What converges

There is also a useful ordered subdomain. If the interaction attachment $y$ is strictly on the same chronological side of both cross-line endpoints, their possible nonzero wavefront covectors at $y$ lie in the same pointed causal cone. They cannot sum to zero. Removing the cross-lines leaves the inherited observable tree, where the forest argument rules out a remaining circulation. Such strictly ordered attachment domains are therefore covered by the admissible product calculation.

At the copied configuration $u,y,x$, the two cross-line orientations at $y$ instead permit cancellation. The preceding proof supplies no uniform estimate there.