{"abstract":"A sign character participates in a magnitude-only comparison.","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; compare magnitude digits in both directions. Exact operational definition: str(abs(n))==str(abs(n))[::-1]","evaluation_group":"model-0536856502f9bef2","failed_approach":"Matching endpoint digits does not verify the interior.","family":"xn-decimal-palindrome-magnitude","id":"FA-5581","implementations":{"attempt":{"sha256":"b59b3417047440c6a5125bad1fa332e3efeb08ceb31649c2b1da7465f50ac30f","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 str(abs(n))[0]==str(abs(n))[-1]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (-121,)', solve(*(-121,)), True)\ncheck('fixture 2: (1231,)', solve(*(1231,)), False)\ncheck('fixture 3: (0,)', solve(*(0,)), True)\ncheck('fixture 4: (1221,)', solve(*(1221,)), True)\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":"74e3e6f28c1c155e0a17c02148dad8251f337ba06cf40c45e21c180ceee6dbc5","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 str(n)==str(n)[::-1]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (-121,)', solve(*(-121,)), True)\ncheck('fixture 2: (1231,)', solve(*(1231,)), False)\ncheck('fixture 3: (0,)', solve(*(0,)), True)\ncheck('fixture 4: (1221,)', solve(*(1221,)), True)\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":"1a7ab3d4830128d0c25bd8595d682dc6f11251f32d52acb634c52f959d795176","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 str(abs(n))==str(abs(n))[::-1]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: (-121,)', solve(*(-121,)), True)\ncheck('fixture 2: (1231,)', solve(*(1231,)), False)\ncheck('fixture 3: (0,)', solve(*(0,)), True)\ncheck('fixture 4: (1221,)', solve(*(1221,)), True)\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-palindrome-magnitude","generated_at":"2026-09-29T14:37:50.988137+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 str(abs(n))==str(abs(n))[::-1]","root_cause":"A sign character participates in a magnitude-only comparison.","sha256":"a418d97e92be42f70990c898dc878304574a69cd660411c59f029465897f7021","title":"Decimal palindrome magnitude · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":41.891,"exit_code":1,"observations":[{"actual":true,"check":"fixture 1: (-121,)","expected":true,"passed":true},{"actual":true,"check":"fixture 2: (1231,)","expected":false,"passed":false},{"actual":true,"check":"fixture 3: (0,)","expected":true,"passed":true},{"actual":true,"check":"fixture 4: (1221,)","expected":true,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (-121,)\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"fixture 2: (1231,)\", \"actual\": true, \"expected\": false, \"passed\": false}, {\"check\": \"fixture 3: (0,)\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"fixture 4: (1221,)\", \"actual\": true, \"expected\": true, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":44.072,"exit_code":1,"observations":[{"actual":false,"check":"fixture 1: (-121,)","expected":true,"passed":false},{"actual":false,"check":"fixture 2: (1231,)","expected":false,"passed":true},{"actual":true,"check":"fixture 3: (0,)","expected":true,"passed":true},{"actual":true,"check":"fixture 4: (1221,)","expected":true,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (-121,)\", \"actual\": false, \"expected\": true, \"passed\": false}, {\"check\": \"fixture 2: (1231,)\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"fixture 3: (0,)\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"fixture 4: (1221,)\", \"actual\": true, \"expected\": true, \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":42.721,"exit_code":0,"observations":[{"actual":true,"check":"fixture 1: (-121,)","expected":true,"passed":true},{"actual":false,"check":"fixture 2: (1231,)","expected":false,"passed":true},{"actual":true,"check":"fixture 3: (0,)","expected":true,"passed":true},{"actual":true,"check":"fixture 4: (1221,)","expected":true,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: (-121,)\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"fixture 2: (1231,)\", \"actual\": false, \"expected\": false, \"passed\": true}, {\"check\": \"fixture 3: (0,)\", \"actual\": true, \"expected\": true, \"passed\": true}, {\"check\": \"fixture 4: (1221,)\", \"actual\": true, \"expected\": true, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}