A Deterministic Phase–Memory Operator for Hysteresis and Path-Dependent Regime Shifts: A Validation Protocol and Application Roadmap

Hysteresis and path-dependent regime shifts occur across biological, engineering, and human-in-the-loop systems, where classical optimization and control strategies can fail under timing drift and geometric misalignment. We present a deterministic phase–memory operator that extracts a triadic latent state—phase deviation, drift, and accumulated memory—from observed signals and yields an interpretable stability functional for early warning of transition regimes. The proposed operator is model-agnostic, requires no retraining, and is designed to operate as a supervisory diagnostic layer rather than a controller. We outline a reproducible calibration and evaluation protocol and summarize an external validation on EEG time series demonstrating strong predictive performance for collapse-like dynamics under fixed-parameter replay. Finally, we provide an application roadmap for deploying the method to other hysteretic systems (including oxygen-delivery monitoring as a representative human-in-the-loop loop), emphasizing falsification criteria and limitations to ensure transparent scientific assessment.