Recovering Baryonic Mass from Galaxy Rotation Curves Without Dark Matter

We consider the inverse problem of recovering baryonic mass distributions directly from observed galaxy kinematics using a parameter-free gravitational mapping. Specifically, we adopt the enhancement functionGeff=(1+1/x2)1/KeffG_{\text{eff}} = (1 + 1/x^2)^{1/K_{\text{eff}}}Geff=(1+1/x2)1/Keff with Keff=1+31+8x2K_{\text{eff}} = 1 + \frac{3}{1 + 8x^2}Keff=1+1+8x23, and solve the implicit relationabary Geff(abary/a0)=v2/ra_{\text{bary}} \, G_{\text{eff}}(a_{\text{bary}}/a_0) = v^2/rabaryGeff(abary/a0)=v2/rat each radius. Applied to 171 galaxies from the SPARC sample (3,375 data points), the inferred baryonic mass profiles are compared to independent estimates derived from Spitzer 3.6 μm photometry and HI 21 cm observations. We find a median ratio of 0.994 between inferred and observed baryonic mass, with 79% of data points recovered within a factor of 2. This indicates that the adopted mapping provides a strong consistency relation between rotation curves and baryonic mass distributions across a wide range of galaxy types. These results suggest that, within this framework, galaxy kinematics encode sufficient information to recover baryonic mass profiles without introducing additional free parameters. The findings should be interpreted as a consistency test of the mapping rather than a definitive exclusion of dark matter.