{"abstract":"The reduction disagrees with its explicit aggregation oracle.","category":"Numerical aggregation","checks":9,"contract":"Two equal-length integer cluster label arrays describe the same observations. Return exact adjusted Rand index from pair-count contingency reduction. Label names have no numerical meaning. Matching degenerate partitions with zero normalization return \"1\"; length mismatch returns None.","evaluation_group":"s3-na-adjusted-partition-pair-agreement","failed_approach":"Taking the smaller marginal also changes chance-adjusted normalization.","family":"s3-numerical-aggregation-adjusted-partition-pair-agreement-ari-ceiling-max","id":"FA-13776","implementations":{"attempt":{"sha256":"f79749a8d0eff4ffea9319be5fff909a98df849ebd8909308be237044246c76a","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    if len(a)!=len(b): return None\n    n=len(a)\n    if n<2: return \"1\"\n    pairs=n*(n-1)//2\n    joint=Counter(zip(a,b))\n    ra,rb=Counter(a),Counter(b)\n    choose=lambda k:k*(k-1)//2\n    same=sum(choose(v) for v in joint.values())\n    x=sum(choose(v) for v in ra.values())\n    y=sum(choose(v) for v in rb.values())\n    expected=Fraction(x*y,pairs)\n    ceiling=Fraction(min(x,y))\n    return \"1\" if ceiling==expected else str((same-expected)/(ceiling-expected))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([0, 0, 1, 1], [4, 4, 5, 5])), '1')\ncheck('regression 2', solve(*([0, 0, 1, 1], [0, 1, 0, 1])), '-1/2')\ncheck('regression 3', solve(*([], [])), '1')\ncheck('regression 4', solve(*([0], [9])), '1')\ncheck('regression 5', solve(*([0, 0, 0, 1, 2], [1, 1, 2, 2, 2])), '-2/23')\ncheck('regression 6', solve(*([0, 1, 2], [8, 9, 10])), '1')\ncheck('regression 7', solve(*([0, 0], [1])), None)\ncheck('regression 8', solve(*([0, 0, 1, 2, 2, 2], [4, 5, 4, 5, 5, 5])), '34/109')\ncheck(\"variable label names\",solve([N,N,N+1,N+1],[7,7,8,8]),\"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":"f34b3980a308a9cdf4097391c746927e50fcb7b402a524d7e71f094a6eab11e4","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    if len(a)!=len(b): return None\n    n=len(a)\n    if n<2: return \"1\"\n    pairs=n*(n-1)//2\n    joint=Counter(zip(a,b))\n    ra,rb=Counter(a),Counter(b)\n    choose=lambda k:k*(k-1)//2\n    same=sum(choose(v) for v in joint.values())\n    x=sum(choose(v) for v in ra.values())\n    y=sum(choose(v) for v in rb.values())\n    expected=Fraction(x*y,pairs)\n    ceiling=Fraction(max(x,y))\n    return \"1\" if ceiling==expected else str((same-expected)/(ceiling-expected))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([0, 0, 1, 1], [4, 4, 5, 5])), '1')\ncheck('regression 2', solve(*([0, 0, 1, 1], [0, 1, 0, 1])), '-1/2')\ncheck('regression 3', solve(*([], [])), '1')\ncheck('regression 4', solve(*([0], [9])), '1')\ncheck('regression 5', solve(*([0, 0, 0, 1, 2], [1, 1, 2, 2, 2])), '-2/23')\ncheck('regression 6', solve(*([0, 1, 2], [8, 9, 10])), '1')\ncheck('regression 7', solve(*([0, 0], [1])), None)\ncheck('regression 8', solve(*([0, 0, 1, 2, 2, 2], [4, 5, 4, 5, 5, 5])), '34/109')\ncheck(\"variable label names\",solve([N,N,N+1,N+1],[7,7,8,8]),\"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"},"fixed":{"sha256":"f1d717731848ae1508be0aed6706e7ae4b085082a44842998adbcafe1bc5ec7c","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    if len(a)!=len(b): return None\n    n=len(a)\n    if n<2: return \"1\"\n    pairs=n*(n-1)//2\n    joint=Counter(zip(a,b))\n    ra,rb=Counter(a),Counter(b)\n    choose=lambda k:k*(k-1)//2\n    same=sum(choose(v) for v in joint.values())\n    x=sum(choose(v) for v in ra.values())\n    y=sum(choose(v) for v in rb.values())\n    expected=Fraction(x*y,pairs)\n    ceiling=Fraction(x+y,2)\n    return \"1\" if ceiling==expected else str((same-expected)/(ceiling-expected))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([0, 0, 1, 1], [4, 4, 5, 5])), '1')\ncheck('regression 2', solve(*([0, 0, 1, 1], [0, 1, 0, 1])), '-1/2')\ncheck('regression 3', solve(*([], [])), '1')\ncheck('regression 4', solve(*([0], [9])), '1')\ncheck('regression 5', solve(*([0, 0, 0, 1, 2], [1, 1, 2, 2, 2])), '-2/23')\ncheck('regression 6', solve(*([0, 1, 2], [8, 9, 10])), '1')\ncheck('regression 7', solve(*([0, 0], [1])), None)\ncheck('regression 8', solve(*([0, 0, 1, 2, 2, 2], [4, 5, 4, 5, 5, 5])), '34/109')\ncheck(\"variable label names\",solve([N,N,N+1,N+1],[7,7,8,8]),\"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-adjusted-partition-pair-agreement-ari-ceiling-max","generated_at":"2026-09-29T14:39:10.357484+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.","repair":"Preserve the adjusted partition pair agreement contract at the identified reduction decision.","root_cause":"The maximum marginal pair count replaces their average normalization ceiling.","sha256":"129373150d2a3eace7e11d99306efafa16ef5f785013a602a5d32521bd9fb4f6","title":"Adjusted partition pair agreement: The maximum marginal pair count replaces their average normalization ceiling. · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":44.25,"exit_code":1,"observations":[{"actual":"1","check":"regression 1","expected":"1","passed":true},{"actual":"-1/2","check":"regression 2","expected":"-1/2","passed":true},{"actual":"1","check":"regression 3","expected":"1","passed":true},{"actual":"1","check":"regression 4","expected":"1","passed":true},{"actual":"-1/9","check":"regression 5","expected":"-2/23","passed":false},{"actual":"1","check":"regression 6","expected":"1","passed":true},{"actual":null,"check":"regression 7","expected":null,"passed":true},{"actual":"17/32","check":"regression 8","expected":"34/109","passed":false},{"actual":"1","check":"variable label names","expected":"1","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"regression 2\", \"actual\": \"-1/2\", \"expected\": \"-1/2\", \"passed\": true}, {\"check\": \"regression 3\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"regression 4\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"regression 5\", \"actual\": \"-1/9\", \"expected\": \"-2/23\", \"passed\": false}, {\"check\": \"regression 6\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"regression 7\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression 8\", \"actual\": \"17/32\", \"expected\": \"34/109\", \"passed\": false}, {\"check\": \"variable label names\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":41.794,"exit_code":1,"observations":[{"actual":"1","check":"regression 1","expected":"1","passed":true},{"actual":"-1/2","check":"regression 2","expected":"-1/2","passed":true},{"actual":"1","check":"regression 3","expected":"1","passed":true},{"actual":"1","check":"regression 4","expected":"1","passed":true},{"actual":"-1/14","check":"regression 5","expected":"-2/23","passed":false},{"actual":"1","check":"regression 6","expected":"1","passed":true},{"actual":null,"check":"regression 7","expected":null,"passed":true},{"actual":"17/77","check":"regression 8","expected":"34/109","passed":false},{"actual":"1","check":"variable label names","expected":"1","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"regression 2\", \"actual\": \"-1/2\", \"expected\": \"-1/2\", \"passed\": true}, {\"check\": \"regression 3\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"regression 4\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"regression 5\", \"actual\": \"-1/14\", \"expected\": \"-2/23\", \"passed\": false}, {\"check\": \"regression 6\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"regression 7\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression 8\", \"actual\": \"17/77\", \"expected\": \"34/109\", \"passed\": false}, {\"check\": \"variable label names\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":42.06,"exit_code":0,"observations":[{"actual":"1","check":"regression 1","expected":"1","passed":true},{"actual":"-1/2","check":"regression 2","expected":"-1/2","passed":true},{"actual":"1","check":"regression 3","expected":"1","passed":true},{"actual":"1","check":"regression 4","expected":"1","passed":true},{"actual":"-2/23","check":"regression 5","expected":"-2/23","passed":true},{"actual":"1","check":"regression 6","expected":"1","passed":true},{"actual":null,"check":"regression 7","expected":null,"passed":true},{"actual":"34/109","check":"regression 8","expected":"34/109","passed":true},{"actual":"1","check":"variable label names","expected":"1","passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"regression 2\", \"actual\": \"-1/2\", \"expected\": \"-1/2\", \"passed\": true}, {\"check\": \"regression 3\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"regression 4\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"regression 5\", \"actual\": \"-2/23\", \"expected\": \"-2/23\", \"passed\": true}, {\"check\": \"regression 6\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"regression 7\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression 8\", \"actual\": \"34/109\", \"expected\": \"34/109\", \"passed\": true}, {\"check\": \"variable label names\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}