A sufficient certified payload allowance

For a declared released dimension $r_{\ast }$, rearranging (eq:fullthreshold) gives the sufficient range

For qubit payloads, one may choose $\ell$ with $2^{\ell }$ below this allowance.

Changing $d$ changes the model or requires an explicitly fixed larger code. For a single device intended to accept every state of a smaller subcode, certify the largest declared code once, then use a fixed isometric subcode embedding and its CPTP left inverse. Contractivity transfers the same error allowance. This is not repeated independent certification of arbitrary unannounced code spaces.