{"abstract":"P8 and P15 are rejected while M8 would be accepted.","category":"Music interval and transposition theory","checks":8,"contract":"Input an interval string: quality from P, M, m, A, d, AA, dd followed by a positive integer. Compound numbers above 8 reduce by 7 until <= 8. P is valid only for 1, 4, 5, 8; M and m only for 2, 3, 6, 7. Inversion maps M<->m, A<->d, AA<->dd, P->P and number n -> 9-n. Invalid input returns None.","contract_signature":"x","evaluation_group":"w2-music-interval-interval-inversion","failed_approach":"Omitting the fourth instead rejects P4 and accepts M4.","family":"w2-music-interval-interval-inversion-perfect-number-set","id":"FA-81251","implementations":{"attempt":{"sha256":"cedc6d39d6a70db275cbade2ed79e7f2865b94833af6ec758860582083796487","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(x):\n    swap = {'M': 'm', 'm': 'M', 'A': 'd', 'd': 'A', 'AA': 'dd', 'dd': 'AA', 'P': 'P'}\n    if not isinstance(x, str):\n        return None\n    q = x.rstrip('0123456789')\n    digits = x[len(q):]\n    if q not in swap or not digits.isdigit() or int(digits) < 1:\n        return None\n    n = int(digits)\n    while n > 8:\n        n -= 7\n    perfect = n in (1, 5, 8)\n    if (q == 'P' and not perfect) or (q in ('M', 'm') and perfect):\n        return None\n    return swap[q] + str(9 - n)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('M3', 'm6'), ('m3', 'M6'), ('P5', 'P4'), ('P4', 'P5'), ('P1', 'P8'), ('P8', 'P1'), ('M4', None), ('P22', 'P1')], [('P4', 'P5'), ('P1', 'P8'), ('P8', 'P1'), ('A4', 'd5'), ('d5', 'A4'), ('M2', 'm7'), ('P15', 'P1'), ('M4', None)], [('P4', 'P5'), ('M2', 'm7'), ('m7', 'M2'), ('M10', 'm6'), ('P15', 'P1'), ('P12', 'P4'), ('M4', None), ('P22', 'P1')], [('P4', 'P5'), ('P8', 'P1'), ('P12', 'P4'), ('AA4', 'dd5'), ('dd5', 'AA4'), ('A1', 'd8'), ('M4', None), ('P22', 'P1')], [('P4', 'P5'), ('P8', 'P1'), ('P15', 'P1'), ('A1', 'd8'), ('d8', 'A1'), ('M6', 'm3'), ('m9', 'M7'), ('M4', None)]]\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":"19bccbf8d032fd7e7f1bfb29b0de15014c67acdf5533320cfffcb4ec0a4c0980","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(x):\n    swap = {'M': 'm', 'm': 'M', 'A': 'd', 'd': 'A', 'AA': 'dd', 'dd': 'AA', 'P': 'P'}\n    if not isinstance(x, str):\n        return None\n    q = x.rstrip('0123456789')\n    digits = x[len(q):]\n    if q not in swap or not digits.isdigit() or int(digits) < 1:\n        return None\n    n = int(digits)\n    while n > 8:\n        n -= 7\n    perfect = n in (1, 4, 5)\n    if (q == 'P' and not perfect) or (q in ('M', 'm') and perfect):\n        return None\n    return swap[q] + str(9 - n)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[('M3', 'm6'), ('m3', 'M6'), ('P5', 'P4'), ('P4', 'P5'), ('P1', 'P8'), ('P8', 'P1'), ('M4', None), ('P22', 'P1')], [('P4', 'P5'), ('P1', 'P8'), ('P8', 'P1'), ('A4', 'd5'), ('d5', 'A4'), ('M2', 'm7'), ('P15', 'P1'), ('M4', None)], [('P4', 'P5'), ('M2', 'm7'), ('m7', 'M2'), ('M10', 'm6'), ('P15', 'P1'), ('P12', 'P4'), ('M4', None), ('P22', 'P1')], [('P4', 'P5'), ('P8', 'P1'), ('P12', 'P4'), ('AA4', 'dd5'), ('dd5', 'AA4'), ('A1', 'd8'), ('M4', None), ('P22', 'P1')], [('P4', 'P5'), ('P8', 'P1'), ('P15', 'P1'), ('A1', 'd8'), ('d8', 'A1'), ('M6', 'm3'), ('m9', 'M7'), ('M4', None)]]\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-interval-inversion-perfect-number-set","generated_at":"2026-09-29T14:50:01.253820+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Pitch spelling and interval arithmetic decide the notes that notation, transposition and analysis tools display or play.","root_cause":"The set of perfect-class numbers omits the octave.","sha256":"9aa8b35100ca7da76aa327677b9e10bf50e71c69df00c7e43e2a55e285dffd8e","title":"Interval inversion by quality and number: octave excluded from perfect intervals · 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":40.986,"exit_code":1,"observations":[{"actual":"m6","check":"oracle 0","expected":"m6","passed":true},{"actual":"M6","check":"oracle 1","expected":"M6","passed":true},{"actual":"P4","check":"oracle 2","expected":"P4","passed":true},{"actual":null,"check":"oracle 3","expected":"P5","passed":false},{"actual":"P8","check":"oracle 4","expected":"P8","passed":true},{"actual":"P1","check":"oracle 5","expected":"P1","passed":true},{"actual":"m5","check":"oracle 6","expected":null,"passed":false},{"actual":"P1","check":"oracle 7","expected":"P1","passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 0\", \"actual\": \"m6\", \"expected\": \"m6\", \"passed\": true}, {\"check\": \"oracle 1\", \"actual\": \"M6\", \"expected\": \"M6\", \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": \"P4\", \"expected\": \"P4\", \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": null, \"expected\": \"P5\", \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": \"P8\", \"expected\": \"P8\", \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": \"P1\", \"expected\": \"P1\", \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": \"m5\", \"expected\": null, \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": \"P1\", \"expected\": \"P1\", \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":42.846,"exit_code":1,"observations":[{"actual":"m6","check":"oracle 0","expected":"m6","passed":true},{"actual":"M6","check":"oracle 1","expected":"M6","passed":true},{"actual":"P4","check":"oracle 2","expected":"P4","passed":true},{"actual":"P5","check":"oracle 3","expected":"P5","passed":true},{"actual":"P8","check":"oracle 4","expected":"P8","passed":true},{"actual":null,"check":"oracle 5","expected":"P1","passed":false},{"actual":null,"check":"oracle 6","expected":null,"passed":true},{"actual":null,"check":"oracle 7","expected":"P1","passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 0\", \"actual\": \"m6\", \"expected\": \"m6\", \"passed\": true}, {\"check\": \"oracle 1\", \"actual\": \"M6\", \"expected\": \"M6\", \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": \"P4\", \"expected\": \"P4\", \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": \"P5\", \"expected\": \"P5\", \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": \"P8\", \"expected\": \"P8\", \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": null, \"expected\": \"P1\", \"passed\": false}, {\"check\": \"oracle 6\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": null, \"expected\": \"P1\", \"passed\": false}], \"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."}}