Gap ratio statistics of Riemann zeros: measurement, mechanism, and the Berry-Keating correction

We report the first precision measurement of the rate at which the gap ratio statistic`` of Riemann zeta zeros converges to the GUE prediction. Using Platt's high-precision zeros up to height T ~ 3x10¹0 (log T = 24), together with Odlyzko's tables at lower heights, we construct a 21-point dataset spanning log T = 9. 7 to 24. 1 and find `` (T) = 0. 59891 (13) + 1. 245 (40) /log² (T), with chi²/dof = 0. 50. The asymptotic value Rᵢnf = 0. 59891 lies 6. 1 sigma below the GUE limit RGUE = 0. 59971, indicating incomplete convergence at log T = 24. The first-order term b/log T is consistent with zero (b = 0. 019 +/- 0. 043), explained by the symmetry r (s1, s2) = r (s2, s1) and the antisymmetry of the Berry-Keating first-order correction. We identify the physical mechanism: Riemann zeros have a narrower spacing distribution than GUE (std (s) < stdGUE) and stronger anti-correlation (Corr (sₙ, s₍+₁) < CorrGUE), both converging as 1/log² (T). Decomposing: cₛtd = +1. 60 (+128%) and ccorr = -0. 36 (-29%), reproducing 99. 5% of the measured coefficient. Independent confirmation comes from the number variance Sigma² (L, T) and spectral rigidity Delta₃ (L, T), which exhibit the Bogomolny-Keating saturation at Lcross = log T/ (2*pi).