Computational Audit and Identifiability Limits for the SPARC Radial Acceleration Relation: Data, Code, and QA/QC Protocol
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We present a comprehensive computational audit of the identifiability limits for structural corrections to the Radial Acceleration Relation (RAR) using a canonical subset of the SPARC database ($N=126$). Rather than proposing a new dynamical law, we establish the observational conditions under which such a law would be mathematically recoverable. Enforcing strict computational reproducibility, we programmatically verify 86 distinct statistical anchors against our data pipeline, ensuring zero drift. We resolve three critical methodological controls that heavily influence RAR interpretations. First, we isolate a $-0.39$ dex residual offset localized entirely within 8 galaxies in the lowest-quality observational tier ($Q=3$). Spatial profiling confirms this offset exhibits an outer asymptote and does not decay to zero, decisively ruling out beam smearing or resolution artifacts as the primary driver. Second, we decouple the architectural limits of the dataset into three distinct, independent constraints: the residual floor ($M_3 = 0.1083$ dex), the absorbable budget ($M_0 - M_3 = 0.0777$ dex), and the analytic error floor. Finally, we provide a 12-cell protocol grid to reconcile Leave-One-Out (LOO) Mean Squared Prediction Error (MSPE) ratios. We demonstrate that reported structural-dynamical couplings must be evaluated with strict adherence to residual definitions (median vs. mean) and baseline denominators to avoid adopting labeling artifacts as new physics.



