Smeared coefficients form a family

Thus root attachment is no longer left at an unspecified product obstruction under the stated $Z_2$ premise. What remains unresolved is the selection of the extension tuple and the normalization of the resulting coefficient.

The family $C_{\bar{p}}$ is not asserted to be independent of its extension constants. Its differences are diagonal contact contributions propagated through the root. Locality of a subtraction in $r$ does not make $a_{f,g}[\varphi ]$, or the final coefficient as a functional of the original fields, local.

No identification with ordinary bulk gravitational counterterms is proved.