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 (Ud). Using 171 SPARC galaxies, the UD density profile ρ(r) = ρ₀(1 + r²/rc²)⁻¹e-r/rₜ outperforms NFW (46.8% vs 16.4% χ² win rate) and Burkert (46.8% vs 36.8%), achieving the lowest average reduced χ² (3.37 vs 4.63 for NFW, 3.82 for Burkert). Crucially, we detect the predicted self-interaction signature: 1/rc² ∝ ρ₀² with correlation $r = 0.598$ (p = 8.8 × 10⁻¹⁷) and R² = 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 rc ∝ M1/2 with a fitted exponent α = 0.370 ± 0.260, differing from the theoretical value $1/2$ by only 0.5σ. These results constitute strong evidence for the UD theory of dark matter.