Spacetime as a Dark-Matter Density Potential (SDMF Theory) — v1.9.5

This preprint presents the Spacetime Dark-Matter Field Model (SDMF), a continuous density-potential field ρ(x, t) whose spatial gradients generate gravitational acceleration and whose temporal variations encode energy flow. In the static weak-field limit SDMF reduces to ∇²ρ = 4πGρₘ and g = −∇ρ, recovering the Newtonian/PPN regime (γ = 1, c_g = c). Small perturbations satisfy the dispersion-free wave equation ∂²ₜ δρ − c²∇²δρ = 0. We test a universal response parameter α across 116 galaxies using a model-selection framework (universal-α vs. free-α) under pre-declared weak-field and quasi-static gates (ε_PN ≤ 10⁻³, τ_relax/τ_orb ≤ 10⁻²). The aggregated results yield ΔBIC_total ≈ +1103.9, providing decisive evidence in favor of a universal α. A standardized QC sweep further identifies 71 Core-Strict galaxies after excluding seven decisively negative cases (NEG8, interpreted as data-limited). The model is formulated via a sign-consistent scalar-field action including explicit matter coupling and optional coarse-grained flux. Dimensional consistency, variational structure, timescale diagnostics, and reproducibility (SDMF_Batch_Kit) are documented. Version 1.9.5 includes corrected linearization terms, clarified relaxation-length definitions, refined QC tables, and expanded appendices. SDMF provides a simple, testable, and observationally supported weak-gravity reinterpretation of spacetime as a density-potential field.