{"abstract":"The reduction disagrees with its explicit aggregation oracle.","category":"Numerical aggregation","checks":9,"contract":"Rows [group label, integer residual or None] are reduced into mean squared residual per group, then arithmetic mean across observed groups. Missing residuals contribute neither count nor group presence; group labels are case-sensitive. Empty observed population returns None. Exact Fraction string.","contract_signature":"rows","evaluation_group":"s3-na-group-balanced-squared-loss","failed_approach":"Dividing each total by number of groups uses the wrong inner population.","family":"s3-numerical-aggregation-group-balanced-squared-loss-macro-group-total","id":"FA-14201","implementations":{"attempt":{"sha256":"7bbae5097c065a599d018d4b40efe509c6f70cb8404a6a52930d97c4b6de8e47","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    groups={}\n    for label,error in rows:\n        if error is None: continue\n        groups.setdefault(label,[]).append(error)\n    if not groups: return None\n    means=[Fraction(sum(e*e for e in values),len(groups)) for values in groups.values()]\n    return str(sum(means)/len(means))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([('a', 1), ('a', 2), ('b', 4)],)), '37/4')\ncheck('regression 2', solve(*([('a', 1), ('a', 3), ('b', 4)],)), '21/2')\ncheck('regression 3', solve(*([],)), None)\ncheck('regression 4', solve(*([('a', None), ('b', None)],)), None)\ncheck('regression 5', solve(*([('a', 0), ('a', 2), ('b', -3), ('b', 1)],)), '7/2')\ncheck('regression 6', solve(*([('a', 1), ('b', 2), ('b', 2), ('b', 2)],)), '5/2')\ncheck('regression 7', solve(*([('a', None), ('a', 2), ('b', 4)],)), '10')\ncheck('regression 8', solve(*([('A', 1), ('a', 4), ('B', 2)],)), '7')\ncheck(\"variable group balance\",solve([(\"a\",N),(\"a\",-N),(\"b\",2*N)]),str(Fraction(5*N*N,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":"c6a0d048cd68b2c0dfcf66fb4b66057350348a2cec94d30c40115948e8f6e868","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    groups={}\n    for label,error in rows:\n        if error is None: continue\n        groups.setdefault(label,[]).append(error)\n    if not groups: return None\n    means=[Fraction(sum(e*e for e in values)) for values in groups.values()]\n    return str(sum(means)/len(means))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([('a', 1), ('a', 2), ('b', 4)],)), '37/4')\ncheck('regression 2', solve(*([('a', 1), ('a', 3), ('b', 4)],)), '21/2')\ncheck('regression 3', solve(*([],)), None)\ncheck('regression 4', solve(*([('a', None), ('b', None)],)), None)\ncheck('regression 5', solve(*([('a', 0), ('a', 2), ('b', -3), ('b', 1)],)), '7/2')\ncheck('regression 6', solve(*([('a', 1), ('b', 2), ('b', 2), ('b', 2)],)), '5/2')\ncheck('regression 7', solve(*([('a', None), ('a', 2), ('b', 4)],)), '10')\ncheck('regression 8', solve(*([('A', 1), ('a', 4), ('B', 2)],)), '7')\ncheck(\"variable group balance\",solve([(\"a\",N),(\"a\",-N),(\"b\",2*N)]),str(Fraction(5*N*N,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-group-balanced-squared-loss-macro-group-total","generated_at":"2026-09-29T14:39:14.981710+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":"Within-group loss totals are not normalized by group sizes.","sha256":"c024bb09076c9a3052375d5f8344383ab030df0e36a2d25bb9ed16b808db2ddd","title":"Group balanced squared loss: Within-group loss totals are not normalized by group sizes. · 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":40.26,"exit_code":1,"observations":[{"actual":"21/4","check":"regression 1","expected":"37/4","passed":false},{"actual":"13/2","check":"regression 2","expected":"21/2","passed":false},{"actual":null,"check":"regression 3","expected":null,"passed":true},{"actual":null,"check":"regression 4","expected":null,"passed":true},{"actual":"7/2","check":"regression 5","expected":"7/2","passed":true},{"actual":"13/4","check":"regression 6","expected":"5/2","passed":false},{"actual":"5","check":"regression 7","expected":"10","passed":false},{"actual":"7/3","check":"regression 8","expected":"7","passed":false},{"actual":"3/2","check":"variable group balance","expected":"5/2","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": \"21/4\", \"expected\": \"37/4\", \"passed\": false}, {\"check\": \"regression 2\", \"actual\": \"13/2\", \"expected\": \"21/2\", \"passed\": false}, {\"check\": \"regression 3\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression 4\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression 5\", \"actual\": \"7/2\", \"expected\": \"7/2\", \"passed\": true}, {\"check\": \"regression 6\", \"actual\": \"13/4\", \"expected\": \"5/2\", \"passed\": false}, {\"check\": \"regression 7\", \"actual\": \"5\", \"expected\": \"10\", \"passed\": false}, {\"check\": \"regression 8\", \"actual\": \"7/3\", \"expected\": \"7\", \"passed\": false}, {\"check\": \"variable group balance\", \"actual\": \"3/2\", \"expected\": \"5/2\", \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":45.986,"exit_code":1,"observations":[{"actual":"21/2","check":"regression 1","expected":"37/4","passed":false},{"actual":"13","check":"regression 2","expected":"21/2","passed":false},{"actual":null,"check":"regression 3","expected":null,"passed":true},{"actual":null,"check":"regression 4","expected":null,"passed":true},{"actual":"7","check":"regression 5","expected":"7/2","passed":false},{"actual":"13/2","check":"regression 6","expected":"5/2","passed":false},{"actual":"10","check":"regression 7","expected":"10","passed":true},{"actual":"7","check":"regression 8","expected":"7","passed":true},{"actual":"3","check":"variable group balance","expected":"5/2","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": \"21/2\", \"expected\": \"37/4\", \"passed\": false}, {\"check\": \"regression 2\", \"actual\": \"13\", \"expected\": \"21/2\", \"passed\": false}, {\"check\": \"regression 3\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression 4\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression 5\", \"actual\": \"7\", \"expected\": \"7/2\", \"passed\": false}, {\"check\": \"regression 6\", \"actual\": \"13/2\", \"expected\": \"5/2\", \"passed\": false}, {\"check\": \"regression 7\", \"actual\": \"10\", \"expected\": \"10\", \"passed\": true}, {\"check\": \"regression 8\", \"actual\": \"7\", \"expected\": \"7\", \"passed\": true}, {\"check\": \"variable group balance\", \"actual\": \"3\", \"expected\": \"5/2\", \"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."}}