Top-down screening starts with the high-order nodes on the PIE-DAG and progressively extends this to lowerorder nodes. This is illustrated at the MBE(3) level in Fig. (a), for an example consisting of non-overlapping primary fragments S primary = {A, B, C, D}. The screening procedure is first applied to the trimers ABC, ABD, ACD, and BCD. Terms that meet the screening criteria serve as initial nodes added to the PIE-DAG, and in this example we assume (for illustrative purposes) that only ABC, ACD, and BCD meet the screening criteria, not ABD. However, the fact that ABD is negligible does not guarantee that any of AB, AD, or BD is negligible, so each of these (and all other dimers) need to be tested. (Again for the sake of illustration, we assume in Fig. that AD and BD are negligible but that AB is not.) Lastly, all one-body (primary) terms are added to the graph, ensuring that it contains all atoms.