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.
Marc Maibom (Wed,) studied this question.