Dark Matter as UD: Evidence for Self-Interaction from SPARC Galaxies

This work tests the UD theory prediction that dark matter is the condensative attribute embedded in space (U_D) rather than a particle species. Starting from the four fundamental axioms of UD theory, we derive a universal dark matter density profile: ρ_DM(r) = ρ_0 (1 + r^2/r_c^2)⁻¹ e-r/r_t. Using 171 galaxies from the SPARC database, we compare the UD profile with NFW and Burkert profiles. The UD profile achieves a reduced χ² win rate of 45.6%, outperforming NFW (19.9%) and Burkert (34.5%), with the lowest average reduced χ² (3.39). A distinctive self-interaction signature predicted by UD theory is directly detected: 1/r_c² ∝ ρ_0², with correlation coefficient r = 0.568 (p = 1.0×10⁻¹⁴, R² = 0.323), which is absent in standard particle dark matter models. For a clean sample of 36 dwarf galaxies, the scaling relation r_c ∝ M1/2 is confirmed with fitted exponent α = 0.475 ± 0.165, consistent with the theoretical prediction at 0.1σ. BIC analysis shows that UD wins decisively in galaxies with extended rotation curves where the exponential truncation is well constrained. These results provide strong observational evidence for the UD theory of dark matter.