Multi-Scale Exponential Law and Quasi-Crystal Structure in Anomalous Riemann Zero Spacings

Does the positional structure of anomalously large Riemann zero spacings carry arithmetic information that the GUE (Gaussian Unitary Ensemble) framework cannot encode? We answer: yes, with a 20.7-sigma separation from GUE and direct spectral evidence for Dyson's quasi-crystal conjecture (50 Bragg peaks, max SNR = 197). However, the specific arithmetic source and the exact identity of the coefficient B remain unknown. We define a normalized spacing weight w_n = delta_t_n * (1/2pi) * ln(t_n/2pi) and classify w_n as "anomalous at level c" if w_n > mu + csigma, where mu and sigma are sample statistics. Our numerical experiments show that the mean gap k(c) between consecutive anomalies satisfies a multi-scale exponential law: k(c) approx A * exp(Bc). At N = 10,000 zeros, we find A = 0.944, B = 1.688 +/- 0.062, with R^2 = 0.999 across four threshold levels, all exhibiting a coefficient of variation (CV) < 0.56 and bootstrap p < 10^-4. This law is absent in random matrix theory: a study of 500 GUE matrices (500 x 500) yields an anomaly CV of 3.228 versus 0.40 for Riemann zeros, representing a gap of 20.7-sigma in the opposite direction. Furthermore, the diffraction spectrum of anomaly positions yields an intensity excess of 3629% over the empirical random baseline. This spectral structure is stable across multiple thresholds and is consistent with the quasi-crystal conjecture. Whether the coefficient B converges to sqrt(3)---the fundamental constant of the number field Q[sqrt(3)] and the I_{2,1} Lorentzian lattice---remains the decisive open question. A comparison with 3,000 zeros of the L-function L(s, chi_3) remains inconclusive at current precision. No proof of the Riemann Hypothesis is claimed.