{"abstract":"The reduction disagrees with its explicit aggregation oracle.","category":"Numerical aggregation","checks":9,"contract":"For nonnegative integer importance weights and positive integer cap, clip each weight to cap, then return Kish effective size (sum clipped weights)**2/sum squared clipped weights as exact Fraction string. Negative weight, invalid cap, or zero total yields None.","contract_signature":"weights, cap","evaluation_group":"s3-na-capped-weight-effective-size","failed_approach":"Nearest integer rounding also loses exact fractional effective size.","family":"s3-numerical-aggregation-capped-weight-effective-size-effective-integer-quotient","id":"FA-14331","implementations":{"attempt":{"sha256":"14e16ffcb2eafe404b5966c46fda5f8b4cc3f332bfc3e1f0451122fdae49116c","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(weights, cap):\n    if cap<=0 or any(w<0 for w in weights): return None\n    ws=[min(w,cap) for w in weights]\n    s=sum(ws)\n    q=sum(w*w for w in ws)\n    return str(Fraction(round(Fraction(s*s,q)))) if q else None\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([1, 2, 4], 3)), '18/7')\ncheck('regression 2', solve(*([0, 0], 3)), None)\ncheck('regression 3', solve(*([], 4)), None)\ncheck('regression 4', solve(*([2, 2, 2], 9)), '3')\ncheck('regression 5', solve(*([10, 1], 2)), '9/5')\ncheck('regression 6', solve(*([-1, 2], 3)), None)\ncheck('regression 7', solve(*([1, 3], 0)), None)\ncheck('regression 8', solve(*([0, 2, 5, 1], 4)), '7/3')\ncheck(\"variable effective-size imbalance\",solve([N,1],N+1),str(Fraction((N+1)**2,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":"4700a01fd71a3f816acc0dbda8d9253c5d26f51999c7b03128c35dd09bc163e1","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(weights, cap):\n    if cap<=0 or any(w<0 for w in weights): return None\n    ws=[min(w,cap) for w in weights]\n    s=sum(ws)\n    q=sum(w*w for w in ws)\n    return str(Fraction(s*s//q)) if q else None\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([1, 2, 4], 3)), '18/7')\ncheck('regression 2', solve(*([0, 0], 3)), None)\ncheck('regression 3', solve(*([], 4)), None)\ncheck('regression 4', solve(*([2, 2, 2], 9)), '3')\ncheck('regression 5', solve(*([10, 1], 2)), '9/5')\ncheck('regression 6', solve(*([-1, 2], 3)), None)\ncheck('regression 7', solve(*([1, 3], 0)), None)\ncheck('regression 8', solve(*([0, 2, 5, 1], 4)), '7/3')\ncheck(\"variable effective-size imbalance\",solve([N,1],N+1),str(Fraction((N+1)**2,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-capped-weight-effective-size-effective-integer-quotient","generated_at":"2026-09-29T14:39:15.814592+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":"Effective size is truncated to an integer.","sha256":"d8b8a2b47689cfb4247fdafd5a093fbc6e879f8d298b4d73ea8207e38321ce5c","title":"Capped weight effective size: Effective size is truncated to an integer. · 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":42.57,"exit_code":1,"observations":[{"actual":"3","check":"regression 1","expected":"18/7","passed":false},{"actual":null,"check":"regression 2","expected":null,"passed":true},{"actual":null,"check":"regression 3","expected":null,"passed":true},{"actual":"3","check":"regression 4","expected":"3","passed":true},{"actual":"2","check":"regression 5","expected":"9/5","passed":false},{"actual":null,"check":"regression 6","expected":null,"passed":true},{"actual":null,"check":"regression 7","expected":null,"passed":true},{"actual":"2","check":"regression 8","expected":"7/3","passed":false},{"actual":"2","check":"variable effective-size imbalance","expected":"2","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": \"3\", \"expected\": \"18/7\", \"passed\": false}, {\"check\": \"regression 2\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression 3\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression 4\", \"actual\": \"3\", \"expected\": \"3\", \"passed\": true}, {\"check\": \"regression 5\", \"actual\": \"2\", \"expected\": \"9/5\", \"passed\": false}, {\"check\": \"regression 6\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression 7\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression 8\", \"actual\": \"2\", \"expected\": \"7/3\", \"passed\": false}, {\"check\": \"variable effective-size imbalance\", \"actual\": \"2\", \"expected\": \"2\", \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.38,"exit_code":1,"observations":[{"actual":"2","check":"regression 1","expected":"18/7","passed":false},{"actual":null,"check":"regression 2","expected":null,"passed":true},{"actual":null,"check":"regression 3","expected":null,"passed":true},{"actual":"3","check":"regression 4","expected":"3","passed":true},{"actual":"1","check":"regression 5","expected":"9/5","passed":false},{"actual":null,"check":"regression 6","expected":null,"passed":true},{"actual":null,"check":"regression 7","expected":null,"passed":true},{"actual":"2","check":"regression 8","expected":"7/3","passed":false},{"actual":"2","check":"variable effective-size imbalance","expected":"2","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": \"2\", \"expected\": \"18/7\", \"passed\": false}, {\"check\": \"regression 2\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression 3\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression 4\", \"actual\": \"3\", \"expected\": \"3\", \"passed\": true}, {\"check\": \"regression 5\", \"actual\": \"1\", \"expected\": \"9/5\", \"passed\": false}, {\"check\": \"regression 6\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression 7\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression 8\", \"actual\": \"2\", \"expected\": \"7/3\", \"passed\": false}, {\"check\": \"variable effective-size imbalance\", \"actual\": \"2\", \"expected\": \"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."}}