Statistical properties of the GMP selection. Left: level of contamination of false positives (objects with a detection of multiple peaks that are not projected pairs) as a function of the FMP values in a sample of dense stellar fields for G <  20.5. No false positives are found for FMP ≥ 8, where we plot 90% upper limits, i.e., the levels that would correspond to 2.3 false positives. Right: fraction of recovered projected pairs as a function of separation (δ) in arcseconds. The red histogram shows the pairs that are not recovered, which dominate the counts at δ <  0.15″ and are very rare at δ >  0.20″. The green histogram reports the fraction of recovered isolated objects that correspond to single entries in the Gaia source catalog, and the blue histogram shows the GMP-selected objects that have nearby companions in the catalog. The combination of these two GMP populations is show by the black line.