Polymath Collaboration Yields Explicit Prime-Gap Bounds, Not Harmonic Ratios — E8 Intelligence Research

FINDING: Polymath collaboration demonstrates scalable collective proof, with the prime-gap project yielding explicit bounds on \(H_m\) (liminf gaps between primes). | MATH: \(H_m := n → ∞ (pₙ₊ₘ - p_n)\); twin prime conjecture ⇔ \(H_1 = 2\). Zhang's breakthrough gave finite \(H_1\), Polymath8 reduced \(H_1\) to 246 (unconditionally) and 6 (assuming Elliott–Halberstam). No new constants or ratios emerge — the core is combinatorial sieve bounds, not harmonic ratios. | CONNECTION: None to 0.382/0.618/1.618 or base-60. However, the structure of prime gaps relates to the additive lattice \(Z\) and its residue classes modulo small primes — a discrete symmetry, not crystallographic in the geometric sense. The collaborative process itself mirrors a distributed search over a combinatorial tree, akin to root-system weight lattices in optimization, but no explicit geometric ratio is present. | DEPTH: 6 — Profound for methodology (crowdsourced proof verification) and fo Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com