Distribution of different types of cluster pairs and sample category. The blue bars represent the total number of pairs in each type of cluster pair, the orange bars indicate those in the full sample, and the red bars correspond to the golden sample. The numbers above each bar indicate the total number of pairs in that subcategory. Cluster pair types include primordial binary clusters (PBCs), tidal capture or resonant trapping binary clusters (TBCs), and hyperbolic encounter pairs (HEPs), as defined in Section 4.2.