Dark Matter as Sub-threshold Substrate Excitation: Physical Derivation of the Isothermal Halo Profile and Test against 150 SPARC Galaxies

Physical first-principles derivation of the pseudo-isothermal halo profile ρ(r) = ρ₀/(1+(r/rc)²) within the U-Cell Model (UCM). The universal cold parameter f_cold = √(2−π/2) ≈ 0.6551 is derived analytically from the substrate dispersion relation without free parameters. Tested against 150 SPARC galaxies (Li et al. 2020): median χ² = 0.73, 71% of fits with χ² < 2. The systematic deterioration at high masses is physically interpreted as the onset of baryonic feedback beyond the current UCM formulation.