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`<r>` of Riemann zeta zeros converges to the GUE prediction. Using Platt's high-precision zeros up to height T ~ 3x10^10 (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 `<r>`(T) = 0.59891(13) + 1.245(40)/log^2(T), with chi^2/dof = 0.50. The asymptotic value R_inf = 0.59891 lies 6.1 sigma below the GUE limit R_GUE = 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) < std_GUE) and stronger anti-correlation (Corr(s_n,sₙ₊₁) < Corr_GUE), both converging as 1/log^2(T). Decomposing: c_std = +1.60 (+128%) and c_corr = -0.36 (-29%), reproducing 99.5% of the measured coefficient. Independent confirmation comes from the number variance Sigma^2(L,T) and spectral rigidity Delta_3(L,T), which exhibit the Bogomolny-Keating saturation at L_cross = log T/(2*pi).