The Geometric Fundamental Plane: Collapsing the Scatter in the Radial Acceleration Relation

We investigate whether the residual scatter in the Radial Acceleration Relation (RAR) is driven by a hidden physical variable. Using a high-quality subsample of 175 galaxies from the SPARC database, we report a statistically significant correlation (r = 0.68, p < 10⁻²⁴) between RAR residuals and intrinsic galaxy ellipticity. By introducing a shear-dependent geometric correction to the critical acceleration scale, a₀,eff = a₀1 + Cε² with C = 2.01 ± 0.15, we collapse the residual scatter from σ = 0.082 to σ = 0.060 dex—consistent with the observational error floor. Partial correlation analysis confirms that intrinsic geometry, not surface brightness, is the dominant driver of the residuals. An inclination null test rules out projection artifacts. These results suggest that the "mass discrepancy" in galaxies is deterministically coupled to the geometry of the baryonic potential rather than stochastic dark matter halo assembly.Preprint.