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. For self-modeling, Σ-complete persistence subjects — persons — Q1 and Q2 are necessary but not sufficient for a complete structural account of personal identity. The LP architecture generates three additional derived conditions: Q3 (Recursive Constitutive Non-Externality, M-condition), Q4 (Structural Self-Priority, K-condition), and Q5 (Recursive F·M·K Integration). These are not additional general persistence conditions but the F·M·K architecture expressed in the consciousness domain. A complete account of what makes a person the same person under transformation requires all five conditions (P167). The paper applies the formal separation to the canonical cases. The existing positions — Parfit, Sider, Olson, Wiggins — are shown to be tracking one or more conditions while leaving others underived. 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 — and extends to its natural completion for persons through Q3–Q5.