Polymath Collaboration and AI Accelerate Bounded Prime Gap Breakthroughs — E8 Intelligence Research

FINDING: Polymath collaboration demonstrates that large-scale, decentralized mathematical problem-solving can crack hard problems (e.g., bounded prime gaps), with AI now accelerating experimental mathematics. | MATH: $H_m := \liminf_{n \to \infty} (p_{n+m} - p_n)$; twin prime conjecture ⇔ $H_1 = 2$; Zhang's bound $H_1 < 7\times10^7$ → Polymath8 reduced to $H_1 \le 246$ (unconditionally), $H_1 \le 6$ under Elliott–Halberstam. | CONNECTION: Prime gaps $H_m$ relate to the distribution of primes — a lattice-like structure in $\mathbb{N}$; the reduction process (7e7 → 246) mirrors iterative refinement toward a fixed point, echoing contraction ratios (e.g., 0.618) in convergence, though no explicit golden ratio appears. | DEPTH: 7 — profound for methodology and number theory, but not a new universal constant or symmetry.

Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com