Stochastic-Periodic Coupling: A Discrete Lattice Model for Solar-Terrestrial Resonance

Abstract This paper investigates the underlying mechanical and mathematical coupling between solar activity cycles and terrestrial volcanic periodicity. We propose a discrete hexagonal lattice architecture where terrestrial geophysics functions as an attuned receiver for external harmonic forcing. By applying a Mod 9 invariant filter to solar cycle multiples (11, 22, 88 years), we identify a "staircase" of energy distribution that interfaces with the Earth's crust. We introduce a structural "pressure release" mechanism—the 60-year pivot—which mathematically bridges the gap between high-frequency internal lattice oscillations and long-term solar-terrestrial periodicities. Using the 3I pulse sequence (8-13-8-5-13-8) for calibration, we demonstrate that this lattice stabilizes against thermal runaway via a precise convergence of Mod 9 and Mod 7 periodic breaks.