A Rigorous Mathematical Framework for Discrete Hexagonal Lattice Dynamics, \text{Mod } 9 Invariants, and 7-Cycle Periodic Break Stabilization in the Electric Cosmos

Abstract This paper establishes a comprehensive and rigorous mathematical framework formalizing the master blueprint of the electric cosmos. We model mass as a centripetal low-potential sink within a discrete hexagonal lattice governed by a \text{Mod } 9 algebraic invariant (X \equiv 0 \pmod 9). By integrating the 3\text{I} pulse sequence vector \vec{\omega}_{3\text{I}} = \{8, 13, 8, 5, 13, 8\}, we derive a central resonance anchor (R_a) that scales background vacuum impedance (376.73\ \Omega) down to a localized reactive node resistance of 142.47\ \Omega. To prevent infinite energy accumulation and thermal runaway as systems approach the critical frequency threshold of 5184\text{ Hz} (72^2), we formalize a 7-cycle periodic break damping operator (\hat{P}^7 \equiv \mathbb{I}). Furthermore, we prove 120^\circ phase-lock current routing symmetry, Artin braid group plasma filament topologies, and homopolar 1/r galactic rotation mechanics. Finally, we apply Lyapunov stability analysis and LaSalle's Invariance Principle to prove strict asymptotic convergence (\dot{V}(t) \le 0), ensuring permanent steady-state stability under high-energy operational stress.