Remark: Normal ordering and quantum corrections

Changing a prescription only in positive powers of $\hslash$ cannot change the contradiction in the classical coefficient. Allowing a new order-${\hslash }^0$ boundary term changes the off-shell insertion unless that term vanishes as a functional. Theorem thm:main does not prohibit changing the observable; it prohibits calling such a change an off-shell quantization of the unchanged observable under Definition def:normalization.