{"abstract":"The exact bareiss determinant result violates the stated contract at row interchange parity.","category":"Numerics","checks":8,"contract":"Input nonempty square integer matrix; return exact determinant using pivoted fraction-free elimination.","contract_signature":"x","evaluation_group":"s3-numerics-bareiss-determinant","failed_approach":"The partial repair -1 still violates the row interchange parity invariant.","family":"s3-numerics-bareiss-determinant-row-interchange-parity","id":"FA-15351","implementations":{"attempt":{"sha256":"815c644afe6cd123419a7720402b29dd67a3a32810c2b4c7d76ac090f3c28790","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport itertools\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    a=[r[:] for r in x];n=len(a);prev=1;sign=1\n    for k in range(n-1):\n     pivot=next((i for i in range(k,n) if a[i][k]!=0),None)\n     if pivot is None:return 0\n     if pivot!=k:\n      a[k],a[pivot]=a[pivot],a[k]\n      sign=-1\n     for i in range(k+1,n):\n      for j in range(k+1,n):a[i][j]=(a[i][j]*a[k][k]-a[i][k]*a[k][j])//prev\n     prev=a[k][k]\n     if not prev:return None\n     for i in range(k+1,n):a[i][k]=0\n    return sign*a[-1][-1]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([[0, -3], [1, -2]], 3), ([[0, 0, -2], [-2, 3, 0], [1, -2, 0]], -2), ([[-1]], -1), ([[-1, -1, 0, 3], [-3, 1, -2, 2], [0, -1, 1, 2], [-3, 2, -3, -2]], 4), ([[2]], 2), ([[2]], 2), ([[1]], 1), ([[3]], 3)], [([[0, 1], [2, 0]], -2), ([[-2, -2, -2, 2], [0, 0, 0, 3], [-3, -1, 0, -2], [3, -3, 2, 1]], -96), ([[-1]], -1), ([[-1, -1, 0, 3], [-3, 1, -2, 2], [0, -1, 1, 2], [-3, 2, -3, -2]], 4), ([[-3]], -3), ([[1]], 1), ([[3]], 3), ([[2]], 2)], [([[0, 1], [3, 3]], -3), ([[0, 0, -2], [-2, 3, 0], [1, -2, 0]], -2), ([[-1]], -1), ([[-1, -1, 0, 3], [-3, 1, -2, 2], [0, -1, 1, 2], [-3, 2, -3, -2]], 4), ([[3]], 3), ([[-2]], -2), ([[-1]], -1), ([[-3]], -3)], [([[0, -3], [2, 1]], 6), ([[-2, -2, -2, 2], [0, 0, 0, 3], [-3, -1, 0, -2], [3, -3, 2, 1]], -96), ([[-1]], -1), ([[-1, -1, 0, 3], [-3, 1, -2, 2], [0, -1, 1, 2], [-3, 2, -3, -2]], 4), ([[2]], 2), ([[-2]], -2), ([[2]], 2), ([[2]], 2)], [([[0, 2], [3, 3]], -6), ([[0, 0, -2], [-2, 3, 0], [1, -2, 0]], -2), ([[-1]], -1), ([[-1, -1, 0, 3], [-3, 1, -2, 2], [0, -1, 1, 2], [-3, 2, -3, -2]], 4), ([[-1, 0], [-3, -2]], 2), ([[0, 3], [0, -3]], 0), ([[-1, 0], [1, 2]], -2), ([[-2, 0], [-2, 0]], 0)]]\nfor i, (args, expected) in enumerate(fixtures[N-1]):\n    check(\"explicit oracle %d\" % i, solve(args), expected)\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":"8c8b6a42f8b67b26f8788fef2f74a688b48fa9e78ccd88c5f2d44e9d1432b19c","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport itertools\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    a=[r[:] for r in x];n=len(a);prev=1;sign=1\n    for k in range(n-1):\n     pivot=next((i for i in range(k,n) if a[i][k]!=0),None)\n     if pivot is None:return 0\n     if pivot!=k:\n      a[k],a[pivot]=a[pivot],a[k]\n      sign=sign\n     for i in range(k+1,n):\n      for j in range(k+1,n):a[i][j]=(a[i][j]*a[k][k]-a[i][k]*a[k][j])//prev\n     prev=a[k][k]\n     if not prev:return None\n     for i in range(k+1,n):a[i][k]=0\n    return sign*a[-1][-1]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([[0, -3], [1, -2]], 3), ([[0, 0, -2], [-2, 3, 0], [1, -2, 0]], -2), ([[-1]], -1), ([[-1, -1, 0, 3], [-3, 1, -2, 2], [0, -1, 1, 2], [-3, 2, -3, -2]], 4), ([[2]], 2), ([[2]], 2), ([[1]], 1), ([[3]], 3)], [([[0, 1], [2, 0]], -2), ([[-2, -2, -2, 2], [0, 0, 0, 3], [-3, -1, 0, -2], [3, -3, 2, 1]], -96), ([[-1]], -1), ([[-1, -1, 0, 3], [-3, 1, -2, 2], [0, -1, 1, 2], [-3, 2, -3, -2]], 4), ([[-3]], -3), ([[1]], 1), ([[3]], 3), ([[2]], 2)], [([[0, 1], [3, 3]], -3), ([[0, 0, -2], [-2, 3, 0], [1, -2, 0]], -2), ([[-1]], -1), ([[-1, -1, 0, 3], [-3, 1, -2, 2], [0, -1, 1, 2], [-3, 2, -3, -2]], 4), ([[3]], 3), ([[-2]], -2), ([[-1]], -1), ([[-3]], -3)], [([[0, -3], [2, 1]], 6), ([[-2, -2, -2, 2], [0, 0, 0, 3], [-3, -1, 0, -2], [3, -3, 2, 1]], -96), ([[-1]], -1), ([[-1, -1, 0, 3], [-3, 1, -2, 2], [0, -1, 1, 2], [-3, 2, -3, -2]], 4), ([[2]], 2), ([[-2]], -2), ([[2]], 2), ([[2]], 2)], [([[0, 2], [3, 3]], -6), ([[0, 0, -2], [-2, 3, 0], [1, -2, 0]], -2), ([[-1]], -1), ([[-1, -1, 0, 3], [-3, 1, -2, 2], [0, -1, 1, 2], [-3, 2, -3, -2]], 4), ([[-1, 0], [-3, -2]], 2), ([[0, 3], [0, -3]], 0), ([[-1, 0], [1, 2]], -2), ([[-2, 0], [-2, 0]], 0)]]\nfor i, (args, expected) in enumerate(fixtures[N-1]):\n    check(\"explicit oracle %d\" % i, solve(args), expected)\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":"A deterministic bounded teaching model. Inputs are restricted to the explicit contract; this is not a production algebra library. 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-numerics-bareiss-determinant-row-interchange-parity","generated_at":"2026-09-29T14:39:25.977715+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Exact discrete arithmetic with observable algorithmic state; no floating point approximation is used.","root_cause":"The row interchange parity step uses sign instead of -sign.","sha256":"720e1d590f559affab9f7dbd8d3ccc71be5337d7d1dcb032ae5679b1625f04bd","title":"Bareiss determinant: row interchange parity · 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":43.632,"exit_code":1,"observations":[{"actual":3,"check":"explicit oracle 0","expected":3,"passed":true},{"actual":2,"check":"explicit oracle 1","expected":-2,"passed":false},{"actual":-1,"check":"explicit oracle 2","expected":-1,"passed":true},{"actual":4,"check":"explicit oracle 3","expected":4,"passed":true},{"actual":2,"check":"explicit oracle 4","expected":2,"passed":true},{"actual":2,"check":"explicit oracle 5","expected":2,"passed":true},{"actual":1,"check":"explicit oracle 6","expected":1,"passed":true},{"actual":3,"check":"explicit oracle 7","expected":3,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": 3, \"expected\": 3, \"passed\": true}, {\"check\": \"explicit oracle 1\", \"actual\": 2, \"expected\": -2, \"passed\": false}, {\"check\": \"explicit oracle 2\", \"actual\": -1, \"expected\": -1, \"passed\": true}, {\"check\": \"explicit oracle 3\", \"actual\": 4, \"expected\": 4, \"passed\": true}, {\"check\": \"explicit oracle 4\", \"actual\": 2, \"expected\": 2, \"passed\": true}, {\"check\": \"explicit oracle 5\", \"actual\": 2, \"expected\": 2, \"passed\": true}, {\"check\": \"explicit oracle 6\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"explicit oracle 7\", \"actual\": 3, \"expected\": 3, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":43.614,"exit_code":1,"observations":[{"actual":-3,"check":"explicit oracle 0","expected":3,"passed":false},{"actual":-2,"check":"explicit oracle 1","expected":-2,"passed":true},{"actual":-1,"check":"explicit oracle 2","expected":-1,"passed":true},{"actual":4,"check":"explicit oracle 3","expected":4,"passed":true},{"actual":2,"check":"explicit oracle 4","expected":2,"passed":true},{"actual":2,"check":"explicit oracle 5","expected":2,"passed":true},{"actual":1,"check":"explicit oracle 6","expected":1,"passed":true},{"actual":3,"check":"explicit oracle 7","expected":3,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": -3, \"expected\": 3, \"passed\": false}, {\"check\": \"explicit oracle 1\", \"actual\": -2, \"expected\": -2, \"passed\": true}, {\"check\": \"explicit oracle 2\", \"actual\": -1, \"expected\": -1, \"passed\": true}, {\"check\": \"explicit oracle 3\", \"actual\": 4, \"expected\": 4, \"passed\": true}, {\"check\": \"explicit oracle 4\", \"actual\": 2, \"expected\": 2, \"passed\": true}, {\"check\": \"explicit oracle 5\", \"actual\": 2, \"expected\": 2, \"passed\": true}, {\"check\": \"explicit oracle 6\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"explicit oracle 7\", \"actual\": 3, \"expected\": 3, \"passed\": true}], \"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."}}