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 (U_D) 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 (U_U, U_D, D_D, D_U) naturally identifies U_D as dark matter—the condensative tendency of space itself. KEY FINDINGS: 1. Profile Fitting (171 SPARC galaxies): UD profile: rho(r) = rho0 (1 + r^2/rc^2)^(-1) exp(-r/rt) UD wins 45% of galaxies by reduced chi2 (vs 19% NFW, 36% Burkert) Average chi2_red: UD 3.39, NFW 4.69, Burkert 3.87 2. Self-Interaction (direct detection): Field equation predicts 1/rc^2 proportional to rho0^2 Observed correlation: r = 0.567, p < 10^-4, R^2 = 0.323 This confirms the lambda4 U_D^3 term, unique to UD theory 3. Cluster Scaling (equilibrium regime): Predicted: rc proportional to M1/3 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 M1/2 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 M1/3 Free fit: alpha = 0.341 +/- 0.042 (0.2sigma from 1/3), R^2 = 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 (U_D), not a particle. The self-interaction signature provides a smoking-gun test that particle dark matter models cannot accommodate.