Distribution of the logarithmic χ² improvement for binary models. In each panel, blue lines denote astrometric binary stars classified by the NSS catalog, while orange lines represent SB1 binaries. In the left panel, the dashed lines are derived from the original DR3 source catalog parallax errors, while solid lines show results after error inflation following the model of El-Badry (2025). In the right panel, the dashed lines use parallaxes from the DR3 source catalog, while solid lines use parallaxes from the NSS catalog, which incorporate binary orbital solutions in their parallax estimates.