Statistical Isomorphism Between Phanerozoic Tectonic Rhythms and Riemann Zeta Zero Spacings: A Random Matrix Theory Perspective

We investigate whether the temporal spacing of major geological boundaries in the Phanerozoic eon (538.8 Ma to present) exhibits statistical signatures characteristic of random matrix ensembles. Using all 102 ICS 2023-standard stage-level boundaries (99 valid intervals), we compare their normalized spacing distribution against the Wigner surmise for GUE (β=2), GOE (β=1), and Poisson statistics via Kolmogorov–Smirnov tests, Anderson–Darling statistics, nearest-neighbor spacing ratios, higher-moment analysis, and bootstrap confidence intervals. Key findings: (1) Poisson is decisively rejected at p = 1.3 × 10⁻⁴ and with an 11.6σ deviation in the spacing ratio statistic; (2) the GOE model provides the best overall fit across all test statistics (KS D = 0.090, p = 0.38; A² = 1.18); (3) the GUE model, while close in spacing ratio (⟨r⟩ = 0.637, only 1.6σ from GUE theory), is marginally rejected by higher-order tests. As a control, we verify that the first 500 non-trivial zeros of the Riemann zeta function conform precisely to GUE statistics. This repository contains analysis code (Python/SciPy), geological boundary data (ICS 2023), Riemann zeta zeros, publication-quality figures, and the manuscript in LaTeX and Word formats.