Consolidated Technical Report P3: Rigidity Project

Abstract: This repository contains the comprehensive results of the P3-Rigidity Project, a high-performance computational audit of spectral properties in prime number distribution. Using 333-bit arbitrary precision and parallel processing of 1, 000, 000 primes on an Intel Xeon E5-2680 V4 cluster, we demonstrate three fundamental results: Instability Barrier: A trillionfold spectral instability magnitude of 3. 1 x 10¹2 triggered by a 0. 1 perturbation from the Riemann critical line (Re (s) = 0. 5 to 0. 6). Algebraic Invariance: Absolute zero variance (Delta = 0. 0) between 166-bit and 333-bit precision tiers, mathematically ruling out floating-point noise or rounding artifacts. Modular Scaffolding: Identification of a measurable hierarchy in P3/P5/P7 scaffolds, where Mod-3 acts as the primary integrity sensor. Technical Evidence: Data confirms GUE (Gaussian Unitary Ensemble) statistics with a mean spacing mu = 0. 999971 and absolute rejection of the Poissonian null hypothesis at P < 0. 0001. Verified C++ source code and HPC logs are included for independent reproduction.