The Mass-Size Plane Does Not Resolve the Identifiability Limit of the Radial Acceleration Relation

Abstract

We present a 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. We resolve three methodological controls that heavily influence RAR interpretations. First, we isolate a -0.39 dex residual offset between the eight galaxies in the lowest-quality observational tier (Q = 3, mean -0.433 dex) and the remaining 118 (mean -0.040 dex). Of five predictions that beam smearing must satisfy, four fail: the radial profile plateaus at -0.331 +/- 0.028 dex rather than decaying to zero, and the offset does not scale with the number of resolution elements across a curve. Beam smearing is disfavoured as the primary driver, though the offset remains a data-quality signature rather than a physical one -- Q = 3 in SPARC flags major asymmetries and strong non-circular motions, conditions under which a rotation curve does not trace the equilibrium potential. Second, we decouple the architectural limits of the dataset into three independently measured quantities -- the no-model point scatter (sigma_M0 = 0.1860 dex), the residual floor after free per-galaxy intercepts (sigma_M3 = 0.1058 dex), and the propagated analytic error floor -- together with the absorbable budget sqrt(sigma_M0^2 - sigma_M3^2) = 0.1530 dex derived from the first two. Finally, we provide an 8-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, signed vs. absolute) and baseline denominators to avoid adopting labeling artifacts as new physics.