Complete sum before a verdict

At any candidate singular scale, the coefficient must be collected from all contributing rows, tensor components, root terms, and vertex terms before cancellation or divergence is declared.

The specialization $f=0,F(b)=b^0$ is not admissible here: the advanced root condition gives $F=0$ when $f=0$. It can only be a separately declared diagnostic model, not a detecting test for this application.

A moving-frequency witness is also insufficient. For example,

gives $A({\Phi }_{\omega })=-i\omega$, although the constant family $t_{\delta }=A$ converges strongly. The moving tests are not a bounded test family.