La Profilée: Identity under Transformation - A Structural Law and Its Consequences

La Profilée (LP) establishes a necessary structural condition governing the persistence of any system under real transformation. The condition has been instantiated across domains ranging from quantum decoherence to cosmological structure, spanning approximately sixty orders of magnitude in physical scale. From two minimal assumptions — determinability and real transformation — it is derived that any persistent system must decompose canonically into three structural components: Frame (F), Module (M), and Coupling (C). The effective integration capacity of any such system is IK = F · I · C, where I is total integration capacity. The persistence condition is: IR = R / (F · I · C) ≤ 1 where R is transformation pressure. This condition is not postulated. It is the uniquely determined quantitative expression of the structural constraints forced by determinability and real transformation. It is domain-independent, representation-invariant, scale-invariant, and falsifiable. This paper provides a unified account of LP: the derivation from minimal assumptions, the formal architecture, the central theorems, the thermodynamic correspondence, the scale invariance result, the domain applications, and the falsification conditions. It is written as a single document in which a reader unfamiliar with the prior LP series can follow the complete argument. LP is a constraint-law. It does not describe the dynamics of any system. It constrains the class of evolutions compatible with persistent identity — in the same formal sense as the second law of thermodynamics, Pauli's exclusion principle, and Landauer's principle constrain evolutions in their respective domains. Its universality follows from structural necessity, not from empirical induction. The persistence condition is not imposed on persistent systems. It is the structural condition any persistent system under real transformation must satisfy.