{"abstract":"The reduction disagrees with its explicit aggregation oracle.","category":"Numerical aggregation","checks":8,"contract":"For 0<=p<=q and q>0, initialise the recursive level to the first observation and update y=(p/q)*x+(1-p/q)*y for each later observation. Empty input returns None; return exact Fraction string.","contract_signature":"xs, p, q","evaluation_group":"s3-na-recursive-exponential-level","failed_approach":"Rounding selects only extreme memory policies for many fractions.","family":"s3-numerical-aggregation-recursive-exponential-level-smoother-integer-alpha","id":"FA-13541","implementations":{"attempt":{"sha256":"b840ac6133f001ac6f0697553c5aa1ca99e8aed3fa538144673e794a12835d7e","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(xs, p, q):\n    if not xs: return None\n    alpha=round(Fraction(p,q))\n    y=Fraction(xs[0])\n    for x in xs[1:]:\n        y=alpha*x+(1-alpha)*y\n    return str(y)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([2, 8, 4], 1, 2)), '9/2')\ncheck('regression 2', solve(*([], 1, 2)), None)\ncheck('regression 3', solve(*([7], 1, 3)), '7')\ncheck('regression 4', solve(*([2, 9], 0, 1)), '2')\ncheck('regression 5', solve(*([3, 8, 1], 1, 1)), '1')\ncheck('regression 6', solve(*([-3, 5, -2], 2, 3)), '-5/9')\ncheck('regression 7', solve(*([0, 0, 8], 1, 4)), '2')\ncheck(\"variable impulse\",solve([0,N,0],1,2),str(Fraction(N,4)))\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":"0fad0b42d11704eefd4966d4c040ba614f40ac6ae70dbd61e41c4f35fa9bdaf2","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(xs, p, q):\n    if not xs: return None\n    alpha=p//q\n    y=Fraction(xs[0])\n    for x in xs[1:]:\n        y=alpha*x+(1-alpha)*y\n    return str(y)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([2, 8, 4], 1, 2)), '9/2')\ncheck('regression 2', solve(*([], 1, 2)), None)\ncheck('regression 3', solve(*([7], 1, 3)), '7')\ncheck('regression 4', solve(*([2, 9], 0, 1)), '2')\ncheck('regression 5', solve(*([3, 8, 1], 1, 1)), '1')\ncheck('regression 6', solve(*([-3, 5, -2], 2, 3)), '-5/9')\ncheck('regression 7', solve(*([0, 0, 8], 1, 4)), '2')\ncheck(\"variable impulse\",solve([0,N,0],1,2),str(Fraction(N,4)))\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-recursive-exponential-level-smoother-integer-alpha","generated_at":"2026-09-29T14:39:08.211376+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 mixing fraction is truncated before use.","sha256":"1942ad65b74b75a692b0718a985928670a429005504af2972f2b32435aeca9f9","title":"Recursive exponential level: The mixing fraction is truncated before use. · 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":45.084,"exit_code":1,"observations":[{"actual":"2","check":"regression 1","expected":"9/2","passed":false},{"actual":null,"check":"regression 2","expected":null,"passed":true},{"actual":"7","check":"regression 3","expected":"7","passed":true},{"actual":"2","check":"regression 4","expected":"2","passed":true},{"actual":"1","check":"regression 5","expected":"1","passed":true},{"actual":"-2","check":"regression 6","expected":"-5/9","passed":false},{"actual":"0","check":"regression 7","expected":"2","passed":false},{"actual":"0","check":"variable impulse","expected":"1/4","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": \"2\", \"expected\": \"9/2\", \"passed\": false}, {\"check\": \"regression 2\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression 3\", \"actual\": \"7\", \"expected\": \"7\", \"passed\": true}, {\"check\": \"regression 4\", \"actual\": \"2\", \"expected\": \"2\", \"passed\": true}, {\"check\": \"regression 5\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"regression 6\", \"actual\": \"-2\", \"expected\": \"-5/9\", \"passed\": false}, {\"check\": \"regression 7\", \"actual\": \"0\", \"expected\": \"2\", \"passed\": false}, {\"check\": \"variable impulse\", \"actual\": \"0\", \"expected\": \"1/4\", \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":43.005,"exit_code":1,"observations":[{"actual":"2","check":"regression 1","expected":"9/2","passed":false},{"actual":null,"check":"regression 2","expected":null,"passed":true},{"actual":"7","check":"regression 3","expected":"7","passed":true},{"actual":"2","check":"regression 4","expected":"2","passed":true},{"actual":"1","check":"regression 5","expected":"1","passed":true},{"actual":"-3","check":"regression 6","expected":"-5/9","passed":false},{"actual":"0","check":"regression 7","expected":"2","passed":false},{"actual":"0","check":"variable impulse","expected":"1/4","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": \"2\", \"expected\": \"9/2\", \"passed\": false}, {\"check\": \"regression 2\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression 3\", \"actual\": \"7\", \"expected\": \"7\", \"passed\": true}, {\"check\": \"regression 4\", \"actual\": \"2\", \"expected\": \"2\", \"passed\": true}, {\"check\": \"regression 5\", \"actual\": \"1\", \"expected\": \"1\", \"passed\": true}, {\"check\": \"regression 6\", \"actual\": \"-3\", \"expected\": \"-5/9\", \"passed\": false}, {\"check\": \"regression 7\", \"actual\": \"0\", \"expected\": \"2\", \"passed\": false}, {\"check\": \"variable impulse\", \"actual\": \"0\", \"expected\": \"1/4\", \"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."}}