Spectral Rigidity in Goldbach Representations: Data and Code for Sub-Poissonian Statistics Analysis (10³ to 10¹⁶)

This repository contains the complete dataset, analysis code, and supplementary materials for the paper "Spectral Rigidity in Goldbach Representations: Sub-Poissonian Statistics Across Thirteen Orders of Magnitude." ## Overview We investigate the variance structure of Goldbach representation counts G(N) — the number of ways to express an even integer N as the sum of two primes — across 13 orders of magnitude (N = 10³ to 10¹⁶). ## Key Findings - The Fano factor α = Var(G)/E[G] converges toward ~0.5 (GUE statistics)- Spacing distribution σ = 0.705 matches GUE prediction (0.707) within 0.3%- Monte Carlo probes at N = 10¹⁶ confirm Hardy-Littlewood formula with only -0.34% bias- Evidence supports spectral rigidity in prime pair distributions ## Contents 1. **Datasets** - LARGE_SCALE_DATASET.csv: Exact G(N) for N ∈ [10³, 2×10⁶] - RACE_TO_10M.csv: Extended data to N = 10⁷ - Monte Carlo probe results for N = 10¹² and 10¹⁶ 2. **Analysis Code** - verify_gue_complete.py: Complete GUE verification script - generate_alpha_100M_optimized.py: Large-scale data generation - Jupyter notebooks for figure generation 3. **Figures** - All publication-quality figures (PDF and PNG) 4. **Manuscript** - LaTeX source and compiled PDF ## Methods - Exact enumeration for N ≤ 10⁷- Monte Carlo sampling for N = 10¹², 10¹⁶- Statistical analysis: Fano factor, spacing distribution, logarithmic extrapolation ## Citation If you use this data or code, please cite:Chen, R. (2026). Spectral Rigidity in Goldbach Representations: Sub-Poissonian Statistics Across Thirteen Orders of Magnitude.