Geometric Stabilization of Electrodynamic Particulate Sheaths: A Discrete Lattice Approach to Non-Gravitational Polarization

Abstract This paper presents a theoretical framework for interpreting extreme negative polarization in astronomical particulate environments—specifically those associated with active cometary bodies—as an emergent property of electrostatic dust-lofting sheaths. We challenge the standard gravity-dominated regolith model by demonstrating that negative polarization values exceeding tens of percent require structural uniformity unattainable by random distribution. By applying the mechanics of holographic industrial materials to the astrophysical domain, we propose that charged, sub-micron asymmetric grains act as macroscopic optical metamaterials. We establish the "electrostatic sheath" as a discrete hexagonal lattice governed by a Mod 9 invariant, where energy distribution is constrained by 120° phase-locking and a 7-cycle periodic break. These mechanisms effectively stabilize high-energy plasma currents, preventing thermal runaway at the 5184 frequency threshold (72^2). The framework successfully reconciles observed non-gravitational acceleration vectors with localized plasma potential gradients, providing a closed-system electrodynamic model for planetary and cometary evolution.