Dark Matter: From Particle to Property — Self-Interaction and Scaling Relations in UD Theory

This paper presents a comprehensive observational test of UD theory's prediction that dark matter is the D attribute of space (UD) rather than an unknown particle. UD theory is a metatheoretical framework based on two fundamental attributes: U (dispersion, expansion, continuity) and D (condensation, localization, fixation). The four-aspect structure (UU, UD, DD, DU) naturally identifies UD as dark matter—the condensative tendency of space itself. KEY FINDINGS: 1. Profile Fitting (171 SPARC galaxies): UD profile: rho (r) = rho0 (1 + r²/rc²) ^ (-1) exp (-r/rt) UD wins 45% of galaxies by reduced chi2 (vs 19% NFW, 36% Burkert) Average chi2ᵣed: UD 3. 39, NFW 4. 69, Burkert 3. 87 2. Self-Interaction (direct detection): Field equation predicts 1/rc² proportional to rho0² Observed correlation: r = 0. 567, p < 10^-4, R² = 0. 323 This confirms the lambda4 UD³ term, unique to UD theory 3. Cluster Scaling (equilibrium regime): Predicted: rc proportional to M^1/3 Observed: alpha = 0. 324 +/- 0. 079 (0. 1sigma from 1/3) 12 clusters, bootstrap validation 4. Clean Dwarf Scaling (self-interaction regime): Predicted: rc proportional to M^1/2 Observed (34 gas-dominated dwarfs): alpha = 0. 484 +/- 0. 167 (0. 1sigma from 1/2) 5. High-Redshift Scaling (early evolution): Predicted: v proportional to M^1/3 Free fit: alpha = 0. 341 +/- 0. 042 (0. 2sigma from 1/3), R² = 0. 892 Cross-validation confirms scaling is intrinsic to data 6. Cosmological Validation: BAO distances predicted with 0. 9% mean error All five redshift points within 1sigma of eBOSS observations CONCLUSION: The convergence of three independent scaling laws, derived from the same UD field equation in different asymptotic limits, constitutes strong evidence that dark matter is a property of space (UD), not a particle. The self-interaction signature provides a smoking-gun test that particle dark matter models cannot accommodate.