Remark: What the witness does not prove

A coordinate gap does not by itself prove a nonzero total smeared on-shell response for every fixed $f,g$. The test can miss it, a resulting compact test can be an equation zero, and the switch contribution in (eq:defectclass) can also be present. If an excluded edge parameter happens to lie in an already chosen interaction plateau, the switch term vanishes and the coordinate term is isolated. No edge plateau is assumed to exist for every $g$.