VII-H is a comparison, not a premise

The supplied prospectus describes VII-H as a free massless Minkowski Wick-square susceptibility, with contact ambiguity $\mathbb{R}\hslash {\delta }_0$ and a prescription-independent pairing

under that construction's hypotheses CheungDossier. This is documentary comparison material only. Its full construction is not assumed here.

The present coefficient is a massive scalar-linear relational response, and its variance coefficient is

It is not VII-H's pairing and is not an inherited gravitational characteristic coefficient. Even if both quantities scale with an effective Planck parameter, that common scaling does not identify their domains, kernels, states, or observables.

No counterterm is introduced in this proof. More generally, a local distributional correction and its propagated image are different objects: for a retarded inverse, propagation can enlarge support. Nothing here replaces the propagated image by the local contact itself.