Polymath Project Narrows Twin Prime Gap Bound to 246 via Collaborative Proof-Refinement — E8 Intelligence Research

FINDING: Polymath project on bounded gaps between primes reduces upper bound for \(H_1\) (twin prime gap) via collaborative, distributed proof-refinement. | MATH: \(H_1 = n → ∞ (pₙ₊₁ - p_n)\); Zhang's original bound \(H_1 ≤ 70,000,000\) reduced to \(H_1 ≤ 246\) (and to \(H_1 ≤ 6\) under Elliott–Halberstam conjecture). Key constant: the Maynard–Tao sieve yields \(H_m m e⁴ᵐ\). | CONNECTION: No direct geometric harmony ratios (0.382, 0.618, etc.) appear. The prime gap distribution relates to the Selberg sieve, which has no crystallographic or base-60 link. | DEPTH: 7 — Profound for analytic number theory and collaborative methodology, but not revealing new universal constants or geometric symmetries. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com