{"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.","evaluation_group":"s3-na-empirical-cdf-supremum","failed_approach":"Arrival order also fails to define an ordered cumulative distribution.","family":"s3-numerical-aggregation-empirical-cdf-supremum-cdf-value-order","id":"FA-13416","implementations":{"attempt":{"sha256":"5a762949c410813b9f582a486f1b8c2f3007634097c44553b00b4837d7660a0c","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 list(ca)+[x for x in cb if x not in ca]:\n        pa+=Fraction(ca[x],len(a))\n        pb+=Fraction(cb[x],len(b))\n        best=max(best,abs(pa-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":"89b17c970e49d11c2aea440925264f14328bddb72cc51b5e6e26f01b5da7b59b","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),key=abs):\n        pa+=Fraction(ca[x],len(a))\n        pb+=Fraction(cb[x],len(b))\n        best=max(best,abs(pa-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"},"fixed":{"sha256":"ddf4ebc36608e574c462ed740eefb855c4c46abcb901c6a609803ce88ef84dbe","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))\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-value-order","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.","repair":"Preserve the empirical cdf supremum contract at the identified reduction decision.","root_cause":"Cumulative support is traversed by magnitude.","sha256":"f7c58ef5bd63b50f6c988418ec1dd8aabcc979d6a05031d5d80461efcdba812d","title":"Empirical cdf supremum: Cumulative support is traversed by magnitude. · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":46.314,"exit_code":1,"observations":[{"actual":"1","check":"regression 1","expected":"1","passed":true},{"actual":"1","check":"regression 2","expected":"1/2","passed":false},{"actual":"1","check":"regression 3","expected":"2/3","passed":false},{"actual":"0","check":"regression 4","expected":"0","passed":true},{"actual":null,"check":"regression 5","expected":null,"passed":true},{"actual":"0","check":"regression 6","expected":"0","passed":true},{"actual":"2/3","check":"regression 7","expected":"5/12","passed":false},{"actual":"3/5","check":"regression 8","expected":"3/10","passed":false},{"actual":"1","check":"regression 9","expected":"1/2","passed":false},{"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\", \"expected\": \"1/2\", \"passed\": false}, {\"check\": \"regression 3\", \"actual\": \"1\", \"expected\": \"2/3\", \"passed\": false}, {\"check\": \"regression 4\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 5\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression 6\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 7\", \"actual\": \"2/3\", \"expected\": \"5/12\", \"passed\": false}, {\"check\": \"regression 8\", \"actual\": \"3/5\", \"expected\": \"3/10\", \"passed\": false}, {\"check\": \"regression 9\", \"actual\": \"1\", \"expected\": \"1/2\", \"passed\": false}, {\"check\": \"variable support\", \"actual\": \"1/2\", \"expected\": \"1/2\", \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":46.006,"exit_code":1,"observations":[{"actual":"1","check":"regression 1","expected":"1","passed":true},{"actual":"1","check":"regression 2","expected":"1/2","passed":false},{"actual":"2/3","check":"regression 3","expected":"2/3","passed":true},{"actual":"0","check":"regression 4","expected":"0","passed":true},{"actual":null,"check":"regression 5","expected":null,"passed":true},{"actual":"0","check":"regression 6","expected":"0","passed":true},{"actual":"5/12","check":"regression 7","expected":"5/12","passed":true},{"actual":"3/10","check":"regression 8","expected":"3/10","passed":true},{"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\", \"expected\": \"1/2\", \"passed\": false}, {\"check\": \"regression 3\", \"actual\": \"2/3\", \"expected\": \"2/3\", \"passed\": true}, {\"check\": \"regression 4\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 5\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression 6\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 7\", \"actual\": \"5/12\", \"expected\": \"5/12\", \"passed\": true}, {\"check\": \"regression 8\", \"actual\": \"3/10\", \"expected\": \"3/10\", \"passed\": true}, {\"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"},"fixed":{"elapsed_ms":45.937,"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":"2/3","check":"regression 3","expected":"2/3","passed":true},{"actual":"0","check":"regression 4","expected":"0","passed":true},{"actual":null,"check":"regression 5","expected":null,"passed":true},{"actual":"0","check":"regression 6","expected":"0","passed":true},{"actual":"5/12","check":"regression 7","expected":"5/12","passed":true},{"actual":"3/10","check":"regression 8","expected":"3/10","passed":true},{"actual":"1/2","check":"regression 9","expected":"1/2","passed":true},{"actual":"1/2","check":"variable support","expected":"1/2","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\": \"2/3\", \"expected\": \"2/3\", \"passed\": true}, {\"check\": \"regression 4\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 5\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression 6\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 7\", \"actual\": \"5/12\", \"expected\": \"5/12\", \"passed\": true}, {\"check\": \"regression 8\", \"actual\": \"3/10\", \"expected\": \"3/10\", \"passed\": true}, {\"check\": \"regression 9\", \"actual\": \"1/2\", \"expected\": \"1/2\", \"passed\": true}, {\"check\": \"variable support\", \"actual\": \"1/2\", \"expected\": \"1/2\", \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}