Proposition: Exhaustive certificates versus feasible strategies

For a fixed finite task:

1. a fully completed exact enumeration of all deterministic admitted strategies gives an exact optimum and hence an upper certificate;

2. one feasible strategy, including a numerically optimized one, gives a lower bound on the maximum;

3. a rigorously justified relaxation with a proved upper optimum can certify an upper bound, even if it is not sharp.

For streaming tasks, the enumerated set must include the exact admitted transition and output rules, not an assumed batch replacement.

Proof. A maximum over an exhausted finite set is its exact maximum. A feasible element cannot exceed that maximum. A containing relaxation has a maximum at least as large as the original one.