A4: ordering acts on functionals

The hypothesis $L_q(u)\ne 0$ is essential. Choosing a rank-one bisolution built from $u\in {\mathcal{C}}_W$ would give zero in this particular test. The theorem proves failure for an explicitly allowed ordering change; it does not assert failure for every smooth difference.

No point of ${\mathcal{C}}_W$ has been transformed by ${\alpha }_d$. The failed statement is preservation of a space of functional symbols. In contrast, preservation of the complete free-shell ideal by the same ordering maps remains an inherited theorem. The rank-one solution lies outside the newly imposed subclass, exactly where its constraint contraction can detect it.