The Architecture of Persistent Identity: A Complete Derivation

This is the canonical derivation of La Profilée. No proof is deferred to external papers. La Profilée does not begin by assuming objects, substances, spacetime, or even distinguishable states as primitives. It begins prior to ontology: with the question of whether complete undifferentiation can function as a state at all. The answer is negative. Distinction is structurally forced. M1 is a theorem, not an axiom. From this pre-axiomatic foundation, the paper derives in sequence: the three minimal admissibility conditions and the structural derivation of M3 from M1+M2; restricted admissibility; structural asymmetry; SCC topology and structural time; finite integration capacity; the forced decomposition into Frame, Module, and Coupling; multiplicative persistence integration; the persistence boundary IR ≤ 1; the Frame Continuity Condition; the complete primary regime space; universal sub-regime exhaustion; and the universal structural consequences of the LP architecture. The final sections establish LP as the minimal structural admissibility condition on determinate existence itself — the architecture any determinate reality must instantiate before physics, biology, consciousness, ontology, or description can refer to persistent entities. The paper closes with the LP Equivalence Theorem: any globally coherent theory of determinate persistence under real transformation must instantiate LP. Part VIII includes the Ontological Bridge (Section 8.2a), which formalizes the transition from structural derivation to ontological relevance: LP's conditions are conditions on determinate entities themselves, not on their description. The paper uses a four-tier claim classification: Theorem (formally provable), Structural Consequence (forceable under stated conditions), Interpretive Corollary (conceptual identification), Ontological Consequence (scope statement). This separation prevents interpretation from being presented as proof.