Detection completeness for HD 112810. Shaded rows show completeness for radial velocity observations (blue), HIPPARCOS-Gaia proper motion analysis (pink), and high-contrast imaging observations (green) along with the debris belt positions (gray). Shaded regions indicate the mass vs separation contours at which 10%, 50%, 90% and 99% of companions would be detectable with in-hand data, as described in Sects. 6.3, 6.4 and 6.1 respectively. The inner and outer belt positions are derived from the SED fit and SPHERE modeling respectively. Planetary mass companions and small brown dwarfs at intermediate and wide separations are largely ruled out from the proper motion and imaging constraints. The radial velocity constraints are weaker, ruling out only massive stellar companions at short periods.