THE PATON FORMULA — APPLIED TEST CASES FOR SCIENTIFIC VALIDATION

The Paton Viability Principle formalises a missing category in scientific and systems reasoning: responsible continuation before breakdown. Rather than asking whether a model is correct, the principle asks whether it may continue to be used. The framework culminates in a minimal recursive admissibility formulation that operates above all domain-specific models without engaging internal structure, mechanism, or ontology. This work presents the final and canonical form of the Paton System. It does not replace existing theories or equations; instead, it governs when their continued use remains responsible. The principle explains why systems often fail before they fail and provides a universal methodological anchor across domains.