The loss ledger

The restriction retains one conditional classical identity. It does not retain unqualified full-shell invariance of the specified coefficient. Parameters outside the declared compact region, or observations and switches violating the uniform support hypothesis, are not covered by that identity. The free differential is retained on the inherited carrier, but a physical or interacting BRST class of $\mathcal{O}$ is not constructed.

The ordinary restriction quotient remains available as a vector-space or pointwise classical construction. Calling it a restricted quantum quotient would conflict with the explicit commutator theorem. The inherited product itself has not failed: its incompatibility with the additional proposed quotient has been proved.