Remark: The two ledgers

In the oracle ledger, a query is a primitive and the circuit cost includes $q$. In the explicit-table construction, one may instead charge

ordinary gates, extra scratch, table provisioning, and physical routing. These are alternative descriptions of implementation cost; one must not charge both a primitive query and its internal gates as independent operations.

Neither polynomial address length nor polynomial query count bounds the cost of constructing $f$ from an ordinary target description. A general table can have exponentially many entries in $m$.