Tree-based distributed termination detection for P = 7 ranks arranged in a complete binary tree. (a) Phase 1: each rank accumulates a local particle-count delta (Δ) and periodically sends it to its parent; interior nodes aggregate their children’s deltas with their own before forwarding. When the root’s global counter reaches zero, Phase 2 is triggered. (b) Phase 2: the root broadcasts a verify signal down the tree (dashed red arrows). Every rank inspects its local state and reports whether it holds zero particles and has no outstanding transfers. Confirmations propagate back up (solid green arrows). If all ranks confirm, the simulation terminates; otherwise, the counter continues to be tracked.