On the Regime Dependence of the Radial Acceleration Relation: A Reproducible Stress Test with SPARC and Independent Dwarf Galaxy Data

Description This repository contains the fully reproducible analysis pipeline and data products for the study: "On the Regime Dependence of the Radial Acceleration Relation: A Reproducible Stress Test with SPARC and Independent Dwarf Galaxy Data". The Radial Acceleration Relation (RAR) establishes a tight empirical connection between the baryonic acceleration (g_bar) and observed centripetal acceleration (g_obs) in rotationally supported galaxies. This work presents a rigorous statistical stress test evaluating whether the RAR can be considered an exact, universal one-parameter dynamical law, or if its residual scatter contains systematic information regarding internal galaxy structure and dynamical regimes. Using the SPARC dataset as the primary sample (3,318 radial points from 169 galaxies) and an independent dwarf galaxy sample from LITTLE THINGS (877 radial points from 26 galaxies) for external validation , the analysis subjects the standard RAR formulation to a comprehensive suite of falsification-oriented statistical checks. Key Findings: Exclusion of the Exact-Law Hypothesis: An uncertainty-weighted fit utilizing observational velocity errors yields a reduced chi-squared value of χ²_red = 202.4640. This deviation from unity by more than two orders of magnitude statistically rules out the RAR as an exact one-parameter law at the level of quoted observational uncertainties, implying the presence of intrinsic scatter or missing physical degrees of freedom. Significant Structure Dependence: Multivariate regression analysis demonstrates that RAR residuals correlate significantly with the internal baryonic structure of galaxies, quantified via a radial structural spread metric. This structural correlation retains a high independent explanatory power (p = 2.734025 x 10^-15) , even after strictly controlling for global scale variables such as maximum rotation velocity, radial extent, surface brightness, and mean baryonic acceleration. Robustness & Limitations: The structure-residual signal is shown to be highly resilient, persisting under shuffle null tests, leave-one-out validation, noise injection up to 20%, and alternative RAR functional forms. However, outlier-removal tests reveal that the effect is concentrated within high-leverage systems rather than being uniformly distributed across the entire galaxy population. Cross-Dataset Validation: Cross-comparison shows that while LITTLE THINGS and SPARC dwarf galaxies occupy statistically consistent observed acceleration scales, they differ significantly in structural and dynamical extent. The lack of a statistically significant internal structure correlation within the dwarf-only sample indicates that the observed deviations are not a simple feature of low-mass systems, but manifest across a broader range of structural regimes. Ultimately, the study concludes that while the RAR serves as an exceptional empirical approximation, its residuals encode structured, regime-dependent information that any viable framework for galaxy dynamics must reproduce. Repository Structure & Reproducible Pipeline: All data products, processed tables, figures, and analysis scripts are organized into a fully scripted, automated pipeline. The entire suite of figures and statistical tables presented in the manuscript can be fully regenerated from the source data using the provided scripts within the project environment (RAR_REVIEWER_STRESS_TEST).