A First-Pass SPARC Test of Orthogonal Defect Residuals in the Radial Acceleration Relation

This note reports a first-pass empirical test of the TSCT Orthogonal Defect Calculus using SPARC galaxy rotation-curve data (175 galaxies, 3,389 points). The test asks whether residuals from the primitive TSCT radial acceleration relation are random or grow in systems where the primitive rendered-screen conditions fail. Primitive law: g_obs = g_bar/[1-exp(-√(g_bar/a_H))], a_H = cH_0/(2π). The ODC predicts residuals δg_RAR ~ O(‖Q_t Δ‖, ‖Q_θ Δ‖, ‖Q_σ Δ‖, ‖Q_env Δ‖, ‖Q_tens Δ‖). Results (Υ_disk=0.6): clean primitive disk galaxies have RMS residuals of 0.117 dex (all radii) and 0.088 dex (R>3 kpc). Non-clean systems remain broader at 0.217 and 0.156 dex respectively. The clean/non-clean separation ratio is 1.85×. Large residuals (|Δ|>0.20 dex) are 7.1× more common in non-clean systems at R>3 kpc. The flag-score correlation is statistically significant (p≈3.9×10⁻⁶). Removing inner radii tightens clean-sample scatter by 25%, consistent with D6's prediction that the primitive law lives in the outer settled screen. Status: Tier 2 preliminary empirical support. RAR residuals behave as structured failed-screen diagnostics, not random point noise.