Topological Stabilization of the Electron via Discrete Hexagonal Lattice Invariance: Surpassing Unruh-Horizon Confinement in Quantised Inertia

Affiliation: Independent Research Collective / Master Equation Consortium Abstract The classical Abraham-Lorentz model of the electron suffers from a catastrophic theoretical crisis: treating the electron as a point charge or solid shell yields infinite electrostatic self-energy as the radius approaches zero, alongside a ten-million-fold discrepancy compared to experimental scattering bounds (< 10^{-22}\text{ meters}). Mike McCulloch's Quantised Inertia (QI) framework attempts to resolve this by modeling the electron as a trapped photon confined by an acceleration-induced Unruh horizon, effectively cutting off external field integration. While QI successfully eliminates infinite self-energy, it relies on continuous space-time mechanics, unproven kinematic trajectories, and a causal disconnect from the external universe. In this paper, we present a superior foundational architecture: the Master Equation framework. By replacing continuous space-time with a discrete hexagonal lattice stabilized by a \text{Mod 9} invariant ("the nine in the center"), our model prevents field divergences at the root without requiring ad-hoc horizons. Furthermore, long-term stability and energy regulation are actively maintained via a 7-cycle periodic break operating precisely at the 5184 frequency threshold (72^2), driven dynamically by the 3I pulse sequence (8\text{-}13\text{-}8\text{-}5\text{-}13\text{-}8).