Topological Stabilization of the Geodynamo via Anomalous Vacuum Viscosity: Resolving the Ekman Number Paradox with APH Theory

Standard magnetohydrodynamic (MHD) simulations of the Earth’s core struggle to reconcile the
vast discrepancy between the theoretical Ekman number (E ∼ 10−15), which governs the ratio
of viscous to Coriolis forces, and the values required for numerical stability (E ∼ 10−4). This
“Viscosity Paradox” implies that the geodynamo possesses an intrinsic suppression mechanism
for small-scale turbulence that standard fluid dynamics cannot explain without arbitrary “eddy
viscosity” parameters. We propose that the outer core fluid interacts with a non-associative vac-
uum manifold governed by Axiomatic Physical Homeostasis (APH). We introduce a fractional
Laplacian drag term, characterized by a vacuum stiffness index β ≈ 1.91, into the Navier-Stokes
equation. This “Geometric Viscosity” naturally suppresses high-wavenumber turbulence, act-
ing as a low-pass filter on the fluid dynamics. Furthermore, we model Geomagnetic Jerks as
discrete flux-tube interchange events analogous to magnetospheric substorms, and we propose
that geomagnetic reversals represent “Zero Divisor” topological resets in the underlying Sede-
nion algebra of the vacuum. Numerical simulations confirm that the APH stiffness parameter
reproduces the observed spectral slope of geomagnetic fluctuations.