A finite verification programme

The proposal to check finite graphs with $N\le 20$ and one exceptional block remains a programme, not an execution claim. An exhaustive computation must specify:

1. a finite catalogue of graphs, schedules, horizons, and register interfaces;

2. a finite exact gate/instrument library, or a symbolic parameterization with proved algebraic coverage;

3. complete outcomes, failure flags, and controller supports;

4. exact or validated numerical arithmetic and its error bounds.

The bound $N\le 20$ alone does not make the class of all quantum instruments finite or justify an exhaustive enumeration.

For a fixed finite network, the factorization identity can be checked on a basis of matrix units in each classical block. For a chosen complementary state $\sigma$, form $K=R_Y\Phi E_{\sigma }$ and test

That is a channel identity, not a sample check on selected input states.