{"abstract":"One fifth down returns 3/2 instead of the fourth 4/3.","category":"Music interval and transposition theory","checks":8,"contract":"Input an integer k with |k| <= 24 (booleans rejected). Return (3/2)**k octave-reduced into [1, 2) as [numerator, denominator]; out-of-range or non-integer input returns None.","contract_signature":"x","evaluation_group":"w2-music-interval-pythagorean-chain","failed_approach":"Inverting the generator fixes negative chains but reverses every positive chain.","family":"w2-music-interval-pythagorean-chain-chain-direction","id":"FA-81106","implementations":{"attempt":{"sha256":"236b72064416684c43c48afb1caecc15f36cb0d107651e85268e92fd5634407e","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    if not isinstance(x, int) or isinstance(x, bool) or abs(x) > 24:\n        return None\n    r = Fraction(2, 3) ** x\n    while r >= 2:\n        r /= 2\n    while r < 1:\n        r *= 2\n    return [r.numerator, r.denominator]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[(0, [1, 1]), (1, [3, 2]), (4, [81, 64]), (-1, [4, 3]), (-3, [32, 27]), (25, None), (-25, None), (30, None)], [(2, [9, 8]), (5, [243, 128]), (-2, [16, 9]), (-5, [256, 243]), (30, None), (True, None), ('1', None), (1.0, None)], [(1, [3, 2]), (2, [9, 8]), (3, [27, 16]), (4, [81, 64]), (6, [729, 512]), (-3, [32, 27]), (-6, [1024, 729]), (1.0, None)], [(3, [27, 16]), (4, [81, 64]), (5, [243, 128]), (6, [729, 512]), (7, [2187, 2048]), (12, [531441, 524288]), (-5, [256, 243]), (-12, [1048576, 531441])], [(5, [243, 128]), (6, [729, 512]), (7, [2187, 2048]), (12, [531441, 524288]), (-1, [4, 3]), (-2, [16, 9]), (-6, [1024, 729]), (-24, [549755813888, 282429536481])]]\nfor i, (args, expected) in enumerate(fixtures[N-1]):\n    check(\"oracle %d\" % i, solve(args), expected)\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":"58912f5126eb4d92f5dcc1176ebdaf1043e3962ffaad57f3916f46eb0729aec4","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    if not isinstance(x, int) or isinstance(x, bool) or abs(x) > 24:\n        return None\n    r = Fraction(3, 2) ** abs(x)\n    while r >= 2:\n        r /= 2\n    while r < 1:\n        r *= 2\n    return [r.numerator, r.denominator]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[(0, [1, 1]), (1, [3, 2]), (4, [81, 64]), (-1, [4, 3]), (-3, [32, 27]), (25, None), (-25, None), (30, None)], [(2, [9, 8]), (5, [243, 128]), (-2, [16, 9]), (-5, [256, 243]), (30, None), (True, None), ('1', None), (1.0, None)], [(1, [3, 2]), (2, [9, 8]), (3, [27, 16]), (4, [81, 64]), (6, [729, 512]), (-3, [32, 27]), (-6, [1024, 729]), (1.0, None)], [(3, [27, 16]), (4, [81, 64]), (5, [243, 128]), (6, [729, 512]), (7, [2187, 2048]), (12, [531441, 524288]), (-5, [256, 243]), (-12, [1048576, 531441])], [(5, [243, 128]), (6, [729, 512]), (7, [2187, 2048]), (12, [531441, 524288]), (-1, [4, 3]), (-2, [16, 9]), (-6, [1024, 729]), (-24, [549755813888, 282429536481])]]\nfor i, (args, expected) in enumerate(fixtures[N-1]):\n    check(\"oracle %d\" % i, solve(args), expected)\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":"A deterministic bounded teaching model with a stipulated toy contract; it is not a complete music notation or theory engine. 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":"w2-music-interval-pythagorean-chain-chain-direction","generated_at":"2026-09-29T14:49:59.938016+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Pythagorean and meantone tuning tools stack fifths and octave-reduce the result.","root_cause":"The exponent discards the sign of the chain length.","sha256":"d50b1f1bd752367cf7d88b212a2b65f9ec9639176430d901673497b33558f62d","title":"Pythagorean ratio for a chain of fifths: flatward chains stacked sharpward · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":42.011,"exit_code":1,"observations":[{"actual":[1,1],"check":"oracle 0","expected":[1,1],"passed":true},{"actual":[4,3],"check":"oracle 1","expected":[3,2],"passed":false},{"actual":[128,81],"check":"oracle 2","expected":[81,64],"passed":false},{"actual":[3,2],"check":"oracle 3","expected":[4,3],"passed":false},{"actual":[27,16],"check":"oracle 4","expected":[32,27],"passed":false},{"actual":null,"check":"oracle 5","expected":null,"passed":true},{"actual":null,"check":"oracle 6","expected":null,"passed":true},{"actual":null,"check":"oracle 7","expected":null,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 0\", \"actual\": [1, 1], \"expected\": [1, 1], \"passed\": true}, {\"check\": \"oracle 1\", \"actual\": [4, 3], \"expected\": [3, 2], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [128, 81], \"expected\": [81, 64], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [3, 2], \"expected\": [4, 3], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [27, 16], \"expected\": [32, 27], \"passed\": false}, {\"check\": \"oracle 5\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": null, \"expected\": null, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":46.133,"exit_code":1,"observations":[{"actual":[1,1],"check":"oracle 0","expected":[1,1],"passed":true},{"actual":[3,2],"check":"oracle 1","expected":[3,2],"passed":true},{"actual":[81,64],"check":"oracle 2","expected":[81,64],"passed":true},{"actual":[3,2],"check":"oracle 3","expected":[4,3],"passed":false},{"actual":[27,16],"check":"oracle 4","expected":[32,27],"passed":false},{"actual":null,"check":"oracle 5","expected":null,"passed":true},{"actual":null,"check":"oracle 6","expected":null,"passed":true},{"actual":null,"check":"oracle 7","expected":null,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 0\", \"actual\": [1, 1], \"expected\": [1, 1], \"passed\": true}, {\"check\": \"oracle 1\", \"actual\": [3, 2], \"expected\": [3, 2], \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": [81, 64], \"expected\": [81, 64], \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": [3, 2], \"expected\": [4, 3], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [27, 16], \"expected\": [32, 27], \"passed\": false}, {\"check\": \"oracle 5\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": null, \"expected\": null, \"passed\": true}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}