An exact off-shell-shadow incompatibility

This proposition has deliberately narrow quantifiers. It excludes an exact off-shell shadow of all old generators. It does not exclude an off-shell representative chosen before an on-shell quotient, nor admission formulated as Definition def:interface.

Thus the phrase “$Q({\mathcal{B}}_f)={\mathcal{B}}_f$ as a classical functional” must specify its configuration space. An exact off-shell representative is meaningful; it cannot be the unrestricted classical-symbol interpretation of XI-B's already-quotiented algebra.