Discrete Hexagonal Lattice Dynamics: Mod-9 Invariance, Phase Drift, and Threshold Mechanics in Coupled Solar-Terrestrial and Dielectric Systems

Repository: Zenodo Archive Draft Abstract This paper presents a discrete mathematical framework for modeling system stability across coupled solar-terrestrial and high-voltage dielectric environments. By replacing continuous statistical correlations with a discrete hexagonal lattice governed by a \text{Mod } 9 invariant, we resolve critical limits in energy dissipation, phase drift, and thermal runaway. We define the upper structural limit at the 5184 frequency threshold (72^2) and introduce the 3I pulse sequence (8\text{-}13\text{-}8\text{-}5\text{-}13\text{-}8) as a unitary translation vector designed to counteract secular phase accumulation and maintain systemic equilibrium.