La Profilée On the Necessity of Admissibility Conditions for Global Persistence Laws - A Formal Extension to the Persistence Admissibility Theorem (PAT)

This paper establishes that the empirical–topological admissibility conditions (Conditions 4–7) used in the Persistence Admissibility Theorem (PAT) are not auxiliary assumptions but necessary conditions for the very existence of a global persistence law. While Conditions 1–3 make the persistence problem meaningful, Conditions 4–7 are shown to be required for its formulation as a single global, empirically testable constraint. It follows that any theory claiming a global law of persistence already presupposes these conditions. Combined with PAT, this yields: any global persistence law is structurally equivalent to R ≤ F·M·K.