Point of No Return: A Structural Threshold for Irreversible Collapse in Admissible Systems

This paper introduces the Point of No Return within the Paton System as a structural threshold beyond which system collapse becomes inevitable. Building on Admissibility Control, Control Cost, and Control Limits, the framework defines the Point of No Return as the final admissible state from which no admissible trajectory can avoid collapse. The paper formalises this threshold through admissibility margin, trajectory accessibility, and structural constraints in constraint space. It establishes a domain-independent method for identifying irreversible system behaviour and distinguishing recoverable from irrecoverable states without modifying underlying governing equations.