{"abstract":"The reduction disagrees with its explicit aggregation oracle.","category":"Numerical aggregation","checks":8,"contract":"Return multiset Jaccard similarity: sum of per-label minimum frequencies divided by sum of per-label maximum frequencies, as exact Fraction string. Both empty returns \"1\". Integer labels are nominal.","contract_signature":"a, b","evaluation_group":"s3-na-multiset-overlap-similarity","failed_approach":"Pairing all occurrences multiplies instead of matching shared mass.","family":"s3-numerical-aggregation-multiset-overlap-similarity-overlap-distinct-numerator","id":"FA-14071","implementations":{"attempt":{"sha256":"b5acc5bebc03b6a000300e5dcf28a6ab1db0fab5e3746124fb2780e0257a93fe","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nfrom collections import Counter, defaultdict\nimport math\nimport itertools\nN = 1\nobservations = []\ndef solve(a, b):\n    ca,cb=Counter(a),Counter(b)\n    keys=set(ca)|set(cb)\n    intersection=sum(ca[k]*cb[k] for k in keys)\n    union=sum(max(ca[k],cb[k]) for k in keys)\n    return str(Fraction(intersection,union)) if union else \"1\"\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([1, 1, 1, 2], [1, 2, 2])), '2/5')\ncheck('regression 2', solve(*([], [])), '1')\ncheck('regression 3', solve(*([1, 2], [])), '0')\ncheck('regression 4', solve(*([2, 2], [2, 2])), '1')\ncheck('regression 5', solve(*([-1, 0, 0], [0, 1])), '1/4')\ncheck('regression 6', solve(*([3, 3, 4], [3, 3, 3, 4, 4])), '3/5')\ncheck('regression 7', solve(*([0], [1])), '0')\ncheck(\"variable overlap mass\",solve([0]*N,[0]*(N+1)),str(Fraction(N,N+1)))\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"2224a2691ee890d14f46c0bf62caeb5f483529f8beae942e9a2cdec8a71a6d34","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nfrom collections import Counter, defaultdict\nimport math\nimport itertools\nN = 1\nobservations = []\ndef solve(a, b):\n    ca,cb=Counter(a),Counter(b)\n    keys=set(ca)|set(cb)\n    intersection=sum(int(ca[k]>0 and cb[k]>0) for k in keys)\n    union=sum(max(ca[k],cb[k]) for k in keys)\n    return str(Fraction(intersection,union)) if union else \"1\"\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([1, 1, 1, 2], [1, 2, 2])), '2/5')\ncheck('regression 2', solve(*([], [])), '1')\ncheck('regression 3', solve(*([1, 2], [])), '0')\ncheck('regression 4', solve(*([2, 2], [2, 2])), '1')\ncheck('regression 5', solve(*([-1, 0, 0], [0, 1])), '1/4')\ncheck('regression 6', solve(*([3, 3, 4], [3, 3, 3, 4, 4])), '3/5')\ncheck('regression 7', solve(*([0], [1])), '0')\ncheck(\"variable overlap mass\",solve([0]*N,[0]*(N+1)),str(Fraction(N,N+1)))\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"Small offline integer/rational inputs only; no performance, statistical inference, or production-library conformance claim. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"s3-numerical-aggregation-multiset-overlap-similarity-overlap-distinct-numerator","generated_at":"2026-09-29T14:39:13.705442+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Exact bounded examples isolate a reduction defect without floating-point or external-service effects.","root_cause":"Shared labels contribute one instead of their shared multiplicity.","sha256":"a67d45603d1a547a06e05c920626ad01c17afdeb2ddccef72624ada172f40b30","title":"Multiset overlap similarity: Shared labels contribute one instead of their shared multiplicity. · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":46.527,"exit_code":1,"observations":[{"actual":"1","check":"regression 1","expected":"2/5","passed":false},{"actual":"1","check":"regression 2","expected":"1","passed":true},{"actual":"0","check":"regression 3","expected":"0","passed":true},{"actual":"2","check":"regression 4","expected":"1","passed":false},{"actual":"1/2","check":"regression 5","expected":"1/4","passed":false},{"actual":"8/5","check":"regression 6","expected":"3/5","passed":false},{"actual":"0","check":"regression 7","expected":"0","passed":true},{"actual":"1","check":"variable overlap mass","expected":"1/2","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": \"1\", \"expected\": \"2/5\", \"passed\": false}, {\"check\": \"regression 2\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"regression 3\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 4\", \"actual\": \"2\", \"expected\": \"1\", \"passed\": false}, {\"check\": \"regression 5\", \"actual\": \"1/2\", \"expected\": \"1/4\", \"passed\": false}, {\"check\": \"regression 6\", \"actual\": \"8/5\", \"expected\": \"3/5\", \"passed\": false}, {\"check\": \"regression 7\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"variable overlap mass\", \"actual\": \"1\", \"expected\": \"1/2\", \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":50.008,"exit_code":1,"observations":[{"actual":"2/5","check":"regression 1","expected":"2/5","passed":true},{"actual":"1","check":"regression 2","expected":"1","passed":true},{"actual":"0","check":"regression 3","expected":"0","passed":true},{"actual":"1/2","check":"regression 4","expected":"1","passed":false},{"actual":"1/4","check":"regression 5","expected":"1/4","passed":true},{"actual":"2/5","check":"regression 6","expected":"3/5","passed":false},{"actual":"0","check":"regression 7","expected":"0","passed":true},{"actual":"1/2","check":"variable overlap mass","expected":"1/2","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": \"2/5\", \"expected\": \"2/5\", \"passed\": true}, {\"check\": \"regression 2\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"regression 3\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 4\", \"actual\": \"1/2\", \"expected\": \"1\", \"passed\": false}, {\"check\": \"regression 5\", \"actual\": \"1/4\", \"expected\": \"1/4\", \"passed\": true}, {\"check\": \"regression 6\", \"actual\": \"2/5\", \"expected\": \"3/5\", \"passed\": false}, {\"check\": \"regression 7\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"variable overlap mass\", \"actual\": \"1/2\", \"expected\": \"1/2\", \"passed\": true}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}