Maynard's Bounded Gaps Advance Twin Prime Conjecture, But Proof Remains Elusive — E8 Intelligence Research

FINDING: Twin prime conjecture remains unproven; recent progress by Maynard shows bounded gaps between primes, but no proof of infinite twin primes. | MATH: Twin prime pairs (p, p+2); Maynard's theorem: for any k, there exist infinitely many primes with gaps ≤ 600 (generalized); no exact constant for twin primes. | CONNECTION: No direct geometric harmony; prime gaps relate to modular arithmetic (mod 6) where twin primes cluster at (6n-1, 6n+1). | DEPTH: 6 — significant analytic number theory advance, but no resolution or geometric link. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com