Theorem: Copied: the evaluation set is not a quotient

For the frozen $W$, the coefficientwise vanishing space ${\mathcal{N}}_W[[\hslash ,\kappa ]]$ is not a two-sided ideal of ${\star }_H$, and its image $({\mathcal{N}}_W/{\mathcal{N}}_{\mathrm{sol}})[[\hslash ,\kappa ]]$ is not a two-sided ideal of ${\mathcal{E}}_H$. There is no unital $\mathbb{C}[[\hslash ,\kappa ]]$-algebra homomorphism from ${\mathcal{E}}_H$ killing the classes of all $L_q$, $q\in {C_c}^{\infty }(W)$, and preserving the inherited brackets, except one with $\hslash 1=0$ in its target. Coefficientwise vanishing on ${\mathcal{C}}_W$ is not preserved by every admissible ordering transport.

Proof. XIII-A's non-ideal theorem, its corollary, and its rank-one ordering calculation, copied as Input statement input:XIIIAD. The mechanism is (eq:commutator): the formal scalar $i\hslash C(q,h)1$ with $C(q,h)>0$ does not vanish on ${\mathcal{C}}_W$, which contains the zero configuration.