Phase-Dynamic Structure and Spectral Rigidity in Prime Residue Dynamics (v3.0)

Executive Summary v3.0 + Appendix A (supplementary tables)This record contains the v3.0 executive summary and supporting appendix for the Prime Field Pathfinder study of prime residue dynamics in the Crystal-9 subspace (mod 81), computed over X in [50M, 100M].Main findingsPhase partitioning: the dynamics split into distinct macroscopic phases (laminar → localized quantum-chaotic → terminal stochastic).Localized spectral rigidity (85M–90M): leader-change spacing statistics show strong suppression of short-range spacings (level repulsion), with Repulsion Index (RI) ≈ 10 (capped) and a window where GUE-like behavior dominates versus Poisson.Global modular invariant (70M–100M): despite local turbulence, the aggregated Z-profile remains biased, with Z_{26} ≈ +0.26 and Z_{80} ≈ −0.26, indicating persistent long-term structure.