Resources and implementation allowances

For a $q$-qubit clock, $r$ catalogue bits, $b$ report bits, $w_{\mathrm{lookup}}$ work qubits, and $p$-qubit payload registers, a conservative preallocated reserve is

The last qubit can implement the optional binary table probe. There are $n$ payload-register exchanges, $n$ report transmissions, and the declared finite local lookup/readout operations. The external reference and any external table storage are separately counted. Processing, readout, and the buffer occur before departure and are included in the experiment's finite duration.

For compatible complete channels, factorwise replacement and diamond-norm contraction give

Indeed, subtract the two compositions, replace one factor at a time, and use the triangle inequality. An event-probability bound follows only for an event in the compared complete output, including its arrival or failure flag if such a flag is claimed. This is finite channel accounting Watrous, not a field approximation or a hardware synthesis certificate.