The logarithm is not a limit obstruction here

VII-C's named word is

For its mollified sharp kernels, its fully contracted ${\hslash }^3$ coefficient has a nonzero logarithmic term for suitable tests. That theorem is about a quantum multiplet product, not the seminorms of $d_{j,\epsilon }$. X-D neither constructs that word nor subtracts its reflected light-ray coefficient.

VII-C's bulk representation, after integration by parts, and X-A's multiplied-equation kernel carry a boundary delta; X-D's limit kernel does not. This identifies the candidate and does not repair VII-C.

VII-C itself excludes only the named normal-topology extension with the stated admission and product requirements. An algebra omitting $W_g$, or a different construction not meeting those requirements, is outside that conclusion. The present scalar-only limit is such a smaller object. Therefore VII-C does not apply and is not contradicted.