{"abstract":"The exact continued fraction convergents result violates the stated contract at denominator seeds.","category":"Numerics","checks":8,"contract":"Input nonempty coefficients with positive terms after first; return every convergent as [numerator,positive denominator].","contract_signature":"x","evaluation_group":"s3-numerics-continued-fraction-convergents","failed_approach":"The partial repair 1,1 still violates the denominator seeds invariant.","family":"s3-numerics-continued-fraction-convergents-denominator-seeds","id":"FA-14446","implementations":{"attempt":{"sha256":"664f7564e287ef49d3950ef952f6118b4b05b138c5448427ae499014a72e484e","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=x\n    p0,p1=0,1\n    q0,q1=1,1\n    out=[]\n    for c in a:\n     p=c*p1+p0\n     q=c*q1+q0\n     out.append([p,q])\n     p0,p1,q0,q1=p1,p,q1,q\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([2], [[2, 1]]), ([1], [[1, 1]]), ([-2, 3, 4], [[-2, 1], [-5, 3], [-22, 13]]), ([3], [[3, 1]]), ([4], [[4, 1]]), ([1, 1], [[1, 1], [2, 1]]), ([1, 2], [[1, 1], [3, 2]]), ([1, 3], [[1, 1], [4, 3]])], [([3], [[3, 1]]), ([4], [[4, 1]]), ([1], [[1, 1]]), ([-2, 3, 4], [[-2, 1], [-5, 3], [-22, 13]]), ([4, 2], [[4, 1], [9, 2]]), ([4, 3], [[4, 1], [13, 3]]), ([4, 4], [[4, 1], [17, 4]]), ([1, 1, 1], [[1, 1], [2, 1], [3, 2]])], [([4], [[4, 1]]), ([1, 3], [[1, 1], [4, 3]]), ([1], [[1, 1]]), ([-2, 3, 4], [[-2, 1], [-5, 3], [-22, 13]]), ([1, 4, 3], [[1, 1], [5, 4], [16, 13]]), ([1, 4, 4], [[1, 1], [5, 4], [21, 17]]), ([2, 1, 1], [[2, 1], [3, 1], [5, 2]]), ([2, 1, 2], [[2, 1], [3, 1], [8, 3]])], [([1, 1], [[1, 1], [2, 1]]), ([2, 2], [[2, 1], [5, 2]]), ([1], [[1, 1]]), ([-2, 3, 4], [[-2, 1], [-5, 3], [-22, 13]]), ([2, 4, 4], [[2, 1], [9, 4], [38, 17]]), ([3, 1, 1], [[3, 1], [4, 1], [7, 2]]), ([3, 1, 2], [[3, 1], [4, 1], [11, 3]]), ([3, 1, 3], [[3, 1], [4, 1], [15, 4]])], [([1, 2], [[1, 1], [3, 2]]), ([3, 1], [[3, 1], [4, 1]]), ([1], [[1, 1]]), ([-2, 3, 4], [[-2, 1], [-5, 3], [-22, 13]]), ([4, 1, 1], [[4, 1], [5, 1], [9, 2]]), ([4, 1, 2], [[4, 1], [5, 1], [14, 3]]), ([4, 1, 3], [[4, 1], [5, 1], [19, 4]]), ([4, 1, 4], [[4, 1], [5, 1], [24, 5]])]]\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":"f88eaa56491a2fc6cf9291bb874b04a3fa00b0fba456afcfbbc19a43e57f0b94","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=x\n    p0,p1=0,1\n    q0,q1=0,1\n    out=[]\n    for c in a:\n     p=c*p1+p0\n     q=c*q1+q0\n     out.append([p,q])\n     p0,p1,q0,q1=p1,p,q1,q\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([2], [[2, 1]]), ([1], [[1, 1]]), ([-2, 3, 4], [[-2, 1], [-5, 3], [-22, 13]]), ([3], [[3, 1]]), ([4], [[4, 1]]), ([1, 1], [[1, 1], [2, 1]]), ([1, 2], [[1, 1], [3, 2]]), ([1, 3], [[1, 1], [4, 3]])], [([3], [[3, 1]]), ([4], [[4, 1]]), ([1], [[1, 1]]), ([-2, 3, 4], [[-2, 1], [-5, 3], [-22, 13]]), ([4, 2], [[4, 1], [9, 2]]), ([4, 3], [[4, 1], [13, 3]]), ([4, 4], [[4, 1], [17, 4]]), ([1, 1, 1], [[1, 1], [2, 1], [3, 2]])], [([4], [[4, 1]]), ([1, 3], [[1, 1], [4, 3]]), ([1], [[1, 1]]), ([-2, 3, 4], [[-2, 1], [-5, 3], [-22, 13]]), ([1, 4, 3], [[1, 1], [5, 4], [16, 13]]), ([1, 4, 4], [[1, 1], [5, 4], [21, 17]]), ([2, 1, 1], [[2, 1], [3, 1], [5, 2]]), ([2, 1, 2], [[2, 1], [3, 1], [8, 3]])], [([1, 1], [[1, 1], [2, 1]]), ([2, 2], [[2, 1], [5, 2]]), ([1], [[1, 1]]), ([-2, 3, 4], [[-2, 1], [-5, 3], [-22, 13]]), ([2, 4, 4], [[2, 1], [9, 4], [38, 17]]), ([3, 1, 1], [[3, 1], [4, 1], [7, 2]]), ([3, 1, 2], [[3, 1], [4, 1], [11, 3]]), ([3, 1, 3], [[3, 1], [4, 1], [15, 4]])], [([1, 2], [[1, 1], [3, 2]]), ([3, 1], [[3, 1], [4, 1]]), ([1], [[1, 1]]), ([-2, 3, 4], [[-2, 1], [-5, 3], [-22, 13]]), ([4, 1, 1], [[4, 1], [5, 1], [9, 2]]), ([4, 1, 2], [[4, 1], [5, 1], [14, 3]]), ([4, 1, 3], [[4, 1], [5, 1], [19, 4]]), ([4, 1, 4], [[4, 1], [5, 1], [24, 5]])]]\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-continued-fraction-convergents-denominator-seeds","generated_at":"2026-09-29T14:39:17.044383+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 denominator seeds step uses 0,1 instead of 1,0.","sha256":"1c9e1b79c92d1a5532f177fea1f34fe35b0444d38135567b846ad463686d227c","title":"Continued fraction convergents: denominator seeds · 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":43.921,"exit_code":1,"observations":[{"actual":[[2,3]],"check":"explicit oracle 0","expected":[[2,1]],"passed":false},{"actual":[[1,2]],"check":"explicit oracle 1","expected":[[1,1]],"passed":false},{"actual":[[-2,-1],[-5,-2],[-22,-9]],"check":"explicit oracle 2","expected":[[-2,1],[-5,3],[-22,13]],"passed":false},{"actual":[[3,4]],"check":"explicit oracle 3","expected":[[3,1]],"passed":false},{"actual":[[4,5]],"check":"explicit oracle 4","expected":[[4,1]],"passed":false},{"actual":[[1,2],[2,3]],"check":"explicit oracle 5","expected":[[1,1],[2,1]],"passed":false},{"actual":[[1,2],[3,5]],"check":"explicit oracle 6","expected":[[1,1],[3,2]],"passed":false},{"actual":[[1,2],[4,7]],"check":"explicit oracle 7","expected":[[1,1],[4,3]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": [[2, 3]], \"expected\": [[2, 1]], \"passed\": false}, {\"check\": \"explicit oracle 1\", \"actual\": [[1, 2]], \"expected\": [[1, 1]], \"passed\": false}, {\"check\": \"explicit oracle 2\", \"actual\": [[-2, -1], [-5, -2], [-22, -9]], \"expected\": [[-2, 1], [-5, 3], [-22, 13]], \"passed\": false}, {\"check\": \"explicit oracle 3\", \"actual\": [[3, 4]], \"expected\": [[3, 1]], \"passed\": false}, {\"check\": \"explicit oracle 4\", \"actual\": [[4, 5]], \"expected\": [[4, 1]], \"passed\": false}, {\"check\": \"explicit oracle 5\", \"actual\": [[1, 2], [2, 3]], \"expected\": [[1, 1], [2, 1]], \"passed\": false}, {\"check\": \"explicit oracle 6\", \"actual\": [[1, 2], [3, 5]], \"expected\": [[1, 1], [3, 2]], \"passed\": false}, {\"check\": \"explicit oracle 7\", \"actual\": [[1, 2], [4, 7]], \"expected\": [[1, 1], [4, 3]], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":41.715,"exit_code":1,"observations":[{"actual":[[2,2]],"check":"explicit oracle 0","expected":[[2,1]],"passed":false},{"actual":[[1,1]],"check":"explicit oracle 1","expected":[[1,1]],"passed":true},{"actual":[[-2,-2],[-5,-5],[-22,-22]],"check":"explicit oracle 2","expected":[[-2,1],[-5,3],[-22,13]],"passed":false},{"actual":[[3,3]],"check":"explicit oracle 3","expected":[[3,1]],"passed":false},{"actual":[[4,4]],"check":"explicit oracle 4","expected":[[4,1]],"passed":false},{"actual":[[1,1],[2,2]],"check":"explicit oracle 5","expected":[[1,1],[2,1]],"passed":false},{"actual":[[1,1],[3,3]],"check":"explicit oracle 6","expected":[[1,1],[3,2]],"passed":false},{"actual":[[1,1],[4,4]],"check":"explicit oracle 7","expected":[[1,1],[4,3]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": [[2, 2]], \"expected\": [[2, 1]], \"passed\": false}, {\"check\": \"explicit oracle 1\", \"actual\": [[1, 1]], \"expected\": [[1, 1]], \"passed\": true}, {\"check\": \"explicit oracle 2\", \"actual\": [[-2, -2], [-5, -5], [-22, -22]], \"expected\": [[-2, 1], [-5, 3], [-22, 13]], \"passed\": false}, {\"check\": \"explicit oracle 3\", \"actual\": [[3, 3]], \"expected\": [[3, 1]], \"passed\": false}, {\"check\": \"explicit oracle 4\", \"actual\": [[4, 4]], \"expected\": [[4, 1]], \"passed\": false}, {\"check\": \"explicit oracle 5\", \"actual\": [[1, 1], [2, 2]], \"expected\": [[1, 1], [2, 1]], \"passed\": false}, {\"check\": \"explicit oracle 6\", \"actual\": [[1, 1], [3, 3]], \"expected\": [[1, 1], [3, 2]], \"passed\": false}, {\"check\": \"explicit oracle 7\", \"actual\": [[1, 1], [4, 4]], \"expected\": [[1, 1], [4, 3]], \"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."}}