Statistical Test Comparison for Entanglement-Weighted Operator Geometry and Condensed Matter Physics: A Complete Statistical Validation

This study performs a comprehensive statistical comparison between predictions derived from Entanglement-Weighted Operator Geometry (EWOG) and traditional Condensed Matter (CM) physics models. Using experimental data from three paradigmatic quantum material classes—heavy-fermion systems, quantum spin liquids, and unconventional superconductors—we apply information-theoretic criteria (AIC, BIC), Bayesian model selection, and frequentist hypothesis testing. Our analysis demonstrates that EWOG models consistently provide superior fits to experimental data with greater parameter efficiency. For $\mathrm{CeCoIn}_{5}$ specific heat data, EWOG yields $\Delta\text{AIC} = 14.5$ and Bayes factor $>10^3$ versus the best CM model. We present complete numerical derivations of all statistical tests, establishing EWOG as a statistically superior framework for describing emergent phenomena in strongly correlated quantum matter.