La Profilée as a Law of Nature - The Structural Derivation of the Persistence Condition

La Profilée (LP) establishes a necessary structural condition for the persistence of any system under real transformation: the Integration Ratio IR = R / (F · I) must not persistently exceed 1. Prior publications have derived this condition formally, demonstrated its thermodynamic correspondence, and applied it across domains from quantum decoherence to cosmological expansion. What has not been assembled in a single document is the complete argument for why this condition qualifies as a law of nature — not a model, not a framework, not a domain-specific regularity, but a structural constraint with the same logical status as conservation principles and exclusion constraints. This paper provides that argument. It proceeds as a single unbroken derivation from two minimal structural assumptions — determinability and real transformation — through the forced exclusion of full transitivity, the induction of identity as maximal bisimulation, the structural necessity of non-invertibility and accumulation, the forced existence of finite integration capacity, and the uniquely determined form of the persistence boundary. Identity is derived, not assumed. The persistence condition IR ≤ 1 is not introduced; it is the necessary quantitative expression of structural constraints that are themselves forced by the two minimal assumptions. The conclusion is that IR ≤ 1 satisfies the criteria for a law of nature in the constraint-law sense — the class that includes the second law of thermodynamics, Pauli's exclusion principle, and Landauer's principle. It does not describe the dynamics of any system. It constrains the class of dynamical evolutions compatible with persistent identity.