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 (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. This is a feature absent in particle dark matter models. The triad of UD scaling relations is confirmed: (i) Clusters in equilibrium yield rc ∝ M^1/3 (α=0. 324±0. 079, 0. 1σ) ; (ii) Clean dwarf galaxies in the self-interaction regime yield rc ∝ M^1/2 (α=0. 484±0. 167, 0. 1σ) ; (iii) High-redshift galaxies validated by local calibration yield v ∝ M^1/3 (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. Keywords: dark matter, UD theory, galaxy rotation curves, self-interaction, scaling relations, SPARC, multi-scale validation