La Profilée: A Universal Constraint Law for Persistence under Real Transformation

This work derives the necessary condition governing persistence under real transformation. Starting from minimal empirical requirements — distinguishability, physically realizable transformation, and irreversible constraint restoration — the following structural balance condition is shown to be necessary: dSᵢdentity/dt = κR (t) · (R_Ω − β (t) ·F*·I) The corresponding dimensionless constraint ratio IR = R_Ω / (β · F* · I) defines the persistence boundary: IR ≤ 1. IR is a constraint ratio, not a dynamical variable. It determines whether a system remains the same system while undergoing transformation — not how it evolves. This condition is not postulated. It is forced by the structural requirements of persistence itself. For IR > 1, structural identity erosion is necessarily ongoing and cannot be halted without restoring IR ≤ 1. Collapse is the terminal consequence of sustained violation. The result is representation-invariant, operationally measurable, and applies to all scientifically well-posed persistence problems. Its universality follows from structural necessity, not from domain-specific dynamics. LP is not a dynamical law. It does not describe trajectories or forces. It specifies the necessary condition under which identity is preserved under transformation. LP identifies not a domain-specific law, but the universal persistence boundary that all domain-specific laws must satisfy in order for identity to be preserved under real transformation. The validity of LP does not follow from empirical instantiations. It follows from structural necessity. Empirical systems confirm the condition — they do not ground it.