Admissibility Margin: A Quantitative Indicator for System Stability and Pre-Collapse Detection

This paper introduces the admissibility margin as a quantitative measure of system stability within the Paton System framework. While admissibility defines whether a system state is permitted, the admissibility margin measures how close a state is to violating governing constraints. The admissibility margin provides a continuous indicator of structural stability, enabling early detection of instability and prediction of system failure prior to collapse. The framework demonstrates that all systems approaching failure exhibit a reduction in admissibility margin. This behaviour is shown across artificial intelligence systems, fluid dynamics, and healthcare systems, establishing the concept as domain-neutral. The admissibility margin enables: • Early detection of instability • Quantifiable system health measurement • Predictive identification of pre-collapse states • Structural intervention before failure This work extends the Paton System from a structural framework into a practical predictive and diagnostic tool.