The Logical Architecture of Persistence - Minimal Assumptions, Derived Necessities, Formal Proofs, and the Regime Structure of Persistent Identity

This paper reconstructs La Profilée in complete logical order. It serves two purposes: clarifying the stratified architecture of the theory, and containing all formal proofs in self-contained form. No proof is deferred to external papers. Starting from three minimal assumptions — distinguishability, real transformation, and determinable persistence relation — all structural necessities follow: restricted admissibility, asymmetry, SCC topology, finite integration capacity, the Frame–Module–Coupling decomposition, and the persistence boundary IR ≤ 1. Two gaps present in earlier formulations are closed: the M2 connection for finite integration, and the derivation of FCC from M1–M3. The paper establishes the Persistence Admissibility Theorem (PAT) in full: four lemmas with complete proofs, the PAT theorem, the Closure Theorem, and the Unavoidability Theorem. The result: IR = R/(F·M·K) ≤ 1 is the unique global persistence condition. Section 6 establishes the complete fundamental regime structure: four logical combinations from Q1 and Q2 (one impossible), three real primary regimes each resolving into two structurally irreducible universal sub-regimes, and the exhaustion of alternative persistence structures. LP is thereby not merely a persistence criterion but a universal typology of identity dynamics under real transformation. Section 9 establishes the domain-specific Q-conditions Q3–Q5 for self-modeling Σ-complete systems.