Testing Unified Substrate Theory: A Dual-Channel > 50σ Detection of Log-Periodic β = 4 Dynamics Before and After Earthquake Mainshocks

This work examines whether seismic activity exhibits the discrete-scale-invariant harmonic structure predicted by the Unified Substrate Theory (UST). Using global earthquake catalogues and aftershock sequences from diverse tectonic environments, the analysis applies the UST harmonic ladder (β = 4, 9, 16, 27.57) to temporal, spatial, and magnitude-resolved windows around major seismic events. Each window is compared against carefully designed null models—including permutation, distance-preserving, and catalogue-randomization controls—to ensure that any detected structure is not a by-product of clustering or catalogue incompleteness. Across all tested sequences, the UST harmonic modes consistently reduce residual variance, with statistical significance exceeding 50σ in several domains, and cross-validation demonstrating predictive power rather than overfitting. These results reveal that earthquakes encode the same log-periodic harmonic behavior seen in UST's cosmological and atmospheric tests, supporting the theory’s central claim that discrete harmonic scaling is a universal feature of dynamical systems approaching criticality.