Quantum and microlocal boundaries

A classical density identity is not a quantum Master Ward identity. It neither supplies time-ordered products nor classifies their renormalization freedom. The general retarded-product and locally covariant frameworks retain their own admission hypotheses DF,BFR.

For a smooth multiplier $g$,

with local equality where $g\ne 0$, by multiplication with the smooth reciprocal there. That elementary observation does not construct the retarded quantum coefficient or remove the finite-initial-surface singularities discussed in the comparison records CheungPrepared,CheungProductTracks.

In particular:

• VII-B, VII-C, VII-D, and VII-I concern separate sharp admission, product, finite-part, and finite-width questions. The present intertwiner does not select their product domains, remove a logarithmic triple, or turn a finite part into an algebra.

• VII-H's free susceptibility is not $C_2[g]$ and is not the inherited characteristic coefficient.

• IX-A through IX-E, X-G, and XI-G address different carriers, variational questions, or free-shell classes. No missing nonlocal one-loop product is defined here.

The quantum certificate therefore remains RG-open. The finite table in Section sec:table is not an evaluated quantum response matrix. Finite linear algebra cannot define a missing distributional product.