{"abstract":"Decimal positional weights replace factorial weights.","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. digits is least-significant-first with 0<=digits[i]<=i; return the factorial-place-value integer. Exact operational definition: sum(d*math.factorial(i) for i,d in enumerate(digits))","evaluation_group":"model-b02c908c4c309199","failed_approach":"The factorial position begins one place too high.","family":"xn-factoradic-digit-value","id":"FA-5756","implementations":{"attempt":{"sha256":"8a09b984a9b52d86210bc7693016c810c14c43b1d5ab14937ccecce12c3c42b3","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(digits):\n    return sum(d*math.factorial(i+1) for i,d in enumerate(digits))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([0, 1, 2],)', solve(*([0, 1, 2],)), 5)\ncheck('fixture 2: ([0, 0, 0, 1],)', solve(*([0, 0, 0, 1],)), 6)\ncheck('fixture 3: ([0],)', solve(*([0],)), 0)\ncheck('fixture 4: ([0, 1, 0, 3],)', solve(*([0, 1, 0, 3],)), 19)\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":"a0ccd0b4ab98f02c8d6b9abd81389f615c61c055a1a8033f4e8e7e5e1e97fa1b","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(digits):\n    return sum(d*10**i for i,d in enumerate(digits))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([0, 1, 2],)', solve(*([0, 1, 2],)), 5)\ncheck('fixture 2: ([0, 0, 0, 1],)', solve(*([0, 0, 0, 1],)), 6)\ncheck('fixture 3: ([0],)', solve(*([0],)), 0)\ncheck('fixture 4: ([0, 1, 0, 3],)', solve(*([0, 1, 0, 3],)), 19)\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":"e551b2c46d8080687ec0afdb15ec4dac1eca09d6ca2d0ca7e406c4d16031b708","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(digits):\n    return sum(d*math.factorial(i) for i,d in enumerate(digits))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([0, 1, 2],)', solve(*([0, 1, 2],)), 5)\ncheck('fixture 2: ([0, 0, 0, 1],)', solve(*([0, 0, 0, 1],)), 6)\ncheck('fixture 3: ([0],)', solve(*([0],)), 0)\ncheck('fixture 4: ([0, 1, 0, 3],)', solve(*([0, 1, 0, 3],)), 19)\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-factoradic-digit-value","generated_at":"2026-09-29T14:37:53.361906+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(d*math.factorial(i) for i,d in enumerate(digits))","root_cause":"Decimal positional weights replace factorial weights.","sha256":"5a20b61b61d4012f5f6ada4cd3ee92ab65eda73798881745b36be6ba2d62bfcf","title":"Factoradic digit value · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":46.462,"exit_code":1,"observations":[{"actual":14,"check":"fixture 1: ([0, 1, 2],)","expected":5,"passed":false},{"actual":24,"check":"fixture 2: ([0, 0, 0, 1],)","expected":6,"passed":false},{"actual":0,"check":"fixture 3: ([0],)","expected":0,"passed":true},{"actual":74,"check":"fixture 4: ([0, 1, 0, 3],)","expected":19,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([0, 1, 2],)\", \"actual\": 14, \"expected\": 5, \"passed\": false}, {\"check\": \"fixture 2: ([0, 0, 0, 1],)\", \"actual\": 24, \"expected\": 6, \"passed\": false}, {\"check\": \"fixture 3: ([0],)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: ([0, 1, 0, 3],)\", \"actual\": 74, \"expected\": 19, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":48.559,"exit_code":1,"observations":[{"actual":210,"check":"fixture 1: ([0, 1, 2],)","expected":5,"passed":false},{"actual":1000,"check":"fixture 2: ([0, 0, 0, 1],)","expected":6,"passed":false},{"actual":0,"check":"fixture 3: ([0],)","expected":0,"passed":true},{"actual":3010,"check":"fixture 4: ([0, 1, 0, 3],)","expected":19,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([0, 1, 2],)\", \"actual\": 210, \"expected\": 5, \"passed\": false}, {\"check\": \"fixture 2: ([0, 0, 0, 1],)\", \"actual\": 1000, \"expected\": 6, \"passed\": false}, {\"check\": \"fixture 3: ([0],)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: ([0, 1, 0, 3],)\", \"actual\": 3010, \"expected\": 19, \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":49.439,"exit_code":0,"observations":[{"actual":5,"check":"fixture 1: ([0, 1, 2],)","expected":5,"passed":true},{"actual":6,"check":"fixture 2: ([0, 0, 0, 1],)","expected":6,"passed":true},{"actual":0,"check":"fixture 3: ([0],)","expected":0,"passed":true},{"actual":19,"check":"fixture 4: ([0, 1, 0, 3],)","expected":19,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([0, 1, 2],)\", \"actual\": 5, \"expected\": 5, \"passed\": true}, {\"check\": \"fixture 2: ([0, 0, 0, 1],)\", \"actual\": 6, \"expected\": 6, \"passed\": true}, {\"check\": \"fixture 3: ([0],)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: ([0, 1, 0, 3],)\", \"actual\": 19, \"expected\": 19, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}