Proposition: Classical principal-symbol comparison

On the compact-test regular polynomial algebra, reduction modulo $\hslash$ returns the classical commuting polynomial. All Wick-ordering corrections are of positive $\hslash$-degree. Consequently, any later admission of the complete frozen lapse with this principal symbol must recover (eq:n1)–(eq:n2), including their rod term and the absence of $Y_2$.

Proof. Each contraction carries one factor of $\hslash$. A finite polynomial has only finitely many contractions, and setting $\hslash =0$ removes all of them. The resulting commutative symbol is the chosen classical polynomial.

The lapse coefficients are already fixed by the classical composition calculation. Their absence or replacement cannot be supplied by a positive-order quantum correction.