Search for Kinetic Magnetism: A Proposal to Detect High-Frequency Vacuum Viscoelasticity via Longitudinal Spin-Jerk Coupling in 129Xe

We propose a sensitive table-top experiment to test non-Riemannian extensions of General Relativity that predict a massive, viscoelastic torsion field (S). While static torsion components are strongly suppressed by the Vainshtein mechanism in dense matter, we derive a dynamical Geometric Spin-Jerk Operator that couples the third time-derivative of the nuclear spin current to the vacuum geometry. We calculate that a longitudinal acoustic standing wave ($f_d \approx 1.2$ GHz) applied to hyperpolarized $^{129}$Xe gas will induce a resonant geometric phase, resulting in a predicted Larmor frequency shift of $\Delta \omega \approx 52 \pm 8$ Hz. We detail a "Hodge Veto" detection topology using a toroidal SQUID geometry that suppresses electromagnetic backgrounds by a factor of $> 10^6$ based on the divergence-free nature of the magnetic field ($\nabla \cdot \mathbf{B} = 0$) versus the curl-free nature of the longitudinal torsion mode ($\nabla \times \mathbf{S} \approx 0$). We present a full noise budget analysis, demonstrating a viable Signal-to-Noise Ratio (SNR) of $\sim 50$ for a $100$s integration time.