Proposition: Optimization status

For a declared finite architecture:

1. completed exact enumeration of all deterministic admitted strategies gives an exact maximum;

2. a feasible best-found strategy gives only a lower bound on that maximum;

3. a containing relaxation gives an upper bound only when its optimum is rigorously bounded.

For streaming architectures, the enumerated transition and output maps must be the actual admitted maps.

Proof. The first assertion is a maximum over an exhausted finite set. A feasible element cannot exceed the set's maximum. A containing relaxation has a maximum at least as large as the original one.