{"abstract":"The exact calkin wilf successors result violates the stated contract at next rational denominator.","category":"Numerics","checks":8,"contract":"Input positive count k<=50; return first k reduced positive rationals in Calkin-Wilf breadth-first order.","evaluation_group":"s3-numerics-calkin-wilf-successors","failed_approach":"The partial repair (2*a+1)*q+p still violates the next rational denominator invariant.","family":"s3-numerics-calkin-wilf-successors-next-rational-denominator","id":"FA-14556","implementations":{"attempt":{"sha256":"9d6d1ea0ab6c3e2a2d70d6947019d484bf8207eeb5b239466d4981b3d79263dd","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    p,q=1,1\n    out=[]\n    for _ in range(x):\n     out.append([p,q])\n     if q==0:return None\n     a=p//q\n     den=(2*a+1)*q+p\n     p,q=q,den\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[(2, [[1, 1], [1, 2]]), (1, [[1, 1]]), (50, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10], [10, 3], [3, 11], [11, 8], [8, 13], [13, 5], [5, 12], [12, 7], [7, 9], [9, 2], [2, 9], [9, 7], [7, 12]]), (3, [[1, 1], [1, 2], [2, 1]]), (4, [[1, 1], [1, 2], [2, 1], [1, 3]]), (5, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2]]), (6, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3]]), (7, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1]])], [(3, [[1, 1], [1, 2], [2, 1]]), (5, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2]]), (1, [[1, 1]]), (50, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10], [10, 3], [3, 11], [11, 8], [8, 13], [13, 5], [5, 12], [12, 7], [7, 9], [9, 2], [2, 9], [9, 7], [7, 12]]), (18, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7]]), (19, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3]]), (20, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8]]), (21, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5]])], [(4, [[1, 1], [1, 2], [2, 1], [1, 3]]), (8, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4]]), (1, [[1, 1]]), (50, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10], [10, 3], [3, 11], [11, 8], [8, 13], [13, 5], [5, 12], [12, 7], [7, 9], [9, 2], [2, 9], [9, 7], [7, 12]]), (35, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4]]), (36, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11]]), (37, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7]]), (38, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10]])], [(5, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2]]), (11, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2]]), (1, [[1, 1]]), (50, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10], [10, 3], [3, 11], [11, 8], [8, 13], [13, 5], [5, 12], [12, 7], [7, 9], [9, 2], [2, 9], [9, 7], [7, 12]]), (2, [[1, 1], [1, 2]]), (3, [[1, 1], [1, 2], [2, 1]]), (4, [[1, 1], [1, 2], [2, 1], [1, 3]]), (6, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3]])], [(6, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3]]), (14, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4]]), (1, [[1, 1]]), (50, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10], [10, 3], [3, 11], [11, 8], [8, 13], [13, 5], [5, 12], [12, 7], [7, 9], [9, 2], [2, 9], [9, 7], [7, 12]]), (19, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3]]), (20, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8]]), (21, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5]]), (22, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7]])]]\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":"14e640100bc0451701679686d00f26def1ef9f4c6c731cc4cadf0cde94ac0024","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    p,q=1,1\n    out=[]\n    for _ in range(x):\n     out.append([p,q])\n     if q==0:return None\n     a=p//q\n     den=(a+1)*q-p\n     p,q=q,den\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[(2, [[1, 1], [1, 2]]), (1, [[1, 1]]), (50, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10], [10, 3], [3, 11], [11, 8], [8, 13], [13, 5], [5, 12], [12, 7], [7, 9], [9, 2], [2, 9], [9, 7], [7, 12]]), (3, [[1, 1], [1, 2], [2, 1]]), (4, [[1, 1], [1, 2], [2, 1], [1, 3]]), (5, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2]]), (6, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3]]), (7, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1]])], [(3, [[1, 1], [1, 2], [2, 1]]), (5, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2]]), (1, [[1, 1]]), (50, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10], [10, 3], [3, 11], [11, 8], [8, 13], [13, 5], [5, 12], [12, 7], [7, 9], [9, 2], [2, 9], [9, 7], [7, 12]]), (18, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7]]), (19, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3]]), (20, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8]]), (21, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5]])], [(4, [[1, 1], [1, 2], [2, 1], [1, 3]]), (8, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4]]), (1, [[1, 1]]), (50, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10], [10, 3], [3, 11], [11, 8], [8, 13], [13, 5], [5, 12], [12, 7], [7, 9], [9, 2], [2, 9], [9, 7], [7, 12]]), (35, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4]]), (36, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11]]), (37, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7]]), (38, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10]])], [(5, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2]]), (11, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2]]), (1, [[1, 1]]), (50, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10], [10, 3], [3, 11], [11, 8], [8, 13], [13, 5], [5, 12], [12, 7], [7, 9], [9, 2], [2, 9], [9, 7], [7, 12]]), (2, [[1, 1], [1, 2]]), (3, [[1, 1], [1, 2], [2, 1]]), (4, [[1, 1], [1, 2], [2, 1], [1, 3]]), (6, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3]])], [(6, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3]]), (14, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4]]), (1, [[1, 1]]), (50, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10], [10, 3], [3, 11], [11, 8], [8, 13], [13, 5], [5, 12], [12, 7], [7, 9], [9, 2], [2, 9], [9, 7], [7, 12]]), (19, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3]]), (20, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8]]), (21, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5]]), (22, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7]])]]\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"},"fixed":{"sha256":"6a8d326cd09756f6f2e37630cfb7a5c8daff307613c3e2207a707fa1bdf91632","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    p,q=1,1\n    out=[]\n    for _ in range(x):\n     out.append([p,q])\n     if q==0:return None\n     a=p//q\n     den=(2*a+1)*q-p\n     p,q=q,den\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[(2, [[1, 1], [1, 2]]), (1, [[1, 1]]), (50, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10], [10, 3], [3, 11], [11, 8], [8, 13], [13, 5], [5, 12], [12, 7], [7, 9], [9, 2], [2, 9], [9, 7], [7, 12]]), (3, [[1, 1], [1, 2], [2, 1]]), (4, [[1, 1], [1, 2], [2, 1], [1, 3]]), (5, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2]]), (6, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3]]), (7, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1]])], [(3, [[1, 1], [1, 2], [2, 1]]), (5, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2]]), (1, [[1, 1]]), (50, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10], [10, 3], [3, 11], [11, 8], [8, 13], [13, 5], [5, 12], [12, 7], [7, 9], [9, 2], [2, 9], [9, 7], [7, 12]]), (18, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7]]), (19, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3]]), (20, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8]]), (21, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5]])], [(4, [[1, 1], [1, 2], [2, 1], [1, 3]]), (8, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4]]), (1, [[1, 1]]), (50, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10], [10, 3], [3, 11], [11, 8], [8, 13], [13, 5], [5, 12], [12, 7], [7, 9], [9, 2], [2, 9], [9, 7], [7, 12]]), (35, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4]]), (36, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11]]), (37, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7]]), (38, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10]])], [(5, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2]]), (11, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2]]), (1, [[1, 1]]), (50, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10], [10, 3], [3, 11], [11, 8], [8, 13], [13, 5], [5, 12], [12, 7], [7, 9], [9, 2], [2, 9], [9, 7], [7, 12]]), (2, [[1, 1], [1, 2]]), (3, [[1, 1], [1, 2], [2, 1]]), (4, [[1, 1], [1, 2], [2, 1], [1, 3]]), (6, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3]])], [(6, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3]]), (14, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4]]), (1, [[1, 1]]), (50, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10], [10, 3], [3, 11], [11, 8], [8, 13], [13, 5], [5, 12], [12, 7], [7, 9], [9, 2], [2, 9], [9, 7], [7, 12]]), (19, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3]]), (20, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8]]), (21, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5]]), (22, [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7]])]]\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-calkin-wilf-successors-next-rational-denominator","generated_at":"2026-09-29T14:39:17.968138+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.","repair":"Use (2*a+1)*q-p at the next rational denominator step.","root_cause":"The next rational denominator step uses (a+1)*q-p instead of (2*a+1)*q-p.","sha256":"530a27a8eea42070ff2f28963d24927b967b6d0a0451386f97c62f50ec0a80e5","title":"Calkin wilf successors: next rational denominator · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":46.186,"exit_code":1,"observations":[{"actual":[[1,1],[1,4]],"check":"explicit oracle 0","expected":[[1,1],[1,2]],"passed":false},{"actual":[[1,1]],"check":"explicit oracle 1","expected":[[1,1]],"passed":true},{"actual":[[1,1],[1,4],[4,5],[5,9],[9,14],[14,23],[23,37],[37,60],[60,97],[97,157],[157,254],[254,411],[411,665],[665,1076],[1076,1741],[1741,2817],[2817,4558],[4558,7375],[7375,11933],[11933,19308],[19308,31241],[31241,50549],[50549,81790],[81790,132339],[132339,214129],[214129,346468],[346468,560597],[560597,907065],[907065,1467662],[1467662,2374727],[2374727,3842389],[3842389,6217116],[6217116,10059505],[10059505,16276621],[16276621,26336126],[26336126,42612747],[42612747,68948873],[68948873,111561620],[111561620,180510493],[180510493,292072113],[292072113,472582606],[472582606,764654719],[764654719,1237237325],[1237237325,2001892044],[2001892044,3239129369],[3239129369,5241021413],[5241021413,8480150782],[8480150782,13721172195],[13721172195,22201322977],[22201322977,35922495172]],"check":"explicit oracle 2","expected":[[1,1],[1,2],[2,1],[1,3],[3,2],[2,3],[3,1],[1,4],[4,3],[3,5],[5,2],[2,5],[5,3],[3,4],[4,1],[1,5],[5,4],[4,7],[7,3],[3,8],[8,5],[5,7],[7,2],[2,7],[7,5],[5,8],[8,3],[3,7],[7,4],[4,5],[5,1],[1,6],[6,5],[5,9],[9,4],[4,11],[11,7],[7,10],[10,3],[3,11],[11,8],[8,13],[13,5],[5,12],[12,7],[7,9],[9,2],[2,9],[9,7],[7,12]],"passed":false},{"actual":[[1,1],[1,4],[4,5]],"check":"explicit oracle 3","expected":[[1,1],[1,2],[2,1]],"passed":false},{"actual":[[1,1],[1,4],[4,5],[5,9]],"check":"explicit oracle 4","expected":[[1,1],[1,2],[2,1],[1,3]],"passed":false},{"actual":[[1,1],[1,4],[4,5],[5,9],[9,14]],"check":"explicit oracle 5","expected":[[1,1],[1,2],[2,1],[1,3],[3,2]],"passed":false},{"actual":[[1,1],[1,4],[4,5],[5,9],[9,14],[14,23]],"check":"explicit oracle 6","expected":[[1,1],[1,2],[2,1],[1,3],[3,2],[2,3]],"passed":false},{"actual":[[1,1],[1,4],[4,5],[5,9],[9,14],[14,23],[23,37]],"check":"explicit oracle 7","expected":[[1,1],[1,2],[2,1],[1,3],[3,2],[2,3],[3,1]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": [[1, 1], [1, 4]], \"expected\": [[1, 1], [1, 2]], \"passed\": false}, {\"check\": \"explicit oracle 1\", \"actual\": [[1, 1]], \"expected\": [[1, 1]], \"passed\": true}, {\"check\": \"explicit oracle 2\", \"actual\": [[1, 1], [1, 4], [4, 5], [5, 9], [9, 14], [14, 23], [23, 37], [37, 60], [60, 97], [97, 157], [157, 254], [254, 411], [411, 665], [665, 1076], [1076, 1741], [1741, 2817], [2817, 4558], [4558, 7375], [7375, 11933], [11933, 19308], [19308, 31241], [31241, 50549], [50549, 81790], [81790, 132339], [132339, 214129], [214129, 346468], [346468, 560597], [560597, 907065], [907065, 1467662], [1467662, 2374727], [2374727, 3842389], [3842389, 6217116], [6217116, 10059505], [10059505, 16276621], [16276621, 26336126], [26336126, 42612747], [42612747, 68948873], [68948873, 111561620], [111561620, 180510493], [180510493, 292072113], [292072113, 472582606], [472582606, 764654719], [764654719, 1237237325], [1237237325, 2001892044], [2001892044, 3239129369], [3239129369, 5241021413], [5241021413, 8480150782], [8480150782, 13721172195], [13721172195, 22201322977], [22201322977, 35922495172]], \"expected\": [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10], [10, 3], [3, 11], [11, 8], [8, 13], [13, 5], [5, 12], [12, 7], [7, 9], [9, 2], [2, 9], [9, 7], [7, 12]], \"passed\": false}, {\"check\": \"explicit oracle 3\", \"actual\": [[1, 1], [1, 4], [4, 5]], \"expected\": [[1, 1], [1, 2], [2, 1]], \"passed\": false}, {\"check\": \"explicit oracle 4\", \"actual\": [[1, 1], [1, 4], [4, 5], [5, 9]], \"expected\": [[1, 1], [1, 2], [2, 1], [1, 3]], \"passed\": false}, {\"check\": \"explicit oracle 5\", \"actual\": [[1, 1], [1, 4], [4, 5], [5, 9], [9, 14]], \"expected\": [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2]], \"passed\": false}, {\"check\": \"explicit oracle 6\", \"actual\": [[1, 1], [1, 4], [4, 5], [5, 9], [9, 14], [14, 23]], \"expected\": [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3]], \"passed\": false}, {\"check\": \"explicit oracle 7\", \"actual\": [[1, 1], [1, 4], [4, 5], [5, 9], [9, 14], [14, 23], [23, 37]], \"expected\": [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1]], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":46.828,"exit_code":1,"observations":[{"actual":[[1,1],[1,1]],"check":"explicit oracle 0","expected":[[1,1],[1,2]],"passed":false},{"actual":[[1,1]],"check":"explicit oracle 1","expected":[[1,1]],"passed":true},{"actual":[[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1]],"check":"explicit oracle 2","expected":[[1,1],[1,2],[2,1],[1,3],[3,2],[2,3],[3,1],[1,4],[4,3],[3,5],[5,2],[2,5],[5,3],[3,4],[4,1],[1,5],[5,4],[4,7],[7,3],[3,8],[8,5],[5,7],[7,2],[2,7],[7,5],[5,8],[8,3],[3,7],[7,4],[4,5],[5,1],[1,6],[6,5],[5,9],[9,4],[4,11],[11,7],[7,10],[10,3],[3,11],[11,8],[8,13],[13,5],[5,12],[12,7],[7,9],[9,2],[2,9],[9,7],[7,12]],"passed":false},{"actual":[[1,1],[1,1],[1,1]],"check":"explicit oracle 3","expected":[[1,1],[1,2],[2,1]],"passed":false},{"actual":[[1,1],[1,1],[1,1],[1,1]],"check":"explicit oracle 4","expected":[[1,1],[1,2],[2,1],[1,3]],"passed":false},{"actual":[[1,1],[1,1],[1,1],[1,1],[1,1]],"check":"explicit oracle 5","expected":[[1,1],[1,2],[2,1],[1,3],[3,2]],"passed":false},{"actual":[[1,1],[1,1],[1,1],[1,1],[1,1],[1,1]],"check":"explicit oracle 6","expected":[[1,1],[1,2],[2,1],[1,3],[3,2],[2,3]],"passed":false},{"actual":[[1,1],[1,1],[1,1],[1,1],[1,1],[1,1],[1,1]],"check":"explicit oracle 7","expected":[[1,1],[1,2],[2,1],[1,3],[3,2],[2,3],[3,1]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": [[1, 1], [1, 1]], \"expected\": [[1, 1], [1, 2]], \"passed\": false}, {\"check\": \"explicit oracle 1\", \"actual\": [[1, 1]], \"expected\": [[1, 1]], \"passed\": true}, {\"check\": \"explicit oracle 2\", \"actual\": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1]], \"expected\": [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10], [10, 3], [3, 11], [11, 8], [8, 13], [13, 5], [5, 12], [12, 7], [7, 9], [9, 2], [2, 9], [9, 7], [7, 12]], \"passed\": false}, {\"check\": \"explicit oracle 3\", \"actual\": [[1, 1], [1, 1], [1, 1]], \"expected\": [[1, 1], [1, 2], [2, 1]], \"passed\": false}, {\"check\": \"explicit oracle 4\", \"actual\": [[1, 1], [1, 1], [1, 1], [1, 1]], \"expected\": [[1, 1], [1, 2], [2, 1], [1, 3]], \"passed\": false}, {\"check\": \"explicit oracle 5\", \"actual\": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1]], \"expected\": [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2]], \"passed\": false}, {\"check\": \"explicit oracle 6\", \"actual\": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1]], \"expected\": [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3]], \"passed\": false}, {\"check\": \"explicit oracle 7\", \"actual\": [[1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1], [1, 1]], \"expected\": [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1]], \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":46.523,"exit_code":0,"observations":[{"actual":[[1,1],[1,2]],"check":"explicit oracle 0","expected":[[1,1],[1,2]],"passed":true},{"actual":[[1,1]],"check":"explicit oracle 1","expected":[[1,1]],"passed":true},{"actual":[[1,1],[1,2],[2,1],[1,3],[3,2],[2,3],[3,1],[1,4],[4,3],[3,5],[5,2],[2,5],[5,3],[3,4],[4,1],[1,5],[5,4],[4,7],[7,3],[3,8],[8,5],[5,7],[7,2],[2,7],[7,5],[5,8],[8,3],[3,7],[7,4],[4,5],[5,1],[1,6],[6,5],[5,9],[9,4],[4,11],[11,7],[7,10],[10,3],[3,11],[11,8],[8,13],[13,5],[5,12],[12,7],[7,9],[9,2],[2,9],[9,7],[7,12]],"check":"explicit oracle 2","expected":[[1,1],[1,2],[2,1],[1,3],[3,2],[2,3],[3,1],[1,4],[4,3],[3,5],[5,2],[2,5],[5,3],[3,4],[4,1],[1,5],[5,4],[4,7],[7,3],[3,8],[8,5],[5,7],[7,2],[2,7],[7,5],[5,8],[8,3],[3,7],[7,4],[4,5],[5,1],[1,6],[6,5],[5,9],[9,4],[4,11],[11,7],[7,10],[10,3],[3,11],[11,8],[8,13],[13,5],[5,12],[12,7],[7,9],[9,2],[2,9],[9,7],[7,12]],"passed":true},{"actual":[[1,1],[1,2],[2,1]],"check":"explicit oracle 3","expected":[[1,1],[1,2],[2,1]],"passed":true},{"actual":[[1,1],[1,2],[2,1],[1,3]],"check":"explicit oracle 4","expected":[[1,1],[1,2],[2,1],[1,3]],"passed":true},{"actual":[[1,1],[1,2],[2,1],[1,3],[3,2]],"check":"explicit oracle 5","expected":[[1,1],[1,2],[2,1],[1,3],[3,2]],"passed":true},{"actual":[[1,1],[1,2],[2,1],[1,3],[3,2],[2,3]],"check":"explicit oracle 6","expected":[[1,1],[1,2],[2,1],[1,3],[3,2],[2,3]],"passed":true},{"actual":[[1,1],[1,2],[2,1],[1,3],[3,2],[2,3],[3,1]],"check":"explicit oracle 7","expected":[[1,1],[1,2],[2,1],[1,3],[3,2],[2,3],[3,1]],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": [[1, 1], [1, 2]], \"expected\": [[1, 1], [1, 2]], \"passed\": true}, {\"check\": \"explicit oracle 1\", \"actual\": [[1, 1]], \"expected\": [[1, 1]], \"passed\": true}, {\"check\": \"explicit oracle 2\", \"actual\": [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10], [10, 3], [3, 11], [11, 8], [8, 13], [13, 5], [5, 12], [12, 7], [7, 9], [9, 2], [2, 9], [9, 7], [7, 12]], \"expected\": [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1], [1, 4], [4, 3], [3, 5], [5, 2], [2, 5], [5, 3], [3, 4], [4, 1], [1, 5], [5, 4], [4, 7], [7, 3], [3, 8], [8, 5], [5, 7], [7, 2], [2, 7], [7, 5], [5, 8], [8, 3], [3, 7], [7, 4], [4, 5], [5, 1], [1, 6], [6, 5], [5, 9], [9, 4], [4, 11], [11, 7], [7, 10], [10, 3], [3, 11], [11, 8], [8, 13], [13, 5], [5, 12], [12, 7], [7, 9], [9, 2], [2, 9], [9, 7], [7, 12]], \"passed\": true}, {\"check\": \"explicit oracle 3\", \"actual\": [[1, 1], [1, 2], [2, 1]], \"expected\": [[1, 1], [1, 2], [2, 1]], \"passed\": true}, {\"check\": \"explicit oracle 4\", \"actual\": [[1, 1], [1, 2], [2, 1], [1, 3]], \"expected\": [[1, 1], [1, 2], [2, 1], [1, 3]], \"passed\": true}, {\"check\": \"explicit oracle 5\", \"actual\": [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2]], \"expected\": [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2]], \"passed\": true}, {\"check\": \"explicit oracle 6\", \"actual\": [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3]], \"expected\": [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3]], \"passed\": true}, {\"check\": \"explicit oracle 7\", \"actual\": [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1]], \"expected\": [[1, 1], [1, 2], [2, 1], [1, 3], [3, 2], [2, 3], [3, 1]], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}