{"abstract":"The reduction disagrees with its explicit aggregation oracle.","category":"Numerical aggregation","checks":8,"contract":"Each row holds two integer values or None. Include a row only when both values are observed; zero is observed. Return [paired count, x sum, y sum, cross-product sum, squared-distance sum]. No imputation and no marginal-only contributions.","contract_signature":"rows","evaluation_group":"s3-na-jointly-observed-pair-summary","failed_approach":"Absolute net residual also permits cancellation and loses squared distance.","family":"s3-numerical-aggregation-jointly-observed-pair-summary-pair-distance-of-totals","id":"FA-14181","implementations":{"attempt":{"sha256":"d03d828721f30b8a3de35937465b767c6a30e5989a1fcb7f247980474619d310","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    pairs=[(x,y) for x,y in rows if x is not None and y is not None]\n    return [len(pairs),sum(x for x,y in pairs),sum(y for x,y in pairs),sum(x*y for x,y in pairs),abs(sum(x-y for x,y in pairs))]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([(1, 2), (None, 9), (3, None), (0, 4)],)), [2, 1, 6, 2, 17])\ncheck('regression 2', solve(*([],)), [0, 0, 0, 0, 0])\ncheck('regression 3', solve(*([(None, None)],)), [0, 0, 0, 0, 0])\ncheck('regression 4', solve(*([(-2, 3), (4, -1), (0, 0)],)), [3, 2, 2, -10, 50])\ncheck('regression 5', solve(*([(3, 3), (3, 3), (None, 4)],)), [2, 6, 6, 18, 0])\ncheck('regression 6', solve(*([(0, 2), (2, 0)],)), [2, 2, 2, 0, 8])\ncheck('regression 7', solve(*([(5, None), (None, 6)],)), [0, 0, 0, 0, 0])\ncheck(\"variable complete pair\",solve([(N,2*N),(None,N),(0,N)]),[2,N,3*N,2*N*N,2*N*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":"236a669b3ac48a8ceec406ff127c9b60c6bd24b1f775ddc3cd23349f582a06f8","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    pairs=[(x,y) for x,y in rows if x is not None and y is not None]\n    return [len(pairs),sum(x for x,y in pairs),sum(y for x,y in pairs),sum(x*y for x,y in pairs),sum(x-y for x,y in pairs)**2]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([(1, 2), (None, 9), (3, None), (0, 4)],)), [2, 1, 6, 2, 17])\ncheck('regression 2', solve(*([],)), [0, 0, 0, 0, 0])\ncheck('regression 3', solve(*([(None, None)],)), [0, 0, 0, 0, 0])\ncheck('regression 4', solve(*([(-2, 3), (4, -1), (0, 0)],)), [3, 2, 2, -10, 50])\ncheck('regression 5', solve(*([(3, 3), (3, 3), (None, 4)],)), [2, 6, 6, 18, 0])\ncheck('regression 6', solve(*([(0, 2), (2, 0)],)), [2, 2, 2, 0, 8])\ncheck('regression 7', solve(*([(5, None), (None, 6)],)), [0, 0, 0, 0, 0])\ncheck(\"variable complete pair\",solve([(N,2*N),(None,N),(0,N)]),[2,N,3*N,2*N*N,2*N*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-jointly-observed-pair-summary-pair-distance-of-totals","generated_at":"2026-09-29T14:39:14.395175+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 distance is computed after summing residuals.","sha256":"a305a8c7888d74c2d49b543c4fb1e7fc863afb4dcb038d1bf7c7a5bf436b28d2","title":"Jointly observed pair summary: Squared distance is computed after summing residuals. · 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":43.253,"exit_code":1,"observations":[{"actual":[2,1,6,2,5],"check":"regression 1","expected":[2,1,6,2,17],"passed":false},{"actual":[0,0,0,0,0],"check":"regression 2","expected":[0,0,0,0,0],"passed":true},{"actual":[0,0,0,0,0],"check":"regression 3","expected":[0,0,0,0,0],"passed":true},{"actual":[3,2,2,-10,0],"check":"regression 4","expected":[3,2,2,-10,50],"passed":false},{"actual":[2,6,6,18,0],"check":"regression 5","expected":[2,6,6,18,0],"passed":true},{"actual":[2,2,2,0,0],"check":"regression 6","expected":[2,2,2,0,8],"passed":false},{"actual":[0,0,0,0,0],"check":"regression 7","expected":[0,0,0,0,0],"passed":true},{"actual":[2,1,3,2,2],"check":"variable complete pair","expected":[2,1,3,2,2],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": [2, 1, 6, 2, 5], \"expected\": [2, 1, 6, 2, 17], \"passed\": false}, {\"check\": \"regression 2\", \"actual\": [0, 0, 0, 0, 0], \"expected\": [0, 0, 0, 0, 0], \"passed\": true}, {\"check\": \"regression 3\", \"actual\": [0, 0, 0, 0, 0], \"expected\": [0, 0, 0, 0, 0], \"passed\": true}, {\"check\": \"regression 4\", \"actual\": [3, 2, 2, -10, 0], \"expected\": [3, 2, 2, -10, 50], \"passed\": false}, {\"check\": \"regression 5\", \"actual\": [2, 6, 6, 18, 0], \"expected\": [2, 6, 6, 18, 0], \"passed\": true}, {\"check\": \"regression 6\", \"actual\": [2, 2, 2, 0, 0], \"expected\": [2, 2, 2, 0, 8], \"passed\": false}, {\"check\": \"regression 7\", \"actual\": [0, 0, 0, 0, 0], \"expected\": [0, 0, 0, 0, 0], \"passed\": true}, {\"check\": \"variable complete pair\", \"actual\": [2, 1, 3, 2, 2], \"expected\": [2, 1, 3, 2, 2], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":45.617,"exit_code":1,"observations":[{"actual":[2,1,6,2,25],"check":"regression 1","expected":[2,1,6,2,17],"passed":false},{"actual":[0,0,0,0,0],"check":"regression 2","expected":[0,0,0,0,0],"passed":true},{"actual":[0,0,0,0,0],"check":"regression 3","expected":[0,0,0,0,0],"passed":true},{"actual":[3,2,2,-10,0],"check":"regression 4","expected":[3,2,2,-10,50],"passed":false},{"actual":[2,6,6,18,0],"check":"regression 5","expected":[2,6,6,18,0],"passed":true},{"actual":[2,2,2,0,0],"check":"regression 6","expected":[2,2,2,0,8],"passed":false},{"actual":[0,0,0,0,0],"check":"regression 7","expected":[0,0,0,0,0],"passed":true},{"actual":[2,1,3,2,4],"check":"variable complete pair","expected":[2,1,3,2,2],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": [2, 1, 6, 2, 25], \"expected\": [2, 1, 6, 2, 17], \"passed\": false}, {\"check\": \"regression 2\", \"actual\": [0, 0, 0, 0, 0], \"expected\": [0, 0, 0, 0, 0], \"passed\": true}, {\"check\": \"regression 3\", \"actual\": [0, 0, 0, 0, 0], \"expected\": [0, 0, 0, 0, 0], \"passed\": true}, {\"check\": \"regression 4\", \"actual\": [3, 2, 2, -10, 0], \"expected\": [3, 2, 2, -10, 50], \"passed\": false}, {\"check\": \"regression 5\", \"actual\": [2, 6, 6, 18, 0], \"expected\": [2, 6, 6, 18, 0], \"passed\": true}, {\"check\": \"regression 6\", \"actual\": [2, 2, 2, 0, 0], \"expected\": [2, 2, 2, 0, 8], \"passed\": false}, {\"check\": \"regression 7\", \"actual\": [0, 0, 0, 0, 0], \"expected\": [0, 0, 0, 0, 0], \"passed\": true}, {\"check\": \"variable complete pair\", \"actual\": [2, 1, 3, 2, 4], \"expected\": [2, 1, 3, 2, 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."}}