Existence and Identity - Why the Persistence Debate Has Not Converged and What Resolves It

The analytic debate over persistence has produced sharply opposed positions — endurantism and perdurantism, animalism and psychological continuity theory — without convergence. This paper argues that the failure to converge is structural: the debate conflates two logically independent questions. The question ‘does the system continue to exist?’ is governed by the persistence condition IR ≤ 1. The question ‘does the continuing system remain the same system?’ is governed by the Frame Continuity Condition (FCC). Neither condition implies the other. 'Existence' in Q1 denotes preservation of structural identity under transformation — not bare ∃x. The formal foundation established in Section 2 makes this precise: identity is not presupposed by the structure but induced from it. Both conditions operate on systems that already carry an induced identity. 'Existence' asks whether that identity can be maintained under transformation load. 'Identity' asks whether it remains the same identity. The paper applies the formal separation to the canonical cases and shows that each resolves into a determinate structural configuration. The existing positions — Parfit, Sider, Olson, Hawley, Wiggins — are shown to be tracking one condition or the other. The paper does not propose a new position. It proposes a level shift: from competing answers to a conflated question, to a formal architecture that makes the question precise.