Fit results illustrating the ability of galaxies to satisfy the MOND limit condition |ε|≪1. Top: Histograms of the radius R_mid for galaxies where we did (blue) and did not (red) find a fit with the restriction |ε|< 0.1. We see that only smaller galaxies tend to be able to satisfy the condition |ε|< 0.1, consistent with the simple estimate ε_* ≳ 0.1 + 0.4 ⋅ (r/18 kpc − 1) from Eq. A.19. Bottom: Minimum possible |ε| for the galaxies where we could find no fit with |ε|< 0.1. We see that many only barely fail to satisfy |ε|< 0.1, and we can get a fit for almost all galaxies with |ε|< 0.4.