Foundation of Persistent Identity - The Structural Law of Identity Under Transformation - Derivation, Architecture, and Evidence

Every theory of change — in physics, biology, organizational science, philosophy, or design — operates on a silent assumption: that the systems it describes persist through the transformations it analyzes. None of these theories derives the condition under which this persistence holds. La Profilée (LP) derives that condition from first principles. Starting from the minimal requirements that make the persistence question well-posed — distinguishable states, real transformation, and determinate persistence verdicts — LP forces a unique structural law: IR = R / (F · M · K) ≤ 1 This is not a model. It is a structural necessity. Any system for which the persistence question is well-posed must satisfy this condition or cease to be determinable as the same system under transformation. This paper presents LP in full: its origin in watch design, its formal derivation from minimal axioms, its operationalization as a diagnostic framework, its evidence base across domains, its relationship to adjacent formal programs, and its implications for science, design, and practice. It is written to be complete, self-contained, and accessible to any reader who wants to understand what LP is, where it comes from, and what it changes.