What a positive finite-time certificate must contain

Theorem thm:regulator makes the following procedure mathematically well posed for another frozen realization:

1. freeze the code, preparation, array, couplings, and packet algebra;

2. select $T,b,m,\Delta$ before computing a certificate;

3. compute all complementary logical matrix units of the finite prepared isometry;

4. certify a residual state or a complete decoder;

5. apply Theorem thm:certificate.

A code dimension $d$ is fixed before the Choi conversion.