Phenomenological Evidence of GUE Statistics and Thermodynamic Stability in Goldbach Partitions

This preprint presents a computational and phenomenological analysis of Goldbach's Conjecture through the combined lenses of spectral theory (GUE random matrix statistics) and statistical mechanics (thermodynamic entropy). Using an integral-refined Hardy–Littlewood heuristic with explicit Singular Series computation, we achieve convergence ratios of ≈1.000 at N = 100,000. Nearest-neighbour spacing analysis of the first 20 Riemann zeta zeros yields variance 0.174, consistent with the GUE prediction of 0.178. A persistent ≈1-bit entropy gap for N ≡ 0 (mod 6) is formalized through a microcanonical ensemble framework. We do not claim a proof of Goldbach's Conjecture; rather, we offer a phenomenological, testable lens grounded in singular-series structure and large-scale spectral evidence. This work was produced through a human-led, AI-assisted collaborative workflow.