{"abstract":"The exact rational mediant walk result violates the stated contract at lower infinite interval seed.","category":"Numerics","checks":8,"contract":"Input path over L/R; return Stern-Brocot interval bounds and its mediant.","evaluation_group":"s3-numerics-rational-mediant-walk","failed_approach":"The partial repair [0,0] still violates the lower infinite interval seed invariant.","family":"s3-numerics-rational-mediant-walk-lower-infinite-interval-seed","id":"FA-14566","implementations":{"attempt":{"sha256":"6808ff32a30b36bf22b1c80c8248873d8e30ea97b26fb7113fba67f5d4c0d951","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    lo=[0,0]\n    hi=[1,0]\n    for step in x:\n     mid=[lo[0]+hi[0],lo[1]+hi[1]]\n     if step=='L': hi=mid\n     else: lo=mid\n    return [lo,hi,[lo[0]+hi[0],lo[1]+hi[1]]]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('', [[0, 1], [1, 0], [1, 1]]), ('RRRRRR', [[6, 1], [1, 0], [7, 1]]), ('L', [[0, 1], [1, 1], [1, 2]]), ('R', [[1, 1], [1, 0], [2, 1]]), ('LL', [[0, 1], [1, 2], [1, 3]]), ('LR', [[1, 2], [1, 1], [2, 3]]), ('RL', [[1, 1], [2, 1], [3, 2]]), ('RR', [[2, 1], [1, 0], [3, 1]])], [('L', [[0, 1], [1, 1], [1, 2]]), ('LL', [[0, 1], [1, 2], [1, 3]]), ('', [[0, 1], [1, 0], [1, 1]]), ('RRRRRR', [[6, 1], [1, 0], [7, 1]]), ('LLRL', [[1, 3], [2, 5], [3, 8]]), ('LLRR', [[2, 5], [1, 2], [3, 7]]), ('LRLL', [[1, 2], [3, 5], [4, 7]]), ('LRLR', [[3, 5], [2, 3], [5, 8]])], [('R', [[1, 1], [1, 0], [2, 1]]), ('RR', [[2, 1], [1, 0], [3, 1]]), ('', [[0, 1], [1, 0], [1, 1]]), ('RRRRRR', [[6, 1], [1, 0], [7, 1]]), ('LLLRR', [[2, 7], [1, 3], [3, 10]]), ('LLRLL', [[1, 3], [3, 8], [4, 11]]), ('LLRLR', [[3, 8], [2, 5], [5, 13]]), ('LLRRL', [[2, 5], [3, 7], [5, 12]])], [('LL', [[0, 1], [1, 2], [1, 3]]), ('LRL', [[1, 2], [2, 3], [3, 5]]), ('', [[0, 1], [1, 0], [1, 1]]), ('RRRRRR', [[6, 1], [1, 0], [7, 1]]), ('RLRLL', [[3, 2], [8, 5], [11, 7]]), ('RLRLR', [[8, 5], [5, 3], [13, 8]]), ('RLRRL', [[5, 3], [7, 4], [12, 7]]), ('RLRRR', [[7, 4], [2, 1], [9, 5]])], [('LR', [[1, 2], [1, 1], [2, 3]]), ('RLR', [[3, 2], [2, 1], [5, 3]]), ('', [[0, 1], [1, 0], [1, 1]]), ('RRRRRR', [[6, 1], [1, 0], [7, 1]]), ('LLLRLR', [[3, 11], [2, 7], [5, 18]]), ('LLLRRL', [[2, 7], [3, 10], [5, 17]]), ('LLLRRR', [[3, 10], [1, 3], [4, 13]]), ('LLRLLL', [[1, 3], [4, 11], [5, 14]])]]\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":"472c1bdfd56b8e8fa1358c6d209795385b1168cf48ce3358236cde3261d60dc4","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    lo=[1,1]\n    hi=[1,0]\n    for step in x:\n     mid=[lo[0]+hi[0],lo[1]+hi[1]]\n     if step=='L': hi=mid\n     else: lo=mid\n    return [lo,hi,[lo[0]+hi[0],lo[1]+hi[1]]]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('', [[0, 1], [1, 0], [1, 1]]), ('RRRRRR', [[6, 1], [1, 0], [7, 1]]), ('L', [[0, 1], [1, 1], [1, 2]]), ('R', [[1, 1], [1, 0], [2, 1]]), ('LL', [[0, 1], [1, 2], [1, 3]]), ('LR', [[1, 2], [1, 1], [2, 3]]), ('RL', [[1, 1], [2, 1], [3, 2]]), ('RR', [[2, 1], [1, 0], [3, 1]])], [('L', [[0, 1], [1, 1], [1, 2]]), ('LL', [[0, 1], [1, 2], [1, 3]]), ('', [[0, 1], [1, 0], [1, 1]]), ('RRRRRR', [[6, 1], [1, 0], [7, 1]]), ('LLRL', [[1, 3], [2, 5], [3, 8]]), ('LLRR', [[2, 5], [1, 2], [3, 7]]), ('LRLL', [[1, 2], [3, 5], [4, 7]]), ('LRLR', [[3, 5], [2, 3], [5, 8]])], [('R', [[1, 1], [1, 0], [2, 1]]), ('RR', [[2, 1], [1, 0], [3, 1]]), ('', [[0, 1], [1, 0], [1, 1]]), ('RRRRRR', [[6, 1], [1, 0], [7, 1]]), ('LLLRR', [[2, 7], [1, 3], [3, 10]]), ('LLRLL', [[1, 3], [3, 8], [4, 11]]), ('LLRLR', [[3, 8], [2, 5], [5, 13]]), ('LLRRL', [[2, 5], [3, 7], [5, 12]])], [('LL', [[0, 1], [1, 2], [1, 3]]), ('LRL', [[1, 2], [2, 3], [3, 5]]), ('', [[0, 1], [1, 0], [1, 1]]), ('RRRRRR', [[6, 1], [1, 0], [7, 1]]), ('RLRLL', [[3, 2], [8, 5], [11, 7]]), ('RLRLR', [[8, 5], [5, 3], [13, 8]]), ('RLRRL', [[5, 3], [7, 4], [12, 7]]), ('RLRRR', [[7, 4], [2, 1], [9, 5]])], [('LR', [[1, 2], [1, 1], [2, 3]]), ('RLR', [[3, 2], [2, 1], [5, 3]]), ('', [[0, 1], [1, 0], [1, 1]]), ('RRRRRR', [[6, 1], [1, 0], [7, 1]]), ('LLLRLR', [[3, 11], [2, 7], [5, 18]]), ('LLLRRL', [[2, 7], [3, 10], [5, 17]]), ('LLLRRR', [[3, 10], [1, 3], [4, 13]]), ('LLRLLL', [[1, 3], [4, 11], [5, 14]])]]\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":"a8d8b987ca907f34d5a6bd245964fe3a0cff6ed80dfc0fee2184dddf511299b5","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    lo=[0,1]\n    hi=[1,0]\n    for step in x:\n     mid=[lo[0]+hi[0],lo[1]+hi[1]]\n     if step=='L': hi=mid\n     else: lo=mid\n    return [lo,hi,[lo[0]+hi[0],lo[1]+hi[1]]]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('', [[0, 1], [1, 0], [1, 1]]), ('RRRRRR', [[6, 1], [1, 0], [7, 1]]), ('L', [[0, 1], [1, 1], [1, 2]]), ('R', [[1, 1], [1, 0], [2, 1]]), ('LL', [[0, 1], [1, 2], [1, 3]]), ('LR', [[1, 2], [1, 1], [2, 3]]), ('RL', [[1, 1], [2, 1], [3, 2]]), ('RR', [[2, 1], [1, 0], [3, 1]])], [('L', [[0, 1], [1, 1], [1, 2]]), ('LL', [[0, 1], [1, 2], [1, 3]]), ('', [[0, 1], [1, 0], [1, 1]]), ('RRRRRR', [[6, 1], [1, 0], [7, 1]]), ('LLRL', [[1, 3], [2, 5], [3, 8]]), ('LLRR', [[2, 5], [1, 2], [3, 7]]), ('LRLL', [[1, 2], [3, 5], [4, 7]]), ('LRLR', [[3, 5], [2, 3], [5, 8]])], [('R', [[1, 1], [1, 0], [2, 1]]), ('RR', [[2, 1], [1, 0], [3, 1]]), ('', [[0, 1], [1, 0], [1, 1]]), ('RRRRRR', [[6, 1], [1, 0], [7, 1]]), ('LLLRR', [[2, 7], [1, 3], [3, 10]]), ('LLRLL', [[1, 3], [3, 8], [4, 11]]), ('LLRLR', [[3, 8], [2, 5], [5, 13]]), ('LLRRL', [[2, 5], [3, 7], [5, 12]])], [('LL', [[0, 1], [1, 2], [1, 3]]), ('LRL', [[1, 2], [2, 3], [3, 5]]), ('', [[0, 1], [1, 0], [1, 1]]), ('RRRRRR', [[6, 1], [1, 0], [7, 1]]), ('RLRLL', [[3, 2], [8, 5], [11, 7]]), ('RLRLR', [[8, 5], [5, 3], [13, 8]]), ('RLRRL', [[5, 3], [7, 4], [12, 7]]), ('RLRRR', [[7, 4], [2, 1], [9, 5]])], [('LR', [[1, 2], [1, 1], [2, 3]]), ('RLR', [[3, 2], [2, 1], [5, 3]]), ('', [[0, 1], [1, 0], [1, 1]]), ('RRRRRR', [[6, 1], [1, 0], [7, 1]]), ('LLLRLR', [[3, 11], [2, 7], [5, 18]]), ('LLLRRL', [[2, 7], [3, 10], [5, 17]]), ('LLLRRR', [[3, 10], [1, 3], [4, 13]]), ('LLRLLL', [[1, 3], [4, 11], [5, 14]])]]\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-rational-mediant-walk-lower-infinite-interval-seed","generated_at":"2026-09-29T14:39:18.223522+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 [0,1] at the lower infinite interval seed step.","root_cause":"The lower infinite interval seed step uses [1,1] instead of [0,1].","sha256":"abca1c91c2ed4ec472d100e08f93635ef9c1e93a5e94b0b6a3c6804bdb9a50c8","title":"Rational mediant walk: lower infinite interval seed · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":43.335,"exit_code":1,"observations":[{"actual":[[0,0],[1,0],[1,0]],"check":"explicit oracle 0","expected":[[0,1],[1,0],[1,1]],"passed":false},{"actual":[[6,0],[1,0],[7,0]],"check":"explicit oracle 1","expected":[[6,1],[1,0],[7,1]],"passed":false},{"actual":[[0,0],[1,0],[1,0]],"check":"explicit oracle 2","expected":[[0,1],[1,1],[1,2]],"passed":false},{"actual":[[1,0],[1,0],[2,0]],"check":"explicit oracle 3","expected":[[1,1],[1,0],[2,1]],"passed":false},{"actual":[[0,0],[1,0],[1,0]],"check":"explicit oracle 4","expected":[[0,1],[1,2],[1,3]],"passed":false},{"actual":[[1,0],[1,0],[2,0]],"check":"explicit oracle 5","expected":[[1,2],[1,1],[2,3]],"passed":false},{"actual":[[1,0],[2,0],[3,0]],"check":"explicit oracle 6","expected":[[1,1],[2,1],[3,2]],"passed":false},{"actual":[[2,0],[1,0],[3,0]],"check":"explicit oracle 7","expected":[[2,1],[1,0],[3,1]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": [[0, 0], [1, 0], [1, 0]], \"expected\": [[0, 1], [1, 0], [1, 1]], \"passed\": false}, {\"check\": \"explicit oracle 1\", \"actual\": [[6, 0], [1, 0], [7, 0]], \"expected\": [[6, 1], [1, 0], [7, 1]], \"passed\": false}, {\"check\": \"explicit oracle 2\", \"actual\": [[0, 0], [1, 0], [1, 0]], \"expected\": [[0, 1], [1, 1], [1, 2]], \"passed\": false}, {\"check\": \"explicit oracle 3\", \"actual\": [[1, 0], [1, 0], [2, 0]], \"expected\": [[1, 1], [1, 0], [2, 1]], \"passed\": false}, {\"check\": \"explicit oracle 4\", \"actual\": [[0, 0], [1, 0], [1, 0]], \"expected\": [[0, 1], [1, 2], [1, 3]], \"passed\": false}, {\"check\": \"explicit oracle 5\", \"actual\": [[1, 0], [1, 0], [2, 0]], \"expected\": [[1, 2], [1, 1], [2, 3]], \"passed\": false}, {\"check\": \"explicit oracle 6\", \"actual\": [[1, 0], [2, 0], [3, 0]], \"expected\": [[1, 1], [2, 1], [3, 2]], \"passed\": false}, {\"check\": \"explicit oracle 7\", \"actual\": [[2, 0], [1, 0], [3, 0]], \"expected\": [[2, 1], [1, 0], [3, 1]], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":43.73,"exit_code":1,"observations":[{"actual":[[1,1],[1,0],[2,1]],"check":"explicit oracle 0","expected":[[0,1],[1,0],[1,1]],"passed":false},{"actual":[[7,1],[1,0],[8,1]],"check":"explicit oracle 1","expected":[[6,1],[1,0],[7,1]],"passed":false},{"actual":[[1,1],[2,1],[3,2]],"check":"explicit oracle 2","expected":[[0,1],[1,1],[1,2]],"passed":false},{"actual":[[2,1],[1,0],[3,1]],"check":"explicit oracle 3","expected":[[1,1],[1,0],[2,1]],"passed":false},{"actual":[[1,1],[3,2],[4,3]],"check":"explicit oracle 4","expected":[[0,1],[1,2],[1,3]],"passed":false},{"actual":[[3,2],[2,1],[5,3]],"check":"explicit oracle 5","expected":[[1,2],[1,1],[2,3]],"passed":false},{"actual":[[2,1],[3,1],[5,2]],"check":"explicit oracle 6","expected":[[1,1],[2,1],[3,2]],"passed":false},{"actual":[[3,1],[1,0],[4,1]],"check":"explicit oracle 7","expected":[[2,1],[1,0],[3,1]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": [[1, 1], [1, 0], [2, 1]], \"expected\": [[0, 1], [1, 0], [1, 1]], \"passed\": false}, {\"check\": \"explicit oracle 1\", \"actual\": [[7, 1], [1, 0], [8, 1]], \"expected\": [[6, 1], [1, 0], [7, 1]], \"passed\": false}, {\"check\": \"explicit oracle 2\", \"actual\": [[1, 1], [2, 1], [3, 2]], \"expected\": [[0, 1], [1, 1], [1, 2]], \"passed\": false}, {\"check\": \"explicit oracle 3\", \"actual\": [[2, 1], [1, 0], [3, 1]], \"expected\": [[1, 1], [1, 0], [2, 1]], \"passed\": false}, {\"check\": \"explicit oracle 4\", \"actual\": [[1, 1], [3, 2], [4, 3]], \"expected\": [[0, 1], [1, 2], [1, 3]], \"passed\": false}, {\"check\": \"explicit oracle 5\", \"actual\": [[3, 2], [2, 1], [5, 3]], \"expected\": [[1, 2], [1, 1], [2, 3]], \"passed\": false}, {\"check\": \"explicit oracle 6\", \"actual\": [[2, 1], [3, 1], [5, 2]], \"expected\": [[1, 1], [2, 1], [3, 2]], \"passed\": false}, {\"check\": \"explicit oracle 7\", \"actual\": [[3, 1], [1, 0], [4, 1]], \"expected\": [[2, 1], [1, 0], [3, 1]], \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":44.987,"exit_code":0,"observations":[{"actual":[[0,1],[1,0],[1,1]],"check":"explicit oracle 0","expected":[[0,1],[1,0],[1,1]],"passed":true},{"actual":[[6,1],[1,0],[7,1]],"check":"explicit oracle 1","expected":[[6,1],[1,0],[7,1]],"passed":true},{"actual":[[0,1],[1,1],[1,2]],"check":"explicit oracle 2","expected":[[0,1],[1,1],[1,2]],"passed":true},{"actual":[[1,1],[1,0],[2,1]],"check":"explicit oracle 3","expected":[[1,1],[1,0],[2,1]],"passed":true},{"actual":[[0,1],[1,2],[1,3]],"check":"explicit oracle 4","expected":[[0,1],[1,2],[1,3]],"passed":true},{"actual":[[1,2],[1,1],[2,3]],"check":"explicit oracle 5","expected":[[1,2],[1,1],[2,3]],"passed":true},{"actual":[[1,1],[2,1],[3,2]],"check":"explicit oracle 6","expected":[[1,1],[2,1],[3,2]],"passed":true},{"actual":[[2,1],[1,0],[3,1]],"check":"explicit oracle 7","expected":[[2,1],[1,0],[3,1]],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": [[0, 1], [1, 0], [1, 1]], \"expected\": [[0, 1], [1, 0], [1, 1]], \"passed\": true}, {\"check\": \"explicit oracle 1\", \"actual\": [[6, 1], [1, 0], [7, 1]], \"expected\": [[6, 1], [1, 0], [7, 1]], \"passed\": true}, {\"check\": \"explicit oracle 2\", \"actual\": [[0, 1], [1, 1], [1, 2]], \"expected\": [[0, 1], [1, 1], [1, 2]], \"passed\": true}, {\"check\": \"explicit oracle 3\", \"actual\": [[1, 1], [1, 0], [2, 1]], \"expected\": [[1, 1], [1, 0], [2, 1]], \"passed\": true}, {\"check\": \"explicit oracle 4\", \"actual\": [[0, 1], [1, 2], [1, 3]], \"expected\": [[0, 1], [1, 2], [1, 3]], \"passed\": true}, {\"check\": \"explicit oracle 5\", \"actual\": [[1, 2], [1, 1], [2, 3]], \"expected\": [[1, 2], [1, 1], [2, 3]], \"passed\": true}, {\"check\": \"explicit oracle 6\", \"actual\": [[1, 1], [2, 1], [3, 2]], \"expected\": [[1, 1], [2, 1], [3, 2]], \"passed\": true}, {\"check\": \"explicit oracle 7\", \"actual\": [[2, 1], [1, 0], [3, 1]], \"expected\": [[2, 1], [1, 0], [3, 1]], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}