Asymptotic Spectral Rigidity and Semiclassical Saturation in the Riemann Zero Spectrum Across 22 Orders of Magnitude

This paper presents a high-fidelity numerical verification of quantum-chaotic signatures in the Riemann zero spectrum using Odlyzko's datasets spanning 22 orders of magnitude in spectral height (γ~10² to γ~10²²). Key results: (1) Local-density unfolding: A localized unfolding operator d(T) = ln(T/2π)/(2π) eliminates truncation errors at extreme heights, achieving mean spacing errors |⟨s⟩-1| < 2×10⁻⁴ uniformly across all datasets including γ~10²². (2) Dyson-Mehta Δ₃ statistic: The variance ratio Δ₃/Δ₃_GUE converges monotonically from 0.460 (zeros1, γ~10²) to 0.497 (zeros5, γ~10²²), approaching 1/2 asymptotically. This is a direct numerical confirmation of Berry's (1985) semiclassical saturation due to discrete prime orbits, with saturation scale L_sat = 2π/ln(T/2π). (3) Spectral form factor K(τ): The arithmetic prime peaks at τ_p = ln(p)/2π are damped by a factor of two over 22 orders of magnitude (K(0.1): 0.196 → 0.094), while high-altitude datasets achieve K(τ=1) ≈ 1.00, confirming ergodic convergence to the GUE plateau. (4) NNSD tests: KS and AD tests confirm full GUE compatibility for zeros3-zeros5 (p > 0.88, A² < 0.33). The low-altitude zeros1 dataset exhibits the expected non-ergodic regime consistent with finite quantum-chaotic spectra. This work constitutes independent empirical support for the spectral interpretation of the Riemann zeros as eigenvalues of a quantum-chaotic operator, complementing the theoretical framework of Martini (2026a,b). Contents:- Martini2026c_GUE_Statistics.pdf: Compiled manuscript (5 pages)- Martini2026c_GUE_Statistics.tex: Full LaTeX source code All rights reserved under authorship of Ariel Fernando Martini. Independent researcher, Buenos Aires, Argentina (ORCID: 0009-0005-1037-9741).