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 by AIC (ΔAIC = +2. 6), MOND is preferred in 85%. The logarithmic model's contribution is not superior goodness-of-fit but a confirmed scaling prediction and consistency with stellar population constraints. 2. Scaling relation. Using baryonic masses computed with fixed mass-to-light ratios (Υdisk = 0. 5, Υbulge = 0. 7) independent of the fitting procedure, the coupling parameter scales as γ ∝ Mbar^α with α = 0. 485 ± 0. 030, consistent with the geometric prediction α = 0. 50 within 0. 5σ. Bootstrap resampling (10⁴ iterations) yields 68% CI = 0. 457, 0. 512 and 95% CI = 0. 431, 0. 540, both containing the predicted value. The result is stable across mass-to-light ratio assumptions (α ∈ 0. 467, 0. 504 for Υdisk ∈ 0. 3, 0. 8). 3. Scale length. The fitted r₀ ≈ 0. 6 kpc shows no significant correlation with baryonic mass (Spearman ρ = 0. 149), galaxy extent (ρ = 0. 108), or outer acceleration (ρ = −0. 083), suggesting it represents a structural property of the velocity correction rather than a scaling of the baryonic distribution. 4. Limitations. Individual gas-dominated dwarf galaxies (e. g. , DDO 154) remain challenging. The high-mass regime shows a flattened local slope (αₗocal ≈ 0. 37), consistent with a mass-dependent deviation from the global scaling. No comparison with NFW halo fits is included. Methodology. Fitting uses Nelder-Mead minimization with Gaussian priors on stellar mass-to-light ratios. Quality cuts require ≥5 data points, successful convergence, and γ > 10 km²/s². MOND comparison uses the RAR interpolation function with free a₀. All analysis code is in Python (NumPy, SciPy). Multi-agent analysis. The analysis was independently cross-checked using multiple large language model systems to detect logical inconsistencies, pipeline errors, and methodological issues. Related work: - TKWC Nodes 734–735: doi: 10. 5281/zenodo. 18650668 - Topological Screening of Dark Energy: doi: 10. 5281/zenodo. 18422868 The Entropy Sink: doi: 10. 5281/zenodo. 18479788