Empirical Constraints on the Locality of Galactic Dynamics from SPARC Rotation Curves

We present a data-driven analysis of galactic rotation curves based on the SPARC database, aimed at testing whether disk galaxy dynamics are governed by locally reconstructed quantities or by system-level constraints. Using observed rotation curves and baryonic mass models, we construct a non-parametric empirical relation between observed radial acceleration and baryonic acceleration, without invoking dark matter halo models or per-galaxy fitting. We demonstrate that this empirical relation is predictive at the galaxy level: when calibrated on a subset of galaxies, it accurately reproduces the dynamics of independent systems under cross-validation. We further examine the residuals of this relation as a function of the local orbital time to test for the presence of a controlling local temporal scale. Both global and per-galaxy analyses show no universal dependence of residuals on orbital time. This absence of a local temporal signature indicates that galactic dynamics are not regulated by locally defined dynamical clocks once the empirical acceleration relation is taken into account. Instead, the data support a system-level organization of galactic dynamics that constrains stellar motion across radii and across galaxies. These results place strong empirical constraints on theories that rely on locally acting dynamical or temporal regulators and highlight the need for interpretations consistent with globally organized galactic dynamics.