{"abstract":"The exact restricted growth strings result violates the stated contract at highest used block tracking.","category":"Numerics","checks":8,"contract":"Input length n (1..6), maximum blocks B>=1; return lexicographic restricted-growth strings a0=0, a_i<=1+max(prefix), using exactly B blocks.","contract_signature":"x","evaluation_group":"s3-numerics-restricted-growth-strings","failed_approach":"The partial repair m+1 still violates the highest used block tracking invariant.","family":"s3-numerics-restricted-growth-strings-highest-used-block-tracking","id":"FA-15261","implementations":{"attempt":{"sha256":"8ed3f6364ee7b8a51068b9b6f7fcaeb834b09bcdbfd43a1a9daac5cc6f132674","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    n,B=x;out=[]\n    def visit(prefix,m):\n     if len(prefix)==n:\n      if m+1==B:out.append(prefix)\n      return\n     for v in range(m+2):\n      if v>=B:continue\n      visit(prefix+[v],m+1)\n    visit([0],0)\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([3, 2], [[0, 0, 1], [0, 1, 0], [0, 1, 1]]), ([2, 1], [[0, 0]]), ([1, 1], [[0]]), ([6, 7], []), ([1, 2], []), ([2, 2], [[0, 1]]), ([2, 3], []), ([3, 1], [[0, 0, 0]])], [([4, 2], [[0, 0, 0, 1], [0, 0, 1, 0], [0, 0, 1, 1], [0, 1, 0, 0], [0, 1, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1]]), ([3, 2], [[0, 0, 1], [0, 1, 0], [0, 1, 1]]), ([1, 1], [[0]]), ([6, 7], []), ([5, 4], [[0, 0, 1, 2, 3], [0, 1, 0, 2, 3], [0, 1, 1, 2, 3], [0, 1, 2, 0, 3], [0, 1, 2, 1, 3], [0, 1, 2, 2, 3], [0, 1, 2, 3, 0], [0, 1, 2, 3, 1], [0, 1, 2, 3, 2], [0, 1, 2, 3, 3]]), ([5, 5], [[0, 1, 2, 3, 4]]), ([5, 6], []), ([6, 1], [[0, 0, 0, 0, 0, 0]])], [([4, 3], [[0, 0, 1, 2], [0, 1, 0, 2], [0, 1, 1, 2], [0, 1, 2, 0], [0, 1, 2, 1], [0, 1, 2, 2]]), ([4, 2], [[0, 0, 0, 1], [0, 0, 1, 0], [0, 0, 1, 1], [0, 1, 0, 0], [0, 1, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1]]), ([1, 1], [[0]]), ([6, 7], []), ([3, 3], [[0, 1, 2]]), ([3, 4], []), ([4, 1], [[0, 0, 0, 0]]), ([4, 4], [[0, 1, 2, 3]])], [([5, 2], [[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 1, 1], [0, 0, 1, 0, 0], [0, 0, 1, 0, 1], [0, 0, 1, 1, 0], [0, 0, 1, 1, 1], [0, 1, 0, 0, 0], [0, 1, 0, 0, 1], [0, 1, 0, 1, 0], [0, 1, 0, 1, 1], [0, 1, 1, 0, 0], [0, 1, 1, 0, 1], [0, 1, 1, 1, 0], [0, 1, 1, 1, 1]]), ([5, 1], [[0, 0, 0, 0, 0]]), ([1, 1], [[0]]), ([6, 7], []), ([6, 5], [[0, 0, 1, 2, 3, 4], [0, 1, 0, 2, 3, 4], [0, 1, 1, 2, 3, 4], [0, 1, 2, 0, 3, 4], [0, 1, 2, 1, 3, 4], [0, 1, 2, 2, 3, 4], [0, 1, 2, 3, 0, 4], [0, 1, 2, 3, 1, 4], [0, 1, 2, 3, 2, 4], [0, 1, 2, 3, 3, 4], [0, 1, 2, 3, 4, 0], [0, 1, 2, 3, 4, 1], [0, 1, 2, 3, 4, 2], [0, 1, 2, 3, 4, 3], [0, 1, 2, 3, 4, 4]]), ([6, 6], [[0, 1, 2, 3, 4, 5]]), ([1, 2], []), ([2, 1], [[0, 0]])], [([5, 3], [[0, 0, 0, 1, 2], [0, 0, 1, 0, 2], [0, 0, 1, 1, 2], [0, 0, 1, 2, 0], [0, 0, 1, 2, 1], [0, 0, 1, 2, 2], [0, 1, 0, 0, 2], [0, 1, 0, 1, 2], [0, 1, 0, 2, 0], [0, 1, 0, 2, 1], [0, 1, 0, 2, 2], [0, 1, 1, 0, 2], [0, 1, 1, 1, 2], [0, 1, 1, 2, 0], [0, 1, 1, 2, 1], [0, 1, 1, 2, 2], [0, 1, 2, 0, 0], [0, 1, 2, 0, 1], [0, 1, 2, 0, 2], [0, 1, 2, 1, 0], [0, 1, 2, 1, 1], [0, 1, 2, 1, 2], [0, 1, 2, 2, 0], [0, 1, 2, 2, 1], [0, 1, 2, 2, 2]]), ([5, 4], [[0, 0, 1, 2, 3], [0, 1, 0, 2, 3], [0, 1, 1, 2, 3], [0, 1, 2, 0, 3], [0, 1, 2, 1, 3], [0, 1, 2, 2, 3], [0, 1, 2, 3, 0], [0, 1, 2, 3, 1], [0, 1, 2, 3, 2], [0, 1, 2, 3, 3]]), ([1, 1], [[0]]), ([6, 7], []), ([5, 1], [[0, 0, 0, 0, 0]]), ([5, 2], [[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 1, 1], [0, 0, 1, 0, 0], [0, 0, 1, 0, 1], [0, 0, 1, 1, 0], [0, 0, 1, 1, 1], [0, 1, 0, 0, 0], [0, 1, 0, 0, 1], [0, 1, 0, 1, 0], [0, 1, 0, 1, 1], [0, 1, 1, 0, 0], [0, 1, 1, 0, 1], [0, 1, 1, 1, 0], [0, 1, 1, 1, 1]]), ([5, 5], [[0, 1, 2, 3, 4]]), ([5, 6], [])]]\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":"b83827db4043d952335fe9adbd955e6a6a08e41e727bf6a146a8fc7675d07dc8","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    n,B=x;out=[]\n    def visit(prefix,m):\n     if len(prefix)==n:\n      if m+1==B:out.append(prefix)\n      return\n     for v in range(m+2):\n      if v>=B:continue\n      visit(prefix+[v],v)\n    visit([0],0)\n    return out\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([3, 2], [[0, 0, 1], [0, 1, 0], [0, 1, 1]]), ([2, 1], [[0, 0]]), ([1, 1], [[0]]), ([6, 7], []), ([1, 2], []), ([2, 2], [[0, 1]]), ([2, 3], []), ([3, 1], [[0, 0, 0]])], [([4, 2], [[0, 0, 0, 1], [0, 0, 1, 0], [0, 0, 1, 1], [0, 1, 0, 0], [0, 1, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1]]), ([3, 2], [[0, 0, 1], [0, 1, 0], [0, 1, 1]]), ([1, 1], [[0]]), ([6, 7], []), ([5, 4], [[0, 0, 1, 2, 3], [0, 1, 0, 2, 3], [0, 1, 1, 2, 3], [0, 1, 2, 0, 3], [0, 1, 2, 1, 3], [0, 1, 2, 2, 3], [0, 1, 2, 3, 0], [0, 1, 2, 3, 1], [0, 1, 2, 3, 2], [0, 1, 2, 3, 3]]), ([5, 5], [[0, 1, 2, 3, 4]]), ([5, 6], []), ([6, 1], [[0, 0, 0, 0, 0, 0]])], [([4, 3], [[0, 0, 1, 2], [0, 1, 0, 2], [0, 1, 1, 2], [0, 1, 2, 0], [0, 1, 2, 1], [0, 1, 2, 2]]), ([4, 2], [[0, 0, 0, 1], [0, 0, 1, 0], [0, 0, 1, 1], [0, 1, 0, 0], [0, 1, 0, 1], [0, 1, 1, 0], [0, 1, 1, 1]]), ([1, 1], [[0]]), ([6, 7], []), ([3, 3], [[0, 1, 2]]), ([3, 4], []), ([4, 1], [[0, 0, 0, 0]]), ([4, 4], [[0, 1, 2, 3]])], [([5, 2], [[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 1, 1], [0, 0, 1, 0, 0], [0, 0, 1, 0, 1], [0, 0, 1, 1, 0], [0, 0, 1, 1, 1], [0, 1, 0, 0, 0], [0, 1, 0, 0, 1], [0, 1, 0, 1, 0], [0, 1, 0, 1, 1], [0, 1, 1, 0, 0], [0, 1, 1, 0, 1], [0, 1, 1, 1, 0], [0, 1, 1, 1, 1]]), ([5, 1], [[0, 0, 0, 0, 0]]), ([1, 1], [[0]]), ([6, 7], []), ([6, 5], [[0, 0, 1, 2, 3, 4], [0, 1, 0, 2, 3, 4], [0, 1, 1, 2, 3, 4], [0, 1, 2, 0, 3, 4], [0, 1, 2, 1, 3, 4], [0, 1, 2, 2, 3, 4], [0, 1, 2, 3, 0, 4], [0, 1, 2, 3, 1, 4], [0, 1, 2, 3, 2, 4], [0, 1, 2, 3, 3, 4], [0, 1, 2, 3, 4, 0], [0, 1, 2, 3, 4, 1], [0, 1, 2, 3, 4, 2], [0, 1, 2, 3, 4, 3], [0, 1, 2, 3, 4, 4]]), ([6, 6], [[0, 1, 2, 3, 4, 5]]), ([1, 2], []), ([2, 1], [[0, 0]])], [([5, 3], [[0, 0, 0, 1, 2], [0, 0, 1, 0, 2], [0, 0, 1, 1, 2], [0, 0, 1, 2, 0], [0, 0, 1, 2, 1], [0, 0, 1, 2, 2], [0, 1, 0, 0, 2], [0, 1, 0, 1, 2], [0, 1, 0, 2, 0], [0, 1, 0, 2, 1], [0, 1, 0, 2, 2], [0, 1, 1, 0, 2], [0, 1, 1, 1, 2], [0, 1, 1, 2, 0], [0, 1, 1, 2, 1], [0, 1, 1, 2, 2], [0, 1, 2, 0, 0], [0, 1, 2, 0, 1], [0, 1, 2, 0, 2], [0, 1, 2, 1, 0], [0, 1, 2, 1, 1], [0, 1, 2, 1, 2], [0, 1, 2, 2, 0], [0, 1, 2, 2, 1], [0, 1, 2, 2, 2]]), ([5, 4], [[0, 0, 1, 2, 3], [0, 1, 0, 2, 3], [0, 1, 1, 2, 3], [0, 1, 2, 0, 3], [0, 1, 2, 1, 3], [0, 1, 2, 2, 3], [0, 1, 2, 3, 0], [0, 1, 2, 3, 1], [0, 1, 2, 3, 2], [0, 1, 2, 3, 3]]), ([1, 1], [[0]]), ([6, 7], []), ([5, 1], [[0, 0, 0, 0, 0]]), ([5, 2], [[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 1, 1], [0, 0, 1, 0, 0], [0, 0, 1, 0, 1], [0, 0, 1, 1, 0], [0, 0, 1, 1, 1], [0, 1, 0, 0, 0], [0, 1, 0, 0, 1], [0, 1, 0, 1, 0], [0, 1, 0, 1, 1], [0, 1, 1, 0, 0], [0, 1, 1, 0, 1], [0, 1, 1, 1, 0], [0, 1, 1, 1, 1]]), ([5, 5], [[0, 1, 2, 3, 4]]), ([5, 6], [])]]\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-restricted-growth-strings-highest-used-block-tracking","generated_at":"2026-09-29T14:39:24.970641+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 highest used block tracking step uses v instead of max(m,v).","sha256":"fb0f09ac8cbc5d8453a2f1f67f4eaab4929386de4809f472f51f30249549d0e2","title":"Restricted growth strings: highest used block tracking · 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":43.363,"exit_code":1,"observations":[{"actual":[],"check":"explicit oracle 0","expected":[[0,0,1],[0,1,0],[0,1,1]],"passed":false},{"actual":[],"check":"explicit oracle 1","expected":[[0,0]],"passed":false},{"actual":[[0]],"check":"explicit oracle 2","expected":[[0]],"passed":true},{"actual":[],"check":"explicit oracle 3","expected":[],"passed":true},{"actual":[],"check":"explicit oracle 4","expected":[],"passed":true},{"actual":[[0,0],[0,1]],"check":"explicit oracle 5","expected":[[0,1]],"passed":false},{"actual":[],"check":"explicit oracle 6","expected":[],"passed":true},{"actual":[],"check":"explicit oracle 7","expected":[[0,0,0]],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": [], \"expected\": [[0, 0, 1], [0, 1, 0], [0, 1, 1]], \"passed\": false}, {\"check\": \"explicit oracle 1\", \"actual\": [], \"expected\": [[0, 0]], \"passed\": false}, {\"check\": \"explicit oracle 2\", \"actual\": [[0]], \"expected\": [[0]], \"passed\": true}, {\"check\": \"explicit oracle 3\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"explicit oracle 4\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"explicit oracle 5\", \"actual\": [[0, 0], [0, 1]], \"expected\": [[0, 1]], \"passed\": false}, {\"check\": \"explicit oracle 6\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"explicit oracle 7\", \"actual\": [], \"expected\": [[0, 0, 0]], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":43.567,"exit_code":1,"observations":[{"actual":[[0,0,1],[0,1,1]],"check":"explicit oracle 0","expected":[[0,0,1],[0,1,0],[0,1,1]],"passed":false},{"actual":[[0,0]],"check":"explicit oracle 1","expected":[[0,0]],"passed":true},{"actual":[[0]],"check":"explicit oracle 2","expected":[[0]],"passed":true},{"actual":[],"check":"explicit oracle 3","expected":[],"passed":true},{"actual":[],"check":"explicit oracle 4","expected":[],"passed":true},{"actual":[[0,1]],"check":"explicit oracle 5","expected":[[0,1]],"passed":true},{"actual":[],"check":"explicit oracle 6","expected":[],"passed":true},{"actual":[[0,0,0]],"check":"explicit oracle 7","expected":[[0,0,0]],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"explicit oracle 0\", \"actual\": [[0, 0, 1], [0, 1, 1]], \"expected\": [[0, 0, 1], [0, 1, 0], [0, 1, 1]], \"passed\": false}, {\"check\": \"explicit oracle 1\", \"actual\": [[0, 0]], \"expected\": [[0, 0]], \"passed\": true}, {\"check\": \"explicit oracle 2\", \"actual\": [[0]], \"expected\": [[0]], \"passed\": true}, {\"check\": \"explicit oracle 3\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"explicit oracle 4\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"explicit oracle 5\", \"actual\": [[0, 1]], \"expected\": [[0, 1]], \"passed\": true}, {\"check\": \"explicit oracle 6\", \"actual\": [], \"expected\": [], \"passed\": true}, {\"check\": \"explicit oracle 7\", \"actual\": [[0, 0, 0]], \"expected\": [[0, 0, 0]], \"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."}}