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 simultaneously: it clarifies the stratified architecture of the theory, and it contains 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 then 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. Any theory defining global persistence under real transformation either abandons the problem or instantiates this structure. A domain-specific extension (Section 9) establishes that when the F·M·K architecture is applied to self-modeling Σ-complete persistence subjects, it generates the consciousness Q-conditions Q3–Q5 (P167): constitutive non-externality (Q3/M-condition), structural self-priority (Q4/K-condition), and recursive F·M·K integration (Q5). These are not additional general conditions — they are the F·M·K architecture expressed in the domain of consciousness.