{"abstract":"All bit strings are counted despite the adjacency constraint.","category":"Combinatorics","checks":4,"contract":"Nonnegative integer counts. Permutation and combination counts are zero when a requested selection exceeds the available objects. Shape sizes satisfy the preconditions stated below. Binary strings no adjacent ones. Exact operational definition: sum(math.comb(n-k+1,k) for k in range((n+1)//2+1))","evaluation_group":"model-31b9a5fa54939a06","failed_approach":"Subtracting the length does not count overlapping forbidden patterns.","family":"xn-binary-strings-no-adjacent-ones","id":"FA-5731","implementations":{"attempt":{"sha256":"0930d7ab26f5918e130b13f29c1006469c87ba31424aa9d34e8e0fca7d976aa4","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport calendar\nimport statistics\nimport itertools\nfrom fractions import Fraction\nfrom datetime import date, datetime, timedelta, timezone\nfrom decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR\n\nN = 1\nobservations = []\ndef solve(n):\n    return 2**n-n\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (0,)', solve(*(0,)), 1)\ncheck('fixture 2: (1,)', solve(*(1,)), 2)\ncheck('fixture 3: (3,)', solve(*(3,)), 5)\ncheck('fixture 4: (4,)', solve(*(4,)), 8)\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":"11143ce4ff9d37818d9a04fb3411fb94720c24fceb68a64374df95fede4d63c7","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport calendar\nimport statistics\nimport itertools\nfrom fractions import Fraction\nfrom datetime import date, datetime, timedelta, timezone\nfrom decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR\n\nN = 1\nobservations = []\ndef solve(n):\n    return 2**n\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (0,)', solve(*(0,)), 1)\ncheck('fixture 2: (1,)', solve(*(1,)), 2)\ncheck('fixture 3: (3,)', solve(*(3,)), 5)\ncheck('fixture 4: (4,)', solve(*(4,)), 8)\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":"ab9f052b152f516f423d5522974821e4aa2d1af446be5dafee8205b4e0e1f90c","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nimport math\nimport calendar\nimport statistics\nimport itertools\nfrom fractions import Fraction\nfrom datetime import date, datetime, timedelta, timezone\nfrom decimal import Decimal, ROUND_HALF_UP, ROUND_DOWN, ROUND_CEILING, ROUND_FLOOR\n\nN = 1\nobservations = []\ndef solve(n):\n    return sum(math.comb(n-k+1,k) for k in range((n+1)//2+1))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (0,)', solve(*(0,)), 1)\ncheck('fixture 2: (1,)', solve(*(1,)), 2)\ncheck('fixture 3: (3,)', solve(*(3,)), 5)\ncheck('fixture 4: (4,)', solve(*(4,)), 8)\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":" 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":"xn-binary-strings-no-adjacent-ones","generated_at":"2026-09-29T14:37:52.871468+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Combinatorics results depend on the stated convention.","repair":"Apply the specified mathematical contract directly, preserving all terms and boundary cases: return sum(math.comb(n-k+1,k) for k in range((n+1)//2+1))","root_cause":"All bit strings are counted despite the adjacency constraint.","sha256":"f4348514714eb6ba10e1d572ab7bbef576594e2e2d2711889559f8eee68a7259","title":"Binary strings no adjacent ones · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":49.197,"exit_code":1,"observations":[{"actual":1,"check":"fixture 1: (0,)","expected":1,"passed":true},{"actual":1,"check":"fixture 2: (1,)","expected":2,"passed":false},{"actual":5,"check":"fixture 3: (3,)","expected":5,"passed":true},{"actual":12,"check":"fixture 4: (4,)","expected":8,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0,)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 2: (1,)\", \"actual\": 1, \"expected\": 2, \"passed\": false}, {\"check\": \"fixture 3: (3,)\", \"actual\": 5, \"expected\": 5, \"passed\": true}, {\"check\": \"fixture 4: (4,)\", \"actual\": 12, \"expected\": 8, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":47.692,"exit_code":1,"observations":[{"actual":1,"check":"fixture 1: (0,)","expected":1,"passed":true},{"actual":2,"check":"fixture 2: (1,)","expected":2,"passed":true},{"actual":8,"check":"fixture 3: (3,)","expected":5,"passed":false},{"actual":16,"check":"fixture 4: (4,)","expected":8,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0,)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 2: (1,)\", \"actual\": 2, \"expected\": 2, \"passed\": true}, {\"check\": \"fixture 3: (3,)\", \"actual\": 8, \"expected\": 5, \"passed\": false}, {\"check\": \"fixture 4: (4,)\", \"actual\": 16, \"expected\": 8, \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":46.027,"exit_code":0,"observations":[{"actual":1,"check":"fixture 1: (0,)","expected":1,"passed":true},{"actual":2,"check":"fixture 2: (1,)","expected":2,"passed":true},{"actual":5,"check":"fixture 3: (3,)","expected":5,"passed":true},{"actual":8,"check":"fixture 4: (4,)","expected":8,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0,)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 2: (1,)\", \"actual\": 2, \"expected\": 2, \"passed\": true}, {\"check\": \"fixture 3: (3,)\", \"actual\": 5, \"expected\": 5, \"passed\": true}, {\"check\": \"fixture 4: (4,)\", \"actual\": 8, \"expected\": 8, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}