What is not proved

The finite circuit is independently constructed below. It is not identified with a circuit obtained by extracting the external proof's order trial, deferred filters, and amplification construction.

There are therefore two different tasks:

Finite endpoint certificate.

A specified allowed circuit, on a specified input, has only correct outputs and has a specified finite resource ledger. This task is completed here.

Source-construction instance certificate.

A specified circuit is the output of the external construction's actual uniform generator, with all of that construction's subroutines and resource bounds checked. This stronger identification is not supplied.

All-input family verification.

One generator and one polynomial work for every input length and every integer of that length. This remains unverified in the present manuscript.

A finite certificate cannot, by itself, bridge the second or third gap.