An Empirical Relaxation Signature in Galactic Dark-Matter Halos

We report the detection of a robust empirical correlation between inner galactic kinematics and a dimensionless proxy for the cumulative scattering history of dark matter in disk galaxies. Using high-quality rotation-curve mass models from the SPARC database, we define a relaxation parameter η as the ratio between the observed inner circular velocity and that predicted by a best-fitting collisionless halo model. We find a strong and monotonic correlation between η and a scattering proxy constructed solely from dark-matter halo properties. The signal remains highly significant under partial correlation control, bootstrap resampling, and permutation-based null tests. The result is entirely observational and model-agnostic, and does not rely on simulations, baryonic feedback prescriptions, or assumptions about dark-matter microphysics. We interpret the correlation as an empirical signature consistent with dynamical relaxation processes operating in galactic dark-matter halos.