Structural Extension of the Radial Acceleration Relation: Evidence for a Two-Dimensional Dynamical Law in Galaxies

We present an empirical extension of the Radial Acceleration Relation (RAR) by introducing a local structural parameter, Θ = d log g_bar / d log r, which encodes the radial variation of the baryonic gravitational field. Using a sample of 8580 data points from 143 galaxies, we show that Θ acts as an independent observable that organizes the residuals of the standard RAR. The inclusion of Θ reduces the conditional scatter by ~40%, removes systematic residual correlations, and improves statistical model selection criteria. We construct an effective two-dimensional relation of the form g_obs = F(g_bar, Θ), which can be interpreted either as a structurally modulated modification of gravity or as an effective halo contribution coupled to the baryonic distribution. Our results suggest that the RAR should be understood as a projection of a higher-dimensional dynamical law, where the internal structure of galaxies plays a fundamental role. This provides a new phenomenological framework for interpreting galaxy dynamics beyond standard one-parameter descriptions.