{"abstract":"The reduction disagrees with its explicit aggregation oracle.","category":"Numerical aggregation","checks":9,"contract":"Rows [integer value, nonnegative frequency] represent replicated observations. Return unnormalised sum of squared deviations from their exact replicated mean as a Fraction string; zero total frequency returns None.","contract_signature":"rows","evaluation_group":"s3-na-frequency-central-scatter","failed_approach":"Sample normalization also produces a variance rather than additive scatter.","family":"s3-numerical-aggregation-frequency-central-scatter-mean-of-squares","id":"FA-13146","implementations":{"attempt":{"sha256":"3b19cfd25a29af8a324519c700f35b69155b04e4d326c9cde4a14944e2d06004","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(rows):\n    total=sum(w for x,w in rows)\n    if total==0: return None\n    center=Fraction(sum(x*w for x,w in rows),total)\n    return str(sum(w*(x-center)**2 for x,w in rows)/max(1,total-1))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([(1, 2), (1, 2), (4, 1)],)), '36/5')\ncheck('regression 2', solve(*([(1, 2), (4, 1)],)), '6')\ncheck('regression 3', solve(*([(0, 1), (0, 3)],)), '0')\ncheck('regression 4', solve(*([],)), None)\ncheck('regression 5', solve(*([(3, 0), (8, 0)],)), None)\ncheck('regression 6', solve(*([(9, 1), (-2, 3), (5, 2)],)), '689/6')\ncheck('regression 7', solve(*([(7, 3), (1, 0)],)), '0')\ncheck('regression 8', solve(*([(1, 1), (2, 1), (5, 1)],)), '26/3')\ncheck(\"variable replication scatter\",solve([(0,N),(2,N)]),str(2*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":"3e5e2b3a24ac0cff623b2c4cb638d32786183c19a069635b2fbde61d268a43b9","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(rows):\n    total=sum(w for x,w in rows)\n    if total==0: return None\n    center=Fraction(sum(x*w for x,w in rows),total)\n    return str(sum(w*(x-center)**2 for x,w in rows)/total)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([(1, 2), (1, 2), (4, 1)],)), '36/5')\ncheck('regression 2', solve(*([(1, 2), (4, 1)],)), '6')\ncheck('regression 3', solve(*([(0, 1), (0, 3)],)), '0')\ncheck('regression 4', solve(*([],)), None)\ncheck('regression 5', solve(*([(3, 0), (8, 0)],)), None)\ncheck('regression 6', solve(*([(9, 1), (-2, 3), (5, 2)],)), '689/6')\ncheck('regression 7', solve(*([(7, 3), (1, 0)],)), '0')\ncheck('regression 8', solve(*([(1, 1), (2, 1), (5, 1)],)), '26/3')\ncheck(\"variable replication scatter\",solve([(0,N),(2,N)]),str(2*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-frequency-central-scatter-mean-of-squares","generated_at":"2026-09-29T14:39:04.229740+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":"Squared deviations are normalized even though the summary stores total scatter.","sha256":"4948a9ac6501913a26edb6bc19d3a816afdc457ad7095ea33192bb8d25a68b7c","title":"Frequency central scatter: Squared deviations are normalized even though the summary stores total scatter. · 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":48.31,"exit_code":1,"observations":[{"actual":"9/5","check":"regression 1","expected":"36/5","passed":false},{"actual":"3","check":"regression 2","expected":"6","passed":false},{"actual":"0","check":"regression 3","expected":"0","passed":true},{"actual":null,"check":"regression 4","expected":null,"passed":true},{"actual":null,"check":"regression 5","expected":null,"passed":true},{"actual":"689/30","check":"regression 6","expected":"689/6","passed":false},{"actual":"0","check":"regression 7","expected":"0","passed":true},{"actual":"13/3","check":"regression 8","expected":"26/3","passed":false},{"actual":"2","check":"variable replication scatter","expected":"2","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": \"9/5\", \"expected\": \"36/5\", \"passed\": false}, {\"check\": \"regression 2\", \"actual\": \"3\", \"expected\": \"6\", \"passed\": false}, {\"check\": \"regression 3\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 4\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression 5\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression 6\", \"actual\": \"689/30\", \"expected\": \"689/6\", \"passed\": false}, {\"check\": \"regression 7\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 8\", \"actual\": \"13/3\", \"expected\": \"26/3\", \"passed\": false}, {\"check\": \"variable replication scatter\", \"actual\": \"2\", \"expected\": \"2\", \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.433,"exit_code":1,"observations":[{"actual":"36/25","check":"regression 1","expected":"36/5","passed":false},{"actual":"2","check":"regression 2","expected":"6","passed":false},{"actual":"0","check":"regression 3","expected":"0","passed":true},{"actual":null,"check":"regression 4","expected":null,"passed":true},{"actual":null,"check":"regression 5","expected":null,"passed":true},{"actual":"689/36","check":"regression 6","expected":"689/6","passed":false},{"actual":"0","check":"regression 7","expected":"0","passed":true},{"actual":"26/9","check":"regression 8","expected":"26/3","passed":false},{"actual":"1","check":"variable replication scatter","expected":"2","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": \"36/25\", \"expected\": \"36/5\", \"passed\": false}, {\"check\": \"regression 2\", \"actual\": \"2\", \"expected\": \"6\", \"passed\": false}, {\"check\": \"regression 3\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 4\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression 5\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression 6\", \"actual\": \"689/36\", \"expected\": \"689/6\", \"passed\": false}, {\"check\": \"regression 7\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 8\", \"actual\": \"26/9\", \"expected\": \"26/3\", \"passed\": false}, {\"check\": \"variable replication scatter\", \"actual\": \"1\", \"expected\": \"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."}}