Dark Matter as UD: Evidence for Self-Interaction and Multi-Scale Scaling in UD Theory

This paper presents a comprehensive observational validation of the UD theory prediction that dark matter is the D attribute in space (U_D). Using 171 SPARC galaxies, the UD density profile ρ(r)=ρ₀(1+r²/r_c²)⁻¹e-r/r_t 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/r_c² ∝ ρ₀² with correlation r=0.567 (p<10⁻⁴) and R²=0.323. This is a feature absent in particle dark matter models. The triad of UD scaling relations is confirmed:(i) Clusters in equilibrium yield r_c ∝ M1/3 (α=0.324±0.079, 0.1σ);(ii) Clean dwarf galaxies in the self-interaction regime yield r_c ∝ M1/2 (α=0.484±0.167, 0.1σ);(iii) High-redshift galaxies validated by local calibration yield v ∝ M1/3 (14.4% prediction error). 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.