Geometric Viscoelastic Origin of the RAR: Evidence from the SPARC Database

We investigate the galactic-scale phenomenological implications of TIDE, a framework in which spacetime exhibits a finite, density-dependent geometric relaxation time. By modeling the dark sector as a viscoelastic geometric medium, we formulate an overdamped constitutive equation for the effective gravitational acceleration. We show that the interplay between the orbital dynamical time and the vacuum geometric relaxation time naturally defines a transition acceleration scale, a 0. Adopting a minimal phenomenological closure for intermediate densities, we derive an effective equation of state for galactic kinematics. In the lowacceleration limit, this formulation analytically recovers the Baryonic Tully-Fisher Relation. We test this effective relation against the SPARC database (175 galaxies, 3389 kinematic points). Assuming a universal vacuum relaxation threshold (a 0 = 1.2 × 10-10 m/s 2) and fixed stellar mass-to-light ratios (ϒ disk = 0.5), the model reproduces the observed Radial Acceleration Relation (RAR) with a mean residual of-0.019 dex and an RMS scatter of 0.205 dex. These results suggest that the kinematic anomalies typically attributed to collisionless dark matter halos can be consistently modeled as the delayed inertial response of the spacetime manifold.