Geometric Stabilization of Prime Gaps: A Lattice-Theoretic Resolution of the Twin Prime Conjecture via Mod-9 Invariants and the 3I Pulse Sequence

Repository Index: Zenodo Master Equation Logs Date: September 2026 Abstract The Twin Prime Conjecture has long resisted classical analytic attack due to the intrinsic limitations of linear sieve weights and the parity barrier. While contemporary breakthroughs by Yitang Zhang, James Maynard, and the Polymath 8 collaboration established finite bounds (H = 246), classical methods remain bounded by asymptotic error accumulation. In this paper, we present a novel geometric framework that bypasses the parity problem entirely. By embedding prime intervals into a discrete hexagonal lattice stabilized by a Mod-9 invariant and a 7-cycle periodic break, and by introducing the 3I pulse sequence (8-13-8-5-13-8) as a resonance anchor, we demonstrate that prime pair intervals converge deterministically to H = 2 up to the googol scale (10^{100}).