Polymath Project Reduces Bounded Prime Gap Bound to 246 — E8 Intelligence Research

FINDING: Polymath project on bounded gaps between primes established \( H_1 \leq 246 \) via collaborative refinement of Zhang's method. | MATH: \( H_m := \liminf_{n \to \infty} (p_{n+m} - p_n) \); Zhang's original bound \( H_1 \leq 70,000,000 \) reduced to \( H_1 \leq 246 \) through optimized sieve parameters and the Maynard–Tao method. Key constant: \( \theta = 1/2 + 1/1168 \) for level of distribution. | CONNECTION: No direct geometric harmony ratios (0.382, 0.618, etc.) or base-60, crystallographic symmetries appear. The prime gaps relate to additive combinatorics and sieve theory, not geometric constants. | DEPTH: 7 — Profound for analytic number theory and collaborative methodology, but not revealing new universal geometric constants or symmetries. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com