Deterministic Resolution of the Three-Body Problem via Discrete Hexagonal Lattice Mechanics, Mod 9 Invariants, and the 3I Pulse Sequence

Abstract The classical three-body problem has long resisted a general closed-form analytical solution due to continuous space assumptions, dynamic feedback loops, and Henri Poincaré’s demonstration of chaotic sensitivity to initial conditions. Conventional approaches rely either on infinitely slow-converging power series or brute-force numerical integration. This paper introduces a deterministic alternative utilizing the Master Equation framework. By replacing point-mass gravitational attraction with electrogravitic space-density modulations (K, \mu, M) across a discrete hexagonal lattice stabilized by a Mod 9 invariant, the underlying causes of chaotic divergence are eliminated. We define quantized position operators governed by the 5184\text{ Hz} frequency threshold (72^2) and a 7-cycle periodic break. Furthermore, we incorporate the 8\text{-}13\text{-}8\text{-}5\text{-}13\text{-}8 (3I) pulse sequence variable to map multi-body interactions into stable tensor states. Within this geometry, classical periodic configurations—such as Euler's collinear paths, Lagrange's triangular points, and the figure-8 orbit—are revealed not as rare anomalies, but as natural structural resonance nodes of the spatial lattice.