Logarithmic Velocity Correction in Galaxy Rotation Curves: An Empirical Test with 151 SPARC Galaxies

We present an empirical test of a logarithmic velocity correction model using 151 galaxy rotation curves from the SPARC database (Lelli, McGaugh & Schombert 2016). Model. The observed rotation velocity is modeled as V²(r) = V²_bar(r) + γ·ln(r/r₀), where V_bar is the baryonic contribution computed from 3.6 μm photometry, γ is a coupling parameter, and r₀ is a characteristic scale length. This velocity ansatz corresponds to an effective potential Φ_eff ∝ [ln(r/r₀)]² and a modified isothermal density profile ρ ∝ [ln(r/r₀)+1]/r². The model is motivated by the Topological Knot-Web Cosmology (TKWC) framework (Feshter 2025, doi:10.5281/zenodo.18650668). Principal results: 1. Statistical performance. Both models…