What these tests do not prove

These are sufficient tests for the specified operations. An intersection in an unverified upper bound does not establish an intersection in the actual wavefront set. Failure of a sufficient test does not, by itself, prove that no alternative construction exists BDHintro.

Nor do these tests alone select extensions across singular diagonals or normalize retarded quantum products. Such extension and normalization problems are separate in perturbative constructions BDF.