Dynamical Maintenance Mechanism of Geomagnetic Fields via Supercritical Taylor-Proudman Structuring and Cosmic Remnant Flux Packing

Topological and thermodynamic paradoxes inherent in standard geodynamo formulations—specifically regarding the absence of insulated boundary conditions in the liquid outer core and the rapid ohmic dissipation of seed fields—are rigorously resolved. A completely deterministic maintenance mechanism is formulated based on the geometric packing of primordial topological remnants and the fluid-dynamic creation of discrete transport channels. Under the rapidly rotating limit, the Taylor-Proudman theorem enforces an invariant constraint along the rotational axis, split-transforming the continuous metallic fluid into a manifold of non-continuous virtual cylinders. To ensure exact structural preservation across geological timescales without relying on transient perturbations, an orthogonal closure condition is established between the non-Hermitian magnetic induction tensor and the non-equilibrium steady state (NESS) fluid Onsager matrix. This algebraic conjugate cancellation dynamic dictates that the magnetic Lorentz force terms are strictly compensated by the boundary NESS fluid flux matrix, guaranteeing that the maximum circulation eigenvalue is locked at identity. Consequently, a fully causal, localized, and deterministic explanation is established for the persistent maintenance of planetary magnetic fields, defining the phenomenon as a structural consequence of rotating fluid dynamics and establishing an invariant natural law framework that dictates the macroscopic magnetohydrodynamic stability limits.