Proposition: Renaming inaccessible access can change the question

Recovery error is not invariant under a comparison that moves an inaccessible diary-bearing factor into the accessible output.

Proof. For $V_{\mathrm{keep}}$, the declared accessible factor $R$ has error $1-d^{-2}$. If $B$ is instead made accessible, its channel is the identity and its error is zero. A comparison that swaps these access roles therefore changes the recovery question. It is not one of the local product comparisons in Definition def:access with the declared roles fixed.