Geometric Origin of Dark Matter: First-Principles Relaxation Dynamics from the De Sitter Causal Horizon

An Extension to Papers I–IV on Holographic UV/IR Coupling. We derive the relaxation dynamics of holographic supersaturation from first principles, establishing that the projection efficiency π/e for the D=2→D=3 dimensional transition is uniquely determined by self-consistent convergence of two independent derivation pathways for Ω_DM. The relaxation rate γ=2 is an algebraic consequence of de Sitter geometry. Three observational anomalies—the +2.75σ excess in H(z) at z≈0.93 (DESI DR2), the ~11% suppression of fσ8 at z≈0.97 (eBOSS DR16), and Ω_Λ≈0.685—are unified as imprints of the same supersaturation event.