Unified Spacetime Fluid Cosmology IV: Emergent CDM-like Dynamics and Its Finite-Wavelength Limit in a Next-Door-Spacetime Realization of USF

Papers I–III of the Unified Spacetime Fluid (USF) program defined a late-time background deformation, a growth-sector response, and a falsifiable observational identity. Here we ask whether the same spacetime dynamics can realize a CDM-like gravitational matter response without an independently added dark-matter component. In an effective next-door-spacetime (NDS) realization, a neighboring four-dimensional relative metric supplies a time-dependent canonical inertia, while a critical linear-dilaton transfer supplies a shared long-range gravitational zero mode. The NDS point-particle action yields the momentum-response rate XQ = (ln Qp)N, which plays the role of Paper II’s friction term. We show that this response is conservative: the sector contains an exactly conserved dust variable, admits a Hamiltonian–Vlasov description with incompressible phase-space flow, and its finite-dispersion Jeans hierarchy loses the explicit XQ term after canonical rescaling. In the limit of vanishing relative-geometry rates the sector reduces to the standard pressureless continuity–Euler–Poisson system. At finite wavenumber, the gravity received by visible matter from the NDS component is filtered on an effective smoothing length ℓ that the present construction does not fix; in our halo-response scan an approximately CDM-like galactic response is reached only for ℓ of a few h−1 kpc or less, well below the representative benchmark ℓ ≃ 0.11 h−1 Mpc, so galaxy-scale dynamics directly constrain this remaining scale. A minimal effective operator reproduces the pre-existing reduced source law without a new fitted amplitude, and a late-time fixed-point realization gives fσ8(z = 0.07) ≃ 0.432, consistent with DESI peculiar-velocity data. We claim neither a unique microscopic completion nor a statistical preference over ΛCDM.