An Empirical Stability Framework for Phase Transition Prediction: Volcanic Validation and Cosmological Extension

We present NXE, an empirical stability framework for phase transition prediction in complex systems, whose mathematical structure is motivated by the Yang-Mills mass gap. The framework defines a stability index Γ from three observables: a dynamic driver x, a basal resistance m₀, and a structural curvature Ω. Calibrated on 10 historical volcanic eruptions, the model achieves an F1-score of 0.842. In prospective testing, NXE correctly predicted all four recent eruptions (Kīlauea, Mayon, Etna, Kanlaon) with 7–11 days of advance notice, providing longer lead times than standard alert-level protocols. Extending the framework to cosmology, we propose that the Hubble tension arises from spatial variations in the effective rigidity κ of the cosmic fabric, modulated by local matter density. An in silico 2D simulation validates the modified Hubble equation H² = H²₀ + ΔP/κ with a maximum numerical error of 2.1%; simulation parameters require physical recalibration before quantitative cosmological comparison. Observational correlations between CMB temperature anomalies and cosmic voids are qualitatively consistent with framework predictions. Limitations, falsifiability criteria, and priority next steps are discussed explicitly.