Apparent Dark Halos as Residual Geometry from the Complete Virial Theorem

What if the apparent dark halo is neither an unobserved mass component nor an ad hoc modified force law, but the radial structure of a bounded gravitational residual slope? Derived from the non-stationary term of the complete scalar Virial Theorem (1/2Ï = 2K + W), this paper recasts the observed acceleration excess qgeom = gobs - gbar into its natural inertial variable: the radial slope mᵣₑₛ(R) = qgeom(R)/R. Key Results & Observational Audits: Universal Empirical Ceiling: Across resolved rotation curves in the SPARC and THINGS samples, mᵣₑₛ in the transition region does not grow without limit, but approaches a sharp upper bound at mceiling ≈ 675--678 (km/s)²/kpc². Physical Scale Organization: The transition slope mₜᵣₐₙₛ organizes the physical extent of the residual halo (R₈₀ʳᵉˢ): lower transition slopes correspond to broad, extended residual halos, whereas higher slopes correspond to compact structures. Exact Multi-Channel Split ($19/15$): Non-relativistic massive tracers sample the scalar dynamical pull (Adyn = 1), whereas light probes the transverse tidal projection on the Sachs screen. Isotropic angular averaging of the symmetric trace-free tensor fixes the optical excess to Aₗₑₙₛ = 1 + 4/15 = 19/15 ≈ 1.2667. Observational Confirmation: Stacked weak-lensing profiles from the KiDS survey yield Aₗₑₙₛ = 1.2674 ± 0.0315, landing directly on the parameter-free theoretical prediction. The reproducibility package includes all LaTeX source files, reduced datasets, execution scripts, and permutation-based null tests required to regenerate every figure and table in the manuscript.