A Universal Coherence Functional Across Complex Systems: Empirical Evidence from Seven Independent Domains

We introduce CΨ, a multiscale coherence functional combining Kuramoto synchrony, mean pairwise correlation, and MST compactness into a single fixed operator. Together with cross-scale tension TΨ and internal fragility SΨ, the framework defines a two-dimensional state space classifying complex system regimes. Applied without modification to seven empirical datasets: cardiac electrophysiology (AUC=0.961, MIT-BIH, n=29; AUC=0.713, Chapman, n=13,257), sleep EEG (F=449.2, n=22,233), financial markets (AUC=0.594–0.762 vs VIX=0.418, 25 years), music (F=43.6), genomics (t=95.3), and seismology. Three mechanistically distinct catastrophe types identified: Type A dissociation, Plein Sync homogenization, and Fragmentation. All code and data publicly available.