Theorem: Restriction release

For every nonempty fixed $W$ satisfying (eq:W):

1. ${\mathcal{C}}_W$ is a nonempty proper classical shell subclass. Under {(UCP${}_W$)}, the full displayed coefficient satisfies ${\Delta }_{\xi }\mathcal{O}{|}_{{\mathcal{C}}_W}=0$ for every $\xi \in {\mathfrak{g}}_W$.

2. There are compact regular smearings $q,h$ for which $[L_q,G_h{]}_{{\star }_H}=i\hslash C(q,h)1$ with $C(q,h)>0$. Therefore the naive coefficientwise restriction quotient is incompatible with the unchanged inherited brackets and faithful formal scalar inclusion.

3. An admissible smooth ordering difference satisfies ${\alpha }_d({L_q}^2)={L_q}^2+\hslash C(q,h{)}^2$. Coefficientwise vanishing on ${\mathcal{C}}_W$ is not universally ordering-preserved.

4. For the copied detecting observation data, the XII-F witness lies outside ${\mathcal{C}}_{\mathrm{def}}(W;f,g)$ and its full-shell remainder class is nonzero. No quantum anomaly or general completion no-go is inferred.

The release is evaluation-only. A quantum domain is not supplied.

Proof. Proposition prop:inclusion, Corollary cor:proper, Theorem thm:classical, Proposition prop:commutator, Lemma lem:compact-pair, Theorem thm:nonideal, Corollary cor:noquotient, Theorem thm:ordering, and the copied witness (eq:copied-witness).