{"abstract":"Most-significant-first balanced ternary is evaluated backwards.","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 most-significant-first and each digit is -1, 0, or 1; return its signed integer value. Empty digits have value zero. Exact operational definition: sum(d*3**i for i,d in enumerate(reversed(digits)))","evaluation_group":"model-1e36ae4d1d0295cb","failed_approach":"A binary place value is used for a ternary numeral.","family":"xn-balanced-ternary-digit-value","id":"FA-5751","implementations":{"attempt":{"sha256":"ace298e6fb5e69f9abe0c99658e77ebbdd612b0eab86f2fcfb922dbd7016749e","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*2**i for i,d in enumerate(reversed(digits)))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([1, 0, -1],)', solve(*([1, 0, -1],)), 8)\ncheck('fixture 2: ([-1, 1],)', solve(*([-1, 1],)), -2)\ncheck('fixture 3: ([0],)', solve(*([0],)), 0)\ncheck('fixture 4: ([1, 1, 1],)', solve(*([1, 1, 1],)), 13)\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":"39c668ed9a94215f5e46b0e41d0d27a7eaf54af4f593d1829bd7f4884969613b","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*3**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: ([1, 0, -1],)', solve(*([1, 0, -1],)), 8)\ncheck('fixture 2: ([-1, 1],)', solve(*([-1, 1],)), -2)\ncheck('fixture 3: ([0],)', solve(*([0],)), 0)\ncheck('fixture 4: ([1, 1, 1],)', solve(*([1, 1, 1],)), 13)\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":"34e0c475e7a035828182c39fdcd2b5655f4788098f9d15d7d2d7a8828e700b90","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*3**i for i,d in enumerate(reversed(digits)))\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('fixture 1: ([1, 0, -1],)', solve(*([1, 0, -1],)), 8)\ncheck('fixture 2: ([-1, 1],)', solve(*([-1, 1],)), -2)\ncheck('fixture 3: ([0],)', solve(*([0],)), 0)\ncheck('fixture 4: ([1, 1, 1],)', solve(*([1, 1, 1],)), 13)\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-balanced-ternary-digit-value","generated_at":"2026-09-29T14:37:53.355029+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*3**i for i,d in enumerate(reversed(digits)))","root_cause":"Most-significant-first balanced ternary is evaluated backwards.","sha256":"6a9d1ff96d9c19745a380503893154a373dbabe588e2315c7a31686fea46249a","title":"Balanced ternary digit value · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":46.198,"exit_code":1,"observations":[{"actual":3,"check":"fixture 1: ([1, 0, -1],)","expected":8,"passed":false},{"actual":-1,"check":"fixture 2: ([-1, 1],)","expected":-2,"passed":false},{"actual":0,"check":"fixture 3: ([0],)","expected":0,"passed":true},{"actual":7,"check":"fixture 4: ([1, 1, 1],)","expected":13,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 0, -1],)\", \"actual\": 3, \"expected\": 8, \"passed\": false}, {\"check\": \"fixture 2: ([-1, 1],)\", \"actual\": -1, \"expected\": -2, \"passed\": false}, {\"check\": \"fixture 3: ([0],)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: ([1, 1, 1],)\", \"actual\": 7, \"expected\": 13, \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":49.257,"exit_code":1,"observations":[{"actual":-8,"check":"fixture 1: ([1, 0, -1],)","expected":8,"passed":false},{"actual":2,"check":"fixture 2: ([-1, 1],)","expected":-2,"passed":false},{"actual":0,"check":"fixture 3: ([0],)","expected":0,"passed":true},{"actual":13,"check":"fixture 4: ([1, 1, 1],)","expected":13,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 0, -1],)\", \"actual\": -8, \"expected\": 8, \"passed\": false}, {\"check\": \"fixture 2: ([-1, 1],)\", \"actual\": 2, \"expected\": -2, \"passed\": false}, {\"check\": \"fixture 3: ([0],)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: ([1, 1, 1],)\", \"actual\": 13, \"expected\": 13, \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":46.841,"exit_code":0,"observations":[{"actual":8,"check":"fixture 1: ([1, 0, -1],)","expected":8,"passed":true},{"actual":-2,"check":"fixture 2: ([-1, 1],)","expected":-2,"passed":true},{"actual":0,"check":"fixture 3: ([0],)","expected":0,"passed":true},{"actual":13,"check":"fixture 4: ([1, 1, 1],)","expected":13,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"fixture 1: ([1, 0, -1],)\", \"actual\": 8, \"expected\": 8, \"passed\": true}, {\"check\": \"fixture 2: ([-1, 1],)\", \"actual\": -2, \"expected\": -2, \"passed\": true}, {\"check\": \"fixture 3: ([0],)\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"fixture 4: ([1, 1, 1],)\", \"actual\": 13, \"expected\": 13, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}