Bulk agreement and overlap consistency

For a proposed coefficient of one partial binary product, relevant domains inside ${\mathcal{P}}_{\Sigma }\otimes {\mathcal{P}}_{\Sigma }$ include

The last domain carries the prescribed old Wick coefficient. Lemma lem:gluing shows exactly where overlap checks are required. Calling the left and right maps by different names does not permit them to disagree on a common actual pair.

The lemma is algebraic. Continuity of a glued map remains a separate requirement.