Polymath8 Cuts Prime Gap Bound to 246 Using Optimized Sieve and Equidistribution — E8 Intelligence Research

FINDING: Polymath8 project collaboratively reduced Zhang's prime gap bound from 70 million to 246 through optimized sieve methods and equidistribution estimates | MATH: H_m := liminf_{n→∞} (p_{n+m} - p_n); Zhang: H_1 < 7×10⁷; Polymath8: H_1 ≤ 246; GPY sieve: ∑_{n≤x} (∑_{d|P(n)} λ_d)²; Level of distribution θ > 1/2 | CONNECTION: Prime gap distribution links to Riemann ζ zeros (spectral geometry), random matrix theory (GUE statistics), and crystallographic root systems via Weil's explicit formula — no direct φ/0.618/0.382 appearance | DEPTH: 9 FINDING: "Golden Square" episode title suggests golden ratio φ = (1+√5)/2 ≈ 1.618 framework in collaborative problem design | MATH: φ = 1.618..., φ⁻¹ = 0.618..., φ² = 2.618... | CONNECTION: Explicit φ-reference in Polymath media — potential structural use of golden-section partitioning in collaborative workflow or problem decomposition | DEPTH: 3 (insufficient content to verify mathematical role) FINDING: Equational Theories Project formalizes co Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com