{"abstract":"The reduction disagrees with its explicit aggregation oracle.","category":"Numerical aggregation","checks":8,"contract":"For a rectangular nonnegative integer count table, return the Pearson sum of (observed-expected)^2/expected under independence, with expected=row marginal*column marginal/grand total. Zero expected cells contribute zero; empty or zero-total tables return \"0\". Exact Fraction string; no inferential p-value claim.","evaluation_group":"s3-na-contingency-pearson-reduction","failed_approach":"A fractional pseudocount still adds evidence where no marginal mass exists.","family":"s3-numerical-aggregation-contingency-pearson-reduction-pearson-zero-marginal","id":"FA-13706","implementations":{"attempt":{"sha256":"7df3e6fe13fd371844afc19c7fc77fb3c74f0558f06ce1520af5ce0cadece6ab","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(table):\n    n=len(table)\n    m=len(table[0]) if n else 0\n    rows=[sum(r) for r in table]\n    cols=[sum(table[i][j] for i in range(n)) for j in range(m)]\n    total=sum(rows)\n    if not total: return \"0\"\n    stat=Fraction(0)\n    for i in range(n):\n        for j in range(m):\n            expected=Fraction(rows[i]*cols[j],total)\n            if expected==0:\n                stat+=Fraction(1,max(1,total))\n                continue\n            stat+=(table[i][j]-expected)**2/expected\n    return str(stat)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([[4, 0], [0, 4]],)), '8')\ncheck('regression 2', solve(*([[2, 3], [4, 6]],)), '0')\ncheck('regression 3', solve(*([],)), '0')\ncheck('regression 4', solve(*([[0, 0], [0, 0]],)), '0')\ncheck('regression 5', solve(*([[2, 0, 1], [3, 4, 0]],)), '30/7')\ncheck('regression 6', solve(*([[0, 0, 0], [1, 2, 3]],)), '0')\ncheck('regression 7', solve(*([[1, 2], [3, 0], [2, 4]],)), '4')\ncheck(\"variable diagonal mass\",solve([[N,0],[0,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":"ea1da584faa23b0b1056115c4e72f63d9bd40a50f34ce8855bce4b0725e78fc5","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(table):\n    n=len(table)\n    m=len(table[0]) if n else 0\n    rows=[sum(r) for r in table]\n    cols=[sum(table[i][j] for i in range(n)) for j in range(m)]\n    total=sum(rows)\n    if not total: return \"0\"\n    stat=Fraction(0)\n    for i in range(n):\n        for j in range(m):\n            expected=Fraction(rows[i]*cols[j],total)\n            if expected==0:\n                stat+=1\n                continue\n            stat+=(table[i][j]-expected)**2/expected\n    return str(stat)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([[4, 0], [0, 4]],)), '8')\ncheck('regression 2', solve(*([[2, 3], [4, 6]],)), '0')\ncheck('regression 3', solve(*([],)), '0')\ncheck('regression 4', solve(*([[0, 0], [0, 0]],)), '0')\ncheck('regression 5', solve(*([[2, 0, 1], [3, 4, 0]],)), '30/7')\ncheck('regression 6', solve(*([[0, 0, 0], [1, 2, 3]],)), '0')\ncheck('regression 7', solve(*([[1, 2], [3, 0], [2, 4]],)), '4')\ncheck(\"variable diagonal mass\",solve([[N,0],[0,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"},"fixed":{"sha256":"a542bad753b06822356152fad5fc9b485291a2b7e3697bb4d919b633d8619773","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(table):\n    n=len(table)\n    m=len(table[0]) if n else 0\n    rows=[sum(r) for r in table]\n    cols=[sum(table[i][j] for i in range(n)) for j in range(m)]\n    total=sum(rows)\n    if not total: return \"0\"\n    stat=Fraction(0)\n    for i in range(n):\n        for j in range(m):\n            expected=Fraction(rows[i]*cols[j],total)\n            if expected==0: continue\n            stat+=(table[i][j]-expected)**2/expected\n    return str(stat)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('regression 1', solve(*([[4, 0], [0, 4]],)), '8')\ncheck('regression 2', solve(*([[2, 3], [4, 6]],)), '0')\ncheck('regression 3', solve(*([],)), '0')\ncheck('regression 4', solve(*([[0, 0], [0, 0]],)), '0')\ncheck('regression 5', solve(*([[2, 0, 1], [3, 4, 0]],)), '30/7')\ncheck('regression 6', solve(*([[0, 0, 0], [1, 2, 3]],)), '0')\ncheck('regression 7', solve(*([[1, 2], [3, 0], [2, 4]],)), '4')\ncheck(\"variable diagonal mass\",solve([[N,0],[0,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-contingency-pearson-reduction-pearson-zero-marginal","generated_at":"2026-09-29T14:39:09.680241+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.","repair":"Preserve the contingency pearson reduction contract at the identified reduction decision.","root_cause":"A zero expected cell is assigned a unit discrepancy.","sha256":"7f41b6a6e29f31a7a9b84f1c09dccb7d660b985bef56e125b31e6f5bb8e348fe","title":"Contingency pearson reduction: A zero expected cell is assigned a unit discrepancy. · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":44.526,"exit_code":1,"observations":[{"actual":"8","check":"regression 1","expected":"8","passed":true},{"actual":"0","check":"regression 2","expected":"0","passed":true},{"actual":"0","check":"regression 3","expected":"0","passed":true},{"actual":"0","check":"regression 4","expected":"0","passed":true},{"actual":"30/7","check":"regression 5","expected":"30/7","passed":true},{"actual":"1/2","check":"regression 6","expected":"0","passed":false},{"actual":"4","check":"regression 7","expected":"4","passed":true},{"actual":"2","check":"variable diagonal mass","expected":"2","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": \"8\", \"expected\": \"8\", \"passed\": true}, {\"check\": \"regression 2\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 3\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 4\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 5\", \"actual\": \"30/7\", \"expected\": \"30/7\", \"passed\": true}, {\"check\": \"regression 6\", \"actual\": \"1/2\", \"expected\": \"0\", \"passed\": false}, {\"check\": \"regression 7\", \"actual\": \"4\", \"expected\": \"4\", \"passed\": true}, {\"check\": \"variable diagonal mass\", \"actual\": \"2\", \"expected\": \"2\", \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":42.496,"exit_code":1,"observations":[{"actual":"8","check":"regression 1","expected":"8","passed":true},{"actual":"0","check":"regression 2","expected":"0","passed":true},{"actual":"0","check":"regression 3","expected":"0","passed":true},{"actual":"0","check":"regression 4","expected":"0","passed":true},{"actual":"30/7","check":"regression 5","expected":"30/7","passed":true},{"actual":"3","check":"regression 6","expected":"0","passed":false},{"actual":"4","check":"regression 7","expected":"4","passed":true},{"actual":"2","check":"variable diagonal mass","expected":"2","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": \"8\", \"expected\": \"8\", \"passed\": true}, {\"check\": \"regression 2\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 3\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 4\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 5\", \"actual\": \"30/7\", \"expected\": \"30/7\", \"passed\": true}, {\"check\": \"regression 6\", \"actual\": \"3\", \"expected\": \"0\", \"passed\": false}, {\"check\": \"regression 7\", \"actual\": \"4\", \"expected\": \"4\", \"passed\": true}, {\"check\": \"variable diagonal mass\", \"actual\": \"2\", \"expected\": \"2\", \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":46.233,"exit_code":0,"observations":[{"actual":"8","check":"regression 1","expected":"8","passed":true},{"actual":"0","check":"regression 2","expected":"0","passed":true},{"actual":"0","check":"regression 3","expected":"0","passed":true},{"actual":"0","check":"regression 4","expected":"0","passed":true},{"actual":"30/7","check":"regression 5","expected":"30/7","passed":true},{"actual":"0","check":"regression 6","expected":"0","passed":true},{"actual":"4","check":"regression 7","expected":"4","passed":true},{"actual":"2","check":"variable diagonal mass","expected":"2","passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression 1\", \"actual\": \"8\", \"expected\": \"8\", \"passed\": true}, {\"check\": \"regression 2\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 3\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 4\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 5\", \"actual\": \"30/7\", \"expected\": \"30/7\", \"passed\": true}, {\"check\": \"regression 6\", \"actual\": \"0\", \"expected\": \"0\", \"passed\": true}, {\"check\": \"regression 7\", \"actual\": \"4\", \"expected\": \"4\", \"passed\": true}, {\"check\": \"variable diagonal mass\", \"actual\": \"2\", \"expected\": \"2\", \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}