Sub-bucket grouping with interaction distance bounds. The sub-buckets of two buckets A and B and the entities populating them are shown. Sub-bucket indices as per Eq. (110) are indicated in italic type. The arrows indicate: the range of possible A–B interactions, as per the bucket interaction distance bound , for the entity highlighted in red (grey, dotted); the range and the rounded range of possible interactions for sub-bucket 1 from bucket A (blue, dotted, and solid). In bucket B, the range of sub-buckets U_B,A(1) in reach of sub-bucket 1 from bucket A (Eq. (112)) are highlighted.