{"id":"greedy-optimality-requires-nonnegative-domain","text":"Greedy algorithms in the repo are provably optimal across their problem domains, but this universal optimality claim is contingent on non-negative input values — at least one greedy sort-then-pair strategy (max_product_difference) is correct only for positive inputs, where magnitude ordering coincides with value ordering.","truth_value":"OUT","source":"","source_url":"","source_hash":"","justifications":[{"type":"SL","antecedents":["greedy-algorithms-provably-optimal"],"outlist":["sort-greedy-positive-only"],"label":"The positive-input-only constraint on one greedy solution gates the universal optimality claim"}],"dependents":[],"metadata":{"source_type":"derived","_retracted":true},"created_at":"","updated_at":"2026-06-17T15:32:16+00:00","reviewed_at":"","verified_at":"","retracted_at":"2026-06-17T15:32:16+00:00","explanation":{"steps":[{"node":"greedy-optimality-requires-nonnegative-domain","truth_value":"OUT","reason":"SL justification invalid","failed_antecedents":[],"label":"The positive-input-only constraint on one greedy solution gates the universal optimality claim","violated_outlist":["sort-greedy-positive-only"]}]}}