Dark Matter as Convergence-Induced Substrate Wrinkling in the U-Cell Model

We derive the dark matter mechanism in the U-Cell Model (UCM) from the substrate wave equation. The unique gravity–matter coupling L_cov, evaluated in the convergent Gullstrand–Painlevé background flow, yields a parametric instability: vacuum fluctuations of the transverse sector are amplified wherever the substrate converges toward mass. Three results follow without free parameters: (i) azimuthal compression forces the wrinkle wavevectors radial (k ∥ r̂), from which the isothermal equation of state P = ρσ² follows as a theorem (not a postulate); (ii) the compression-to-redistribution ratio Γ_comp/Γ_redist = √2 is constant at all radii, explaining why dark matter halos form on all mass scales; (iii) the isothermal density profile ρ ∝ 1/(1+(r/r_c)²) with flat rotation curves emerges from hydrostatic equilibrium. The cold parameter f_cold = √(2 − π/2) is reinterpreted as the longitudinal-to-transverse conversion efficiency: 21.5% of inflow kinetic energy becomes dark matter. Combined with the companion paper on Ω_Λ = 0.6834, the UCM accounts for 95% of the cosmic energy budget (excluding baryons) from a single substrate constant. UCM preprint series, Paper 43. Companion to Paper 1 (Ω_Λ derivation, Zenodo 10.5281/zenodo.19387201).