{"abstract":"First-inversion triads are labelled 64 and second-inversion triads 6.","category":"Music interval and transposition theory","checks":8,"contract":"Input 3 or 4 MIDI integers in any order. The pitch-class set must match a template relative to some root (triads 047 037 036 048; sevenths 047t 037t 047e 036t 0369, t=10 e=11); roots are tried in ascending pitch-class order. The bass is the lowest MIDI note. Return [root_pc, figure] with figures \"\", \"6\", \"64\" for triads and \"7\", \"65\", \"43\", \"42\" for sevenths by the bass position in the template; otherwise None.","contract_signature":"x","evaluation_group":"w2-music-interval-figured-bass","failed_approach":"Writing 46 instead of 64 corrupts the second-inversion figure.","family":"w2-music-interval-figured-bass-triad-figure-order","id":"FA-81331","implementations":{"attempt":{"sha256":"963f10c23be12540dcdd21ca9f191cd128a1aa1ce295b318d4e3afe686f3f6de","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(x):\n    if not isinstance(x, list) or not 3 <= len(x) <= 4 or not all(isinstance(v, int) for v in x):\n        return None\n    bass = min(x)\n    pcs = sorted(set(v % 12 for v in x))\n    for r in pcs:\n        rel = sorted((p - r) % 12 for p in pcs)\n        if rel in ([0, 4, 7], [0, 3, 7], [0, 3, 6], [0, 4, 8], [0, 4, 7, 10], [0, 3, 7, 10], [0, 4, 7, 11], [0, 3, 6, 10], [0, 3, 6, 9]):\n            pos = rel.index((bass - r) % 12)\n            figs = ['', '6', '46'] if len(rel) == 3 else ['7', '65', '43', '42']\n            return [r, figs[pos]]\n    return None\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([60, 64, 67], [0, '']), ([64, 67, 72], [0, '6']), ([67, 72, 76], [0, '64']), ([72, 64, 67], [0, '6']), ([76, 60, 67], [0, '']), ([55, 59, 62, 65], [7, '7']), ([59, 62, 65, 67], [7, '65']), ([62, 65, 67, 71], [7, '43'])], [([67, 72, 76], [0, '64']), ([59, 62, 65, 67], [7, '65']), ([62, 65, 67, 71], [7, '43']), ([65, 67, 71, 74], [7, '42']), ([60, 64, 67, 72], [0, '']), ([48, 64, 67, 72], [0, '']), ([60, 63, 66, 69], [0, '7']), ([71, 62, 65], [11, '6'])], [([64, 67, 72], [0, '6']), ([67, 72, 76], [0, '64']), ([72, 64, 67], [0, '6']), ([60, 64, 67, 72], [0, '']), ([48, 64, 67, 72], [0, '']), ([60, 63, 66, 69], [0, '7']), ([62, 65, 68, 71], [2, '7']), ([59, 62, 65, 69], [11, '7'])], [([67, 72, 76], [0, '64']), ([62, 65, 68, 71], [2, '7']), ([59, 62, 65, 69], [11, '7']), ([57, 60, 64], [9, '']), ([60, 62, 67], None), ([60, 64, 68], [0, '']), ([64, 60, 67], [0, '']), ([71, 62, 65], [11, '6'])], [([64, 67, 72], [0, '6']), ([67, 72, 76], [0, '64']), ([72, 64, 67], [0, '6']), ([60, 62, 67], None), ([60, 64, 68], [0, '']), ([64, 60, 67], [0, '']), ([60, 61, 62], None), ([60, 64], 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":"1c25d0cf63b69e8f54fc40a6ea07e00edbc2eab6479bbe744845f9ed2c81a7e1","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(x):\n    if not isinstance(x, list) or not 3 <= len(x) <= 4 or not all(isinstance(v, int) for v in x):\n        return None\n    bass = min(x)\n    pcs = sorted(set(v % 12 for v in x))\n    for r in pcs:\n        rel = sorted((p - r) % 12 for p in pcs)\n        if rel in ([0, 4, 7], [0, 3, 7], [0, 3, 6], [0, 4, 8], [0, 4, 7, 10], [0, 3, 7, 10], [0, 4, 7, 11], [0, 3, 6, 10], [0, 3, 6, 9]):\n            pos = rel.index((bass - r) % 12)\n            figs = ['', '64', '6'] if len(rel) == 3 else ['7', '65', '43', '42']\n            return [r, figs[pos]]\n    return None\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([60, 64, 67], [0, '']), ([64, 67, 72], [0, '6']), ([67, 72, 76], [0, '64']), ([72, 64, 67], [0, '6']), ([76, 60, 67], [0, '']), ([55, 59, 62, 65], [7, '7']), ([59, 62, 65, 67], [7, '65']), ([62, 65, 67, 71], [7, '43'])], [([67, 72, 76], [0, '64']), ([59, 62, 65, 67], [7, '65']), ([62, 65, 67, 71], [7, '43']), ([65, 67, 71, 74], [7, '42']), ([60, 64, 67, 72], [0, '']), ([48, 64, 67, 72], [0, '']), ([60, 63, 66, 69], [0, '7']), ([71, 62, 65], [11, '6'])], [([64, 67, 72], [0, '6']), ([67, 72, 76], [0, '64']), ([72, 64, 67], [0, '6']), ([60, 64, 67, 72], [0, '']), ([48, 64, 67, 72], [0, '']), ([60, 63, 66, 69], [0, '7']), ([62, 65, 68, 71], [2, '7']), ([59, 62, 65, 69], [11, '7'])], [([67, 72, 76], [0, '64']), ([62, 65, 68, 71], [2, '7']), ([59, 62, 65, 69], [11, '7']), ([57, 60, 64], [9, '']), ([60, 62, 67], None), ([60, 64, 68], [0, '']), ([64, 60, 67], [0, '']), ([71, 62, 65], [11, '6'])], [([64, 67, 72], [0, '6']), ([67, 72, 76], [0, '64']), ([72, 64, 67], [0, '6']), ([60, 62, 67], None), ([60, 64, 68], [0, '']), ([64, 60, 67], [0, '']), ([60, 61, 62], None), ([60, 64], 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-figured-bass-triad-figure-order","generated_at":"2026-09-29T14:50:01.904376+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Figured-bass realisation and harmonic analysis depend on identifying chord root and inversion.","root_cause":"The triad figure list is ordered with the second-inversion figure before the first.","sha256":"fea22ad6c66c9f59450af955971d54f307edee3c6bac6fe7b5b380d7937e8543","title":"Triad and seventh inversion figures: inversion figures swapped · 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":43.108,"exit_code":1,"observations":[{"actual":[0,""],"check":"oracle 0","expected":[0,""],"passed":true},{"actual":[0,"6"],"check":"oracle 1","expected":[0,"6"],"passed":true},{"actual":[0,"46"],"check":"oracle 2","expected":[0,"64"],"passed":false},{"actual":[0,"6"],"check":"oracle 3","expected":[0,"6"],"passed":true},{"actual":[0,""],"check":"oracle 4","expected":[0,""],"passed":true},{"actual":[7,"7"],"check":"oracle 5","expected":[7,"7"],"passed":true},{"actual":[7,"65"],"check":"oracle 6","expected":[7,"65"],"passed":true},{"actual":[7,"43"],"check":"oracle 7","expected":[7,"43"],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 0\", \"actual\": [0, \"\"], \"expected\": [0, \"\"], \"passed\": true}, {\"check\": \"oracle 1\", \"actual\": [0, \"6\"], \"expected\": [0, \"6\"], \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": [0, \"46\"], \"expected\": [0, \"64\"], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [0, \"6\"], \"expected\": [0, \"6\"], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [0, \"\"], \"expected\": [0, \"\"], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [7, \"7\"], \"expected\": [7, \"7\"], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [7, \"65\"], \"expected\": [7, \"65\"], \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": [7, \"43\"], \"expected\": [7, \"43\"], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":40.614,"exit_code":1,"observations":[{"actual":[0,""],"check":"oracle 0","expected":[0,""],"passed":true},{"actual":[0,"64"],"check":"oracle 1","expected":[0,"6"],"passed":false},{"actual":[0,"6"],"check":"oracle 2","expected":[0,"64"],"passed":false},{"actual":[0,"64"],"check":"oracle 3","expected":[0,"6"],"passed":false},{"actual":[0,""],"check":"oracle 4","expected":[0,""],"passed":true},{"actual":[7,"7"],"check":"oracle 5","expected":[7,"7"],"passed":true},{"actual":[7,"65"],"check":"oracle 6","expected":[7,"65"],"passed":true},{"actual":[7,"43"],"check":"oracle 7","expected":[7,"43"],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 0\", \"actual\": [0, \"\"], \"expected\": [0, \"\"], \"passed\": true}, {\"check\": \"oracle 1\", \"actual\": [0, \"64\"], \"expected\": [0, \"6\"], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [0, \"6\"], \"expected\": [0, \"64\"], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [0, \"64\"], \"expected\": [0, \"6\"], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [0, \"\"], \"expected\": [0, \"\"], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [7, \"7\"], \"expected\": [7, \"7\"], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [7, \"65\"], \"expected\": [7, \"65\"], \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": [7, \"43\"], \"expected\": [7, \"43\"], \"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."}}