{"abstract":"The reduction disagrees with its explicit aggregation oracle.","category":"Numerical aggregation","checks":8,"contract":"For nonempty integer samples with equal total probability after separate normalization, return integral of absolute CDF difference over the real line as a Fraction string. Empty either side returns None.","contract_signature":"a, b","evaluation_group":"s3-na-empirical-transport-distance","failed_approach":"Leaving the signed result computes mean displacement rather than transport cost.","family":"s3-numerical-aggregation-empirical-transport-distance-transport-cancellation","id":"FA-13431","implementations":{"attempt":{"sha256":"f239be0f7b93673c4baefedba9691d667b64d0cff503d0b5aef0b9e62d8ed75f","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 not a or not b: return None\n    ca,cb=Counter(a),Counter(b)\n    points=sorted(set(ca)|set(cb))\n    pa=pb=Fraction(0)\n    area=Fraction(0)\n    for i,x in enumerate(points[:-1]):\n        pa+=Fraction(ca[x],len(a))\n        pb+=Fraction(cb[x],len(b))\n        area+=(pa-pb)*(points[i+1]-x)\n    return str(area)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([0, 0, 9], [1, 4])), '17/6')\ncheck('regression 2', solve(*([2], [7])), '5')\ncheck('regression 3', solve(*([1, 2], [1, 2])), '0')\ncheck('regression 4', solve(*([], [1])), None)\ncheck('regression 5', solve(*([-8, -1, 4], [-3, 9, 9])), '20/3')\ncheck('regression 6', solve(*([0, 2, 8], [0, 8])), '4/3')\ncheck('regression 7', solve(*([0, 10], [4, 6])), '4')\ncheck(\"variable transport span\",solve([0],[N]),str(N))\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":"d8c90b320be13499d6e950ae79d88f301f16e8b3e9c04d25178f6f4558f69a23","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 not a or not b: return None\n    ca,cb=Counter(a),Counter(b)\n    points=sorted(set(ca)|set(cb))\n    pa=pb=Fraction(0)\n    area=Fraction(0)\n    for i,x in enumerate(points[:-1]):\n        pa+=Fraction(ca[x],len(a))\n        pb+=Fraction(cb[x],len(b))\n        area+=(pa-pb)*(points[i+1]-x)\n    return str(abs(area))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([0, 0, 9], [1, 4])), '17/6')\ncheck('regression 2', solve(*([2], [7])), '5')\ncheck('regression 3', solve(*([1, 2], [1, 2])), '0')\ncheck('regression 4', solve(*([], [1])), None)\ncheck('regression 5', solve(*([-8, -1, 4], [-3, 9, 9])), '20/3')\ncheck('regression 6', solve(*([0, 2, 8], [0, 8])), '4/3')\ncheck('regression 7', solve(*([0, 10], [4, 6])), '4')\ncheck(\"variable transport span\",solve([0],[N]),str(N))\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-empirical-transport-distance-transport-cancellation","generated_at":"2026-09-29T14:39:07.201975+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":"Signed CDF differences cancel before absolute value.","sha256":"71954716431ad78f099649ba5d44f04f25c5ec121c24c139d9f15dbafb2dc50c","title":"Empirical transport distance: Signed CDF differences cancel before absolute value. · 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":45.412,"exit_code":1,"observations":[{"actual":"-1/2","check":"regression 1","expected":"17/6","passed":false},{"actual":"5","check":"regression 2","expected":"5","passed":true},{"actual":"0","check":"regression 3","expected":"0","passed":true},{"actual":null,"check":"regression 4","expected":null,"passed":true},{"actual":"20/3","check":"regression 5","expected":"20/3","passed":true},{"actual":"2/3","check":"regression 6","expected":"4/3","passed":false},{"actual":"0","check":"regression 7","expected":"4","passed":false},{"actual":"1","check":"variable transport span","expected":"1","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": \"-1/2\", \"expected\": \"17/6\", \"passed\": false}, {\"check\": \"regression 2\", \"actual\": \"5\", \"expected\": \"5\", \"passed\": true}, {\"check\": \"regression 3\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 4\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression 5\", \"actual\": \"20/3\", \"expected\": \"20/3\", \"passed\": true}, {\"check\": \"regression 6\", \"actual\": \"2/3\", \"expected\": \"4/3\", \"passed\": false}, {\"check\": \"regression 7\", \"actual\": \"0\", \"expected\": \"4\", \"passed\": false}, {\"check\": \"variable transport span\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":45.972,"exit_code":1,"observations":[{"actual":"1/2","check":"regression 1","expected":"17/6","passed":false},{"actual":"5","check":"regression 2","expected":"5","passed":true},{"actual":"0","check":"regression 3","expected":"0","passed":true},{"actual":null,"check":"regression 4","expected":null,"passed":true},{"actual":"20/3","check":"regression 5","expected":"20/3","passed":true},{"actual":"2/3","check":"regression 6","expected":"4/3","passed":false},{"actual":"0","check":"regression 7","expected":"4","passed":false},{"actual":"1","check":"variable transport span","expected":"1","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": \"1/2\", \"expected\": \"17/6\", \"passed\": false}, {\"check\": \"regression 2\", \"actual\": \"5\", \"expected\": \"5\", \"passed\": true}, {\"check\": \"regression 3\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 4\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression 5\", \"actual\": \"20/3\", \"expected\": \"20/3\", \"passed\": true}, {\"check\": \"regression 6\", \"actual\": \"2/3\", \"expected\": \"4/3\", \"passed\": false}, {\"check\": \"regression 7\", \"actual\": \"0\", \"expected\": \"4\", \"passed\": false}, {\"check\": \"variable transport span\", \"actual\": \"1\", \"expected\": \"1\", \"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."}}