Galaxy Rotation Curves from Saturation of Vacuum Stiffness Transport

We present a revised formulation of galactic dynamics within Stiffness Field Cosmology (SFC), addressing the quantitative failure of earlier gradient-only models. Spatial gradients of the vacuum stiffness field K alone cannot sustain flat rotation curves, as the associated acceleration decays too rapidly at large radii. We identify a fundamental limit on elastic energy transport in the vacuum, arising from its finite propagation speed and finite sustainable energy flux. When this transport bound is reached, the stiffness response saturates, giving rise to a universal acceleration scale a∗. This scale emerges directly from the non-metric SFC Lagrangian [5] and depends solely on intrinsic vacuum properties, independent of galaxy-specific parameters. In the saturated regime, the radial acceleration asymptotically approaches a∗, naturally producing flat rotation curves and reproducing the baryonic Tully–Fisher relation v 4 flat = GMba∗ without dark matter or modifications to local gravity. The small value of a∗ ∼ 10−10 m s−2 reflects the macroscopic state of the vacuum during the late soft phase of cosmic evolution [6] and is naturally linked to the energy scale of the cosmic microwave background. The saturation mechanism is active only in the ultra-weak, quasi-static regime, leaving Solar System tests, binary pulsars, and gravitational-wave observations unaffected. Vacuum stiffness saturation thus provides a predictive, falsifiable non-metric alternative to particle dark matter for explaining galactic dynamics.