A Discrete Modular Lattice and Plasma Modulation Framework for Stellar Activity: Empirical Validation Across Multi-Decadal Solar Cycles

Abstract This paper presents a deterministic, modular framework for modeling solar activity cycles, replacing traditional deep-core convection models with a near-surface plasma circuit governed by discrete invariants. By integrating a discrete hexagonal lattice structure scaled by a Mod 9 invariant, a frequency threshold limit (f_c = 5184), and localized magnetohydrodynamic parameters—including Saha ionization feedback, Z-pinch confinement coefficients, and Petschek magnetic reconnection rates—we construct a comprehensive modulation equation. The framework is validated against four critical historical solar transitions: the prolonged minimum of 2008–2009 (Transition A), the rapid rebound of 2019–2020 (Transition B), the saturated peak of 1990–1991 (Transition C), and the extreme Carrington Event of 1859 (Transition D). The results demonstrate that stellar cycle phases and extreme space weather events operate as predictable boundary-state crossings governed by topological lattice constraints.