Taking the diagram for an operator R pq â † p âq , we can connect the unlinked Fermion lines to create its trace diagram. If this diagram is connected, there exists a walk which visits every Fermion line exactly once, referred to as an Euler circuit. Because a walk of implied proximity only terminates upon reaching a node which has no unused outgoing Fermion lines anymore, it must be an Euler circuit for connected trace diagrams. Taking p as the arbitrary starting node of this walk, it is possible to arrange the Euler circuit such that the Fermion line connecting p and q is the last Fermion line in the walk. Cutting this line apart to regenerate the diagram for R pq â † p âq reveals a chain of implied proximity between p and q for any connected diagram. Importantly, it thus holds that: lim d(p,q)→∞ R pq = 0 (B2)