We present a parameter-free explanation for the Milky Way's flat rotation curve without invoking dark matter. The Spacetime Viscosity and Centrifugal Force (SVCF) framework derives fundamental constants from 37-dimensional manifold topology and predicts that vacuum hoop stress—analogous to tensile stress in a rotating cylinder—provides the additional centripetal force traditionally attributed to dark matter halos. Using only baryonic (visible) matter and SVCF constants, we predict v_circ = 223 km/s at the solar radius (R ≈ 8 kpc), matching observations of 220 ± 10 km/s with 98.6% accuracy and zero free parameters. This eliminates the need for ≈10¹² M_☉ of undetected dark matter in the Milky Way. The prediction was publicly timestamped on November 16, 2025 constituting Domain 14 validation of the SVCF framework. The mechanism generalizes to external galaxies, where the πΨ hoop stress factor (with Ψ = √2−1 derived from manifold topology) quantitatively reproduces the Tully-Fisher relation and explains flat rotation curves across six orders of magnitude in galactic mass without adjustable parameters. AAS submission number AAS74214 this paper publicly timestamped currently submitted to the AAS part of the SVCF unified field theory