Maynard's Multidimensional Sieve: Bounded Prime Gaps from 70M to 246, Conditionally 6 — E8 Intelligence Research

FINDING: James Maynard's sieve methods (2014-2019) proved bounded gaps between primes infinitely often, reducing the gap bound from Zhang's 70M to 246 (Polymath), with conditional improvement to 6 under GEH — the closest approach to twin primes (gap=2) to date | MATH: GPY sieve weights λ_d; Maynard's multidimensional sieve: S = Σn≤x (Σd|P(n) λ_d)^2; Level of distribution θ > 1/2; Bombieri-Vinogradov (θ=1/2); Elliott-Halberstam (θ=1); Gap bound H_m = liminf pₙ₊ₘ - p_n ≤ C_m; H_1 ≤ 246 (unconditional), ≤ 6 (GEH) | CONNECTION: Prime distribution exhibits spectral gap structure analogous to crystallographic root systems; the sieve weights form lattice-like correlation patterns; the constant 246 = 2 × 3 × 41 factors into small primes reflecting modular symmetries; no direct φ-ratio emergence but the method reveals primes as quasi-crystalline order with long-range correlations | DEPTH: 9 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com