What the certificate says about operational capacity

The ordinary coding theorem and the one-use ensemble give the unconditional lower bound

The upper endpoint in (eq:final-interval) is an upper bound for the one-use Holevo information. It is not presented as an independently verified upper bound for $C({\mathcal{A}}_{1/2,1/4})$.

If the external repeated-use theorem is independently established, then Proposition prop:conditional transfers the same interval to $C$. That is an additional theorem input, not a consequence of evaluating one scalar maximum.