{"abstract":"The minus sign is counted as a decimal digit.","category":"Number theory","checks":4,"contract":"Integer inputs; n is positive unless a zero or negative fixture explicitly extends that operation. A modulus is greater than one; p is prime; exponent k may be signed when an inverse exists. n is any signed integer; count magnitude decimal digits, with one digit for zero. Exact operational definition: len(str(abs(n)))","evaluation_group":"model-fbcb5139014b620f","failed_approach":"Binary width does not count decimal digits.","family":"xn-decimal-digit-count","id":"FA-5576","implementations":{"attempt":{"sha256":"bc61b695807275f4982b8ffb8b5bb779abe46e7741e686addd964889a1748ff8","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 abs(n).bit_length()\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: (-100,)', solve(*(-100,)), 3)\ncheck('fixture 3: (9,)', solve(*(9,)), 1)\ncheck('fixture 4: (1000,)', solve(*(1000,)), 4)\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":"821cee881dcaae7a4f1af15dfd34ab8e9bf0af631355ae9a2d296399cc306a6e","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 len(str(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: (-100,)', solve(*(-100,)), 3)\ncheck('fixture 3: (9,)', solve(*(9,)), 1)\ncheck('fixture 4: (1000,)', solve(*(1000,)), 4)\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":"2ce7a28685830cc1ad904d11cc3e603b9f13e4c116344109c88637a409cbe6ad","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 len(str(abs(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: (-100,)', solve(*(-100,)), 3)\ncheck('fixture 3: (9,)', solve(*(9,)), 1)\ncheck('fixture 4: (1000,)', solve(*(1000,)), 4)\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-decimal-digit-count","generated_at":"2026-09-29T14:37:50.984080+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. Number theory results depend on the stated convention.","repair":"Apply the specified mathematical contract directly, preserving all terms and boundary cases: return len(str(abs(n)))","root_cause":"The minus sign is counted as a decimal digit.","sha256":"e5917a9639bc791bd13dedf9e6b1b6daecb8676928113b00454ec774a9410eea","title":"Decimal digit count · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":40.917,"exit_code":1,"observations":[{"actual":0,"check":"fixture 1: (0,)","expected":1,"passed":false},{"actual":7,"check":"fixture 2: (-100,)","expected":3,"passed":false},{"actual":4,"check":"fixture 3: (9,)","expected":1,"passed":false},{"actual":10,"check":"fixture 4: (1000,)","expected":4,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0,)\", \"actual\": 0, \"expected\": 1, \"passed\": false}, {\"check\": \"fixture 2: (-100,)\", \"actual\": 7, \"expected\": 3, \"passed\": false}, {\"check\": \"fixture 3: (9,)\", \"actual\": 4, \"expected\": 1, \"passed\": false}, {\"check\": \"fixture 4: (1000,)\", \"actual\": 10, \"expected\": 4, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":45.991,"exit_code":1,"observations":[{"actual":1,"check":"fixture 1: (0,)","expected":1,"passed":true},{"actual":4,"check":"fixture 2: (-100,)","expected":3,"passed":false},{"actual":1,"check":"fixture 3: (9,)","expected":1,"passed":true},{"actual":4,"check":"fixture 4: (1000,)","expected":4,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0,)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 2: (-100,)\", \"actual\": 4, \"expected\": 3, \"passed\": false}, {\"check\": \"fixture 3: (9,)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 4: (1000,)\", \"actual\": 4, \"expected\": 4, \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":43.015,"exit_code":0,"observations":[{"actual":1,"check":"fixture 1: (0,)","expected":1,"passed":true},{"actual":3,"check":"fixture 2: (-100,)","expected":3,"passed":true},{"actual":1,"check":"fixture 3: (9,)","expected":1,"passed":true},{"actual":4,"check":"fixture 4: (1000,)","expected":4,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (0,)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 2: (-100,)\", \"actual\": 3, \"expected\": 3, \"passed\": true}, {\"check\": \"fixture 3: (9,)\", \"actual\": 1, \"expected\": 1, \"passed\": true}, {\"check\": \"fixture 4: (1000,)\", \"actual\": 4, \"expected\": 4, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}