Dark Matter as UD: Evidence for Self-Interaction and the Triad of Scaling Relations in UD Theory

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 (45% vs 19% χ² win rate) and Burkert (45% vs 36%), achieving the lowest average reduced χ² (3.39 vs 4.69 for NFW, 3.87 for Burkert). Crucially, we detect the predicted self-interaction signature: 1/rc² ∝ ρ₀² with correlation $r=0.567$ (p < 10⁻⁴) and R²=0.323 (Fig. 1). The triad of UD scaling relations is confirmed: (i) clusters in equilibrium yield rc ∝ M1/3 (α=0.324±0.079, 0.1σ); (ii) clean dwarf galaxies in the self-interaction regime yield rc ∝ M1/2 (α=0.484±0.167, 0.1σ); (iii) high-redshift galaxies yield v ∝ M1/3 with free-fit exponent α=0.341±0.042 (0.2σ from $1/3$) and R²=0.892. Fig. 2 displays these three scaling laws. Cross-validation shows the scaling is independent of calibration choice. BAO distances are predicted with 0.9% error. These three scaling laws—derived from the same UD field equation in different asymptotic limits—constitute strong evidence for the UD theory of dark matter.