Cosmic Plasma Electrodynamics: Scaling Localized Mod 9 Invariant Lattices to Intergalactic Birkeland Currents and Galactic Rotation Models

Abstract This paper extends our localized discrete hexagonal lattice framework (anchored at 5184\text{ Hz} with Mod 9 invariance) to macro-scale astrophysical phenomena, presenting a unified electrical model of the cosmos. By transitioning from a 2D lattice to a 3D cylindrical tensor network, we demonstrate how cosmic Birkeland currents maintain structural stability through the Bennett pinch effect without requiring dark matter. The primary contributions of this extension are: 1. Birkeland Current Scaling & 3D Braiding Mechanics: We adapt the 3I pulse sequence vector \vec{P} = \begin{pmatrix} 8 & 13 & 8 & 5 & 13 & 8 \end{pmatrix} and magnetic helicity conservation (H_M \equiv 1 \pmod 9) to govern 6-strand plasma braids, ensuring self-constricting filaments avoid chaotic turbulence or thermal runaway. 2. Galactic Adjacency and Homopolar Motor Models: By treating spiral galaxies as active circuits driven by central current anchors (\nabla \cdot \mathbf{E}_{\text{center}} = 9), we derive flat rotation curves via radial current density scaling (\mathbf{J}_r \propto 1/r), eliminating the need for hypothetical dark matter halos. 3. Cosmic Harmonic Constants and Orbital Resonance: We map the 3I sequence to macro-cosmic orbital shells, proving that global structural closure (\sum P_k \equiv 1 \pmod 9) and 7-cycle periodic phase-inversion act as natural regulators for planetary and stellar positioning.