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

This paper introduces the admissibility margin as a quantitative indicator of system stability within the Paton System. While admissibility defines whether system states are permitted, the admissibility margin measures proximity to governing constraint boundaries. The framework demonstrates that systems approaching failure exhibit a reduction in admissibility margin prior to collapse. This reduction reflects progressive constraint misalignment (drift) and provides a measurable pre-collapse signature. The behaviour is shown to be structurally invariant across domains, including artificial intelligence systems, fluid dynamics, and healthcare systems. The admissibility margin enables early detection of instability, prediction of system failure, and intervention prior to closure. It extends the Paton System from a structural framework into a predictive and diagnostic tool.