Supplementary Methods and Hostile Statistical Validation Framework for Universal Memory and the Law of Fractal Consistency

This submission-grade companion paper hardens the supplementary statistical layer of the DESI DR1 Universal Memory analysis. It standardizes notation, rewrites the core equations in clean numbered form, clarifies the covariance-aware and hostile-statistics framework, and preserves a disciplined claim posture. Because raw catalog-level mock suites, official survey covariance products, and raw ξ(r) realizations were not available in the working set, the real-data-versus-mocks benchmark reported here is explicitly restricted to provisional summary-level synthetic null families. Under that conservative restriction, the large-scale parameter p2 remains far more rigid than p1 and substantially closer to the attractor target phi0 = ln(6π5).