Distributions of galaxy–galaxy pair properties. Left panel shows the projected separation r_p, middle panel shows the difference in line-of-sight velocity Δv, and right panel shows the isolation criterion ρ. In all panels, the observed galaxy pairs are highlighted as a grey filled histogram, while the mock-observed simulation data are shown as lines for the base (blue dashed) and full (red solid) sample, as well as the two randomized test samples with shuffled velocities but retained positions (green dotted) and randomized positions (yellow dotted).