Remark: Local source symbol versus response symbol

Equation (eq:Qsymbol) is a symbol of the local operator ${\mathsf{Q}}_G$, on the diagonal operator relation. It is not the symbol of

and still less the common symbol of the coordinate and scalar response legs after their cross-line composition.

In the untested kernel, the residual metric variable $z$ remains present in the local source incidence. Testing it against $G$ is not an internal-symbol theorem in all variables.