CMP.4:4.6 - Return the strongest result actually obtained

On finding a witness, return it with the meaning of its admissibility. For optimization, include its objective value and any remaining bound that the recipient needs. On complete exhaustion, sound exclusions and covering extensions justify optimality if a feasible answer was found, or absence of a feasible answer if none was found.

On interruption, return the available candidate and unresolved possibility. “No witness found within this run” is useful information but does not establish that no witness exists. If only a satisfactory candidate was requested, its obtaining can complete the work without exhausting the search.

Use an initial and changed-condition case to check which conclusion the recipient can actually use. Changing an output from one optimum to all optima, or changing a domain, directly tests the exclusion’s scope.