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 (r) =₀ (1+r²/rc²) ^-1e^-r/rₜ outperforms NFW (45% vs 19% ² win rate) and Burkert (45% vs 36%), achieving the lowest average reduced ² (3. 39 vs 4. 69 for NFW, 3. 87 for Burkert). Crucially, we detect the predicted self-interaction signature: 1/rc² ₀² 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 M^1/3 (=0. 3240. 079, 0. 1) ; (ii) clean dwarf galaxies in the self-interaction regime yield rc M^1/2 (=0. 4840. 167, 0. 1) ; (iii) high-redshift galaxies yield v M^1/3 with free-fit exponent =0. 3410. 042 (0. 2 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.