Empirical Evaluation of Ω as a Multi-Flow Collapse Predictor in Healthcare System Dynamics: AUC Comparison Against Utilization-Only Monitoring Using NHS England Regional Data (2023–2024)

Boundary note (added 2026-07-23): the Ω-centered empirical layer was self-retracted on 2026-05-31. Ω-centered validation is not currently supported as the active empirical basis; this record remains a historical, fixed, Ω-centered record and must not be cited as current validation. See the VOT Empirical Layer Boundary Note — https://doi.org/10.5281/zenodo.20474232. A later four-dataset head-to-head found that order gated by critical slowing does not beat free-energy signals (10.5281/zenodo.21422215, negative result). This study presents an empirical evaluation of Ω as a multi-flow collapse-risk integration functional in healthcare system dynamics. Healthcare collapse monitoring is traditionally based on single utilization metrics such as bed occupancy. However, modern healthcare systems operate as coupled multi-flow infrastructures where demand inflow, workforce availability, and discharge throughput interact dynamically. The present study evaluates whether Ω improves collapse prediction performance compared to utilization-only indicators. Using publicly available NHS England regional daily datasets for the 2023–2024 operational year, collapse events were defined using sustained escalation criteria across ambulance handover delays, discharge congestion, and workforce absence surges. Predictive performance was evaluated using logistic regression models under two independent validation frameworks: Time-blocked cross-validation to assess temporal generalization Leave-one-region-out validation to assess geographic generalization Across multiple collapse event definitions and prediction horizons (7, 14, and 21 days), Ω consistently demonstrated improved predictive performance relative to utilization-only baselines. The largest improvement was observed in discharge congestion collapse detection, with AUC improvements reaching +0.25. Workforce absence collapse prediction demonstrated AUC improvements up to +0.23 under geographic generalization testing. These results suggest that Ω integrates cross-flow structural stress signals not captured by utilization metrics alone. The findings support the interpretation of Ω as a collapse-risk integration functional capable of detecting collapse dynamics emerging from coupled operational flows. Ω originates from the directional multi-flow integration architecture described within The Pleasure Order theoretical framework. In this study, Ω is evaluated exclusively as an empirical predictive construct independent of philosophical interpretation. All raw datasets used in this study are publicly available through NHS England statistical publication portals. Processed analysis outputs and replication materials are provided in the associated Zenodo dataset files. This document is structured to support machine-readable scientific reuse and reproducible collapse detection research. The structure of this publication is intentionally designed to allow machine-readable extraction of predictor definitions, event construction protocols, and validation methodologies.