Summary of binarity criteria. Top row: AB systems with both components successfully matched to Gaia sources (Table D.1). Bottom row: All possible pairs from AB-member candidate sets, excluding those in the top row. The left panels illustrate angular separation as a function of parallax, with limits from Eq. (12) (s < 1 pc) as a hatched grey region. The centre panels show parallax consistency; dashed black lines mark the criteria from Eq. (11). The right panels show the total orbital velocity difference versus projected separation (log-log scale), with theoretical ΔV_tot values from Eq. (13) for M_tot = 3, 4, and 5 M_⊙. Crosses, circles, and stars represent pairs that only satisfy one, two, or three binary conditions, respectively. Well-known bona fide wide binaries 16 Cygni, HD 80806/07, HIP 99727/29, and HAT-P-4 are shown as pink, orange, green, and purple diamonds, respectively. Genuine wide binary candidates are expected to lie within the white area of each plot. KIC 6501237 and KIC 10094545, highlighted as blue and orange stars, respectively, are identified as likely genuine wide binaries.