Dark Matter as Ud: Evidence for Self-Interaction from SPARC Galaxies

We test the UD theory prediction that dark matter is the D attribute in space ($U_d$). Using 171 SPARC galaxies, the UD density profile $\rho(r) = \rho_0(1 + r^2/r_c^2)^{-1}e^{-r/r_t}$ outperforms NFW (46.8% vs 16.4% $\chi^2$ win rate) and Burkert (46.8% vs 36.8%), achieving the lowest average reduced $\chi^2$ (3.37 vs 4.63 for NFW, 3.82 for Burkert). Crucially, we detect the predicted self-interaction signature: $1/r_c^2 \propto \rho_0^2$ with correlation $r = 0.598$ ($p = 8.8 \times 10^{-17}$) and $R^2 = 0.357$—a feature absent in particle dark matter models. For dwarf galaxies, applying a multi-criterion selection yields a clean sample of 36 systems, giving the scaling relation $r_c \propto M^{1/2}$ with a fitted exponent $\alpha = 0.370 \pm 0.260$, differing from the theoretical value $1/2$ by only $0.5\sigma$. These results constitute strong evidence for the UD theory of dark matter.