An off-locus reference does not select its extension

For example,

as follows by pairing with a test and differentiating $q\psi (q)$ at zero. Its two summands are individually nonzero. A presentation-degree projection that breaks this relation does not automatically descend.

Lemma lem:descent and Proposition prop:extension explain why an off-locus reference, finite normal-jet array, or descent criterion is not the missing full characteristic operation. They do not prove that every possible operation fails.