The Paton Envelope Horizon: A Viability-Based Framework for Estimating System Stability Before Breakdown

Modern systems often fail not because they violate formal rules, but because they quietly exhaust their tolerance through sustained near-limit operation. Existing analytical approaches typically emphasise correctness, performance, or prediction, offering limited insight into how close a system is to losing its capacity to remain viable. This work introduces the Paton Envelope Horizon (PEH), a pre-theoretical, non-interfering framework for estimating how much of a system’s tolerable operating envelope has already been consumed. Rather than identifying final tipping points or hidden dynamics, the method infers remaining viable capacity from observable proximity-to-boundary behaviour and path-dependent accumulation of strain. A single scalar measure, the Paton Envelope Horizon Index (PEHI), is defined in an ISO-style format and integrated into a recursive multi-scale framework with hysteresis to prevent instability, false triggering, or scale chatter. Extensive internal stress-testing demonstrates boundedness, path dependence, resistance to adversarial behaviour, and safe degradation under sparse or incomplete information. The Paton Envelope Horizon is intended as a general early-warning standard applicable across engineering, environmental systems, organisations, artificial intelligence, governance, and human factors. Open peer review, independent testing, and critical evaluation are explicitly invited.