Smooth reordering is still a domain-sensitive operation

If $W^{\prime }$ has the same canonical part and $W^{\prime }-W=d$ is a smooth real symmetric bisolution, compact Wick coordinates change by

For the quadratic insertion, this is exactly one contraction.

For the native insertion the change requires the noncompact pairing

Smoothness alone does not ensure its existence. Proposition prop:IRfailure supplies the relevant counterexample mechanism. Hence compact ordering transport does not automatically give native ordering transport.

Likewise, a defect can be repaired by a declared normalization class only when the actual defect lies in the actual image of its normalization map. Finite tests or membership in an image closure are not that statement CheungXVIIIA (locator :ward). No complete physical counterterm image is constructed here.