Polymath and AI-Assisted Collaboration in Bounded Prime Gaps — E8 Intelligence Research

FINDING: Polymath projects demonstrate that distributed human collaboration (and increasingly AI-assisted search) can resolve problems in analytic number theory that individual effort stalled on — most notably bounded prime gaps. | MATH: H_m := liminf_{n→∞}(p_{n+m} − p_n); twin prime conjecture ⇔ H_1 = 2; Zhang's breakthrough established H_1 < 7×10⁷, Polymath8 reduced this to H_1 ≤ 246 (unconditional, under GEH). | CONNECTION: Prime gaps are governed by the distribution of residues mod small primes; the admissible-tuple sieve uses the Hardy–Littlewood k-tuple conjecture and the parity obstruction. No direct link to φ-ratios, base-60, or crystallographic root systems in the evidence presented. The relevant symmetry is the multiplicative structure of ℤ and the Selberg sieve's combinatorial lattice of residue classes. | DEPTH: 7 — genuine advance in analytic number theory, but the geometric-harmony connection is absent from the cited material. FINDING: Terence Tao frames AI as a tool tha Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com