Formal order is not a numerical remainder estimate

A nonzero ${\hslash }^0$ residual cannot be canceled by a correction divisible by $\hslash$. This follows immediately from coefficientwise formal equality and applies to the classical cutoff residual of XX-E.

Reduction modulo $\hslash$, whenever the quantum insertion is admitted with the chosen symbol, recovers (eq:O). The original one-rod term survives, and $Y_2$ is absent for ${\partial }_i{N}_0=0$.

This is a formal classical-symbol statement, not a pseudodifferential principal-symbol theorem, an expectation-value limit, or a numerical $O({\hslash }^2)$ estimate.

Finite self-contraction of a quadratic regular polynomial terminates algebraically. That fact does not bound the missing interacting coefficient, its complete quantum remainder, or a regulator-removal family.