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) /EG 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** - LARGESCALEDATASET. csv: Exact G (N) for N ∈ 10³, 2×10⁶ - RACETO₁0M. csv: Extended data to N = 10⁷ - Monte Carlo probe results for N = 10¹² and 10¹⁶ 2. **Analysis Code** - verifyguecomplete. py: Complete GUE verification script - generateₐlpha₁00Mₒptimized. 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.
Ruqing Chen (Sun,) studied this question.