Vacuum Folding Dynamics: Emergent Dark Matter from Holographic Vacuum Screening — The Dual-Residue Mechanism and the Cosmic Coincidence

A previous paper in this series showed that the holographic screening factor κ = (l_P/R_H)^n reduces the VFD vacuum energy V(σ₀) ≈ 2.2×10⁻¹⁵ GeV⁴ to the observed cosmological constant Λ_obs ≈ 2.9×10⁻⁴⁷ GeV⁴ for the exponent n_Λ ≈ 0.848. The screening operates on the uniform component of the vacuum energy — the spatially homogeneous part of T_μν^(σ) that acts as dark energy. The present paper shows that in the presence of matter, the chameleon mechanism modifies the effective IR cutoff of the holographic bound from R_H to a density-dependent scale L_eff(ρ), splitting the holographic residue into two components: a uniform piece with exponent n_Λ = 0.848 (dark energy) and a matter-coupled piece with exponent n_DM = n_Λ − Δn (emergent dark matter). The shift Δn = n_Λ − n_DM = 0.0024 arises from the chameleon-induced replacement R_H → L_eff(ρ) in the Cohen–Kaplan–Nelson (CKN) bound combined with the saturated holographic renormalisation group (HRG) running, and is calculable from the VFD parameters m₀, σ₀, and α₀. The resulting cosmological dark-matter density ρ_DM^cosmo = Ω_DM ρ_crit is reproduced to within 1σ of Planck 2018, and the ratio Ω_DM/Ω_Λ ≈ 0.4 emerges as a natural consequence of Δn << n_Λ. The matter-coupled residue is not a particle; it is the gravitational imprint of the vacuum's holographic response to the baryonic density field. It is collisionless (self-interaction suppressed by ζ ~ 10⁻⁵²–10⁻⁴⁶ GeV), tracks the chameleon profile rather than the baryonic density directly, and produces an effective halo profile that we compute for a Milky Way-like galaxy. The model explains (i) the null results of 40 years of direct-detection experiments, (ii) the cosmic coincidence Ω_DM ~ Ω_Λ, (iii) the Bullet Cluster phenomenology (collisionless separation from baryons), and (iv) the qualitative shape of galactic rotation curves. Testable predictions include a specific relationship between the dark-matter fraction and the local baryonic density, deviations from NFW universality correlated with the chameleon screening radius, and a time-dependent Ω_DM/Ω_Λ ratio that tracks the holographic RG flow of n(μ).