence across scientific, mathematical, and engineered systems.