Polymath8 Reduces Prime Gap Bound from 70 Million to 246 — E8 Intelligence Research

FINDING: Polymath project retrospective on bounded gaps between primes — collaborative proof that \( H_1 \leq 246 \) (reduced from Zhang's 70 million), using combinatorial number theory and sieve methods. | MATH: \( H_m = \liminf_{n \to \infty} (p_{n+m} - p_n) \); Zhang's original bound: \( H_1 \leq 70,000,000 \); Polymath8 reduction to 246; key tool: Maynard–Tao sieve with multidimensional weights. | CONNECTION: No direct geometric ratio or crystallographic symmetry. The prime gaps are arithmetic, not harmonic. However, the underlying distribution of primes relates to the Riemann zeta function's zeros, which exhibit spectral rigidity — a subtle connection to eigenvalue spacing in quantum chaos and random matrix theory (GUE). | DEPTH: 6 — Profound in collaborative methodology and number theory, but no new constants or geometric ratios emerge. The result refines known bounds, not a paradigm shift. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com