The Structure of Residuals in Galaxy Rotation Curve Modeling: A Second-Order Out-of-Sample Analysis

This work presents a second-order analysis of residuals in galaxy rotation curve modeling, extending the global phenomenological model introduced in Paper A (DOI: 10.5281/zenodo.19386393). Using strict galaxy-level Monte Carlo Cross-Validation (MCCV), we investigate whether deviations between observed and predicted rotational velocities represent stochastic noise or structured physical signals. The analysis is performed on the SPARC dataset and focuses on residual dependencies across three key variables: galactocentric radius, surface brightness (as a proxy for baryonic surface density), and baryonic acceleration. Key findings: - Residuals exhibit clear radial structure, transitioning from high-variance inner regions to more stable outer regions- Strong anti-correlation between residuals and surface brightness (Spearman ρ = −0.445, p < 10^-150)- Systematic dependence on baryonic acceleration, with increased variance in low-acceleration regimes- Consistent patterns across all Monte Carlo cross-validation splits, confirming robustness under strict out-of-sample evaluation These results demonstrate that residuals are not dominated by random noise but encode physically meaningful structure related to local galaxy properties. This work provides a data-driven framework for analyzing second-order structure in galaxy dynamics and serves as a bridge toward unified nonlinear modeling approaches explored in subsequent work (Paper B). CONTENTS:- Full manuscript (PDF)- Figures used in the analysis AUTHOR:Krzysztof TylecIndependent Researcher --- RESEARCH CONTEXT: This work is part of a structured research sequence:Paper A → global model validation (DOI: 10.5281/zenodo.19386393)