{"abstract":"The reduction disagrees with its explicit aggregation oracle.","category":"Numerical aggregation","checks":10,"contract":"Return the maximum absolute difference between the right-continuous empirical cumulative distributions of two nonempty integer samples as a Fraction string. Empty either side returns None.","contract_signature":"a, b","evaluation_group":"s3-na-empirical-cdf-supremum","failed_approach":"Reversing the tied jump order still introduces a nonexistent intermediate CDF state.","family":"s3-numerical-aggregation-empirical-cdf-supremum-cdf-interleaved-ties","id":"FA-13401","implementations":{"attempt":{"sha256":"42830f4a45ff5714db59acd33244257baa7885174667bd083a866950d7a9ee6f","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    pa=pb=Fraction(0)\n    best=Fraction(0)\n    for x in sorted(set(ca)|set(cb)):\n        pa+=Fraction(ca[x],len(a))\n        pb+=Fraction(cb[x],len(b))\n        best=max(best,abs(pa-pb),abs((pa-Fraction(ca[x],len(a)))-pb))\n    return str(best)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([3], [0])), '1')\ncheck('regression 2', solve(*([-5, 3], [-2, 1])), '1/2')\ncheck('regression 3', solve(*([1, 1, 4], [2, 3])), '2/3')\ncheck('regression 4', solve(*([0, 0, 0], [0])), '0')\ncheck('regression 5', solve(*([], [1])), None)\ncheck('regression 6', solve(*([1, 2], [1, 2])), '0')\ncheck('regression 7', solve(*([-5, 0, 8], [-2, 8, 8, 8])), '5/12')\ncheck('regression 8', solve(*([0, 4], [0, 1, 2, 3, 4])), '3/10')\ncheck('regression 9', solve(*([2, 2], [1, 1, 3, 3])), '1/2')\ncheck(\"variable support\",solve([0,N],[N,N]),\"1/2\")\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":"b859dfb545267c09836dfcdadc080fa2936907b2913060663bb8987675dc01c5","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    pa=pb=Fraction(0)\n    best=Fraction(0)\n    for x in sorted(set(ca)|set(cb)):\n        pa+=Fraction(ca[x],len(a))\n        pb+=Fraction(cb[x],len(b))\n        best=max(best,abs(pa-pb),abs(pa-(pb-Fraction(cb[x],len(b)))))\n    return str(best)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([3], [0])), '1')\ncheck('regression 2', solve(*([-5, 3], [-2, 1])), '1/2')\ncheck('regression 3', solve(*([1, 1, 4], [2, 3])), '2/3')\ncheck('regression 4', solve(*([0, 0, 0], [0])), '0')\ncheck('regression 5', solve(*([], [1])), None)\ncheck('regression 6', solve(*([1, 2], [1, 2])), '0')\ncheck('regression 7', solve(*([-5, 0, 8], [-2, 8, 8, 8])), '5/12')\ncheck('regression 8', solve(*([0, 4], [0, 1, 2, 3, 4])), '3/10')\ncheck('regression 9', solve(*([2, 2], [1, 1, 3, 3])), '1/2')\ncheck(\"variable support\",solve([0,N],[N,N]),\"1/2\")\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-cdf-supremum-cdf-interleaved-ties","generated_at":"2026-09-29T14:39:06.766723+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":"The discrepancy is measured between simultaneous equal-value jumps.","sha256":"27327a392bfde0bf5467dae694908b7f10a0b58c262516af05770af781fda213","title":"Empirical cdf supremum: The discrepancy is measured between simultaneous equal-value jumps. · 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":46.096,"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":"2/3","check":"regression 3","expected":"2/3","passed":true},{"actual":"1","check":"regression 4","expected":"0","passed":false},{"actual":null,"check":"regression 5","expected":null,"passed":true},{"actual":"1/2","check":"regression 6","expected":"0","passed":false},{"actual":"5/12","check":"regression 7","expected":"5/12","passed":true},{"actual":"1/2","check":"regression 8","expected":"3/10","passed":false},{"actual":"1/2","check":"regression 9","expected":"1/2","passed":true},{"actual":"1/2","check":"variable support","expected":"1/2","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\": \"2/3\", \"expected\": \"2/3\", \"passed\": true}, {\"check\": \"regression 4\", \"actual\": \"1\", \"expected\": \"0\", \"passed\": false}, {\"check\": \"regression 5\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression 6\", \"actual\": \"1/2\", \"expected\": \"0\", \"passed\": false}, {\"check\": \"regression 7\", \"actual\": \"5/12\", \"expected\": \"5/12\", \"passed\": true}, {\"check\": \"regression 8\", \"actual\": \"1/2\", \"expected\": \"3/10\", \"passed\": false}, {\"check\": \"regression 9\", \"actual\": \"1/2\", \"expected\": \"1/2\", \"passed\": true}, {\"check\": \"variable support\", \"actual\": \"1/2\", \"expected\": \"1/2\", \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.507,"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":"2/3","check":"regression 3","expected":"2/3","passed":true},{"actual":"1","check":"regression 4","expected":"0","passed":false},{"actual":null,"check":"regression 5","expected":null,"passed":true},{"actual":"1/2","check":"regression 6","expected":"0","passed":false},{"actual":"3/4","check":"regression 7","expected":"5/12","passed":false},{"actual":"1/2","check":"regression 8","expected":"3/10","passed":false},{"actual":"1/2","check":"regression 9","expected":"1/2","passed":true},{"actual":"1","check":"variable support","expected":"1/2","passed":false}],"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\": \"2/3\", \"expected\": \"2/3\", \"passed\": true}, {\"check\": \"regression 4\", \"actual\": \"1\", \"expected\": \"0\", \"passed\": false}, {\"check\": \"regression 5\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression 6\", \"actual\": \"1/2\", \"expected\": \"0\", \"passed\": false}, {\"check\": \"regression 7\", \"actual\": \"3/4\", \"expected\": \"5/12\", \"passed\": false}, {\"check\": \"regression 8\", \"actual\": \"1/2\", \"expected\": \"3/10\", \"passed\": false}, {\"check\": \"regression 9\", \"actual\": \"1/2\", \"expected\": \"1/2\", \"passed\": true}, {\"check\": \"variable support\", \"actual\": \"1\", \"expected\": \"1/2\", \"passed\": false}], \"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."}}