Identity Persistence Calculus_A Downstream Method for Applying the Forcing Theorem

Zenodo abstract Identity Persistence Calculus presents a derived application layer for evaluating identity persistence claims under transformation. It does not extend the Tier-1 forcing theorem for identity persistence; rather, it translates that theorem into a usable diagnostic procedure. The calculus requires any same/not-same persistence claim to specify an identity-bearing unit, state space, admissible transformations, identity-relevant quotient, continuation map, invariant vector, governance scalar, and drift bound. It then returns one of five verdicts: PERSIST, BREAK, BRANCH, UNDEFINED, or REGIME-CHANGE. The method is applied to four cases: Ship of Theseus, software artifact / VERIFY bundle identity, identity under flux in Heraclitus’s river and biological organisms, and AI model-version identity under replay and drift. Across these cases, apparent paradoxes are shown to arise from under-specified identity-bearing regimes rather than from identity persistence itself. The result is not a new metaphysical theory and does not claim ontological instantiation. It is a structured evaluation method for determining whether a persistence claim has been made coherently, non-arbitrarily, and within a declared admissibility regime.