{"abstract":"A set containing -1 is analysed as if it contained 1, so [-1,0,4] gets the wrong vector.","category":"Music interval and transposition theory","checks":8,"contract":"Input a list of integers, reduced mod 12 and deduplicated. For each unordered pair count its interval class min(d, 12-d) in 1..6. Return the six counts [ic1..ic6]; non-integer input returns None.","evaluation_group":"w2-music-interval-interval-class-vector","failed_approach":"Adding twelve once leaves values below -12 negative, so duplicates like 11 and -1 are no longer merged.","family":"w2-music-interval-interval-class-vector-negative-reduction","id":"FA-81081","implementations":{"attempt":{"sha256":"2c8ae9104085e0b10713cbaf5cdd0afc005161c442ac4163d12f178154db2a36","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 all(isinstance(v, int) for v in x):\n        return None\n    pcs = sorted(set(v % 12 if v >= 0 else 12 + v for v in x))\n    vec = [0] * 6\n    for i in range(len(pcs)):\n        for j in range(i + 1, len(pcs)):\n            d = (pcs[j] - pcs[i]) % 12\n            ic = min(d, 12 - d)\n            vec[ic - 1] += 1\n    return vec\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([0, 4, 7], [0, 0, 1, 1, 1, 0]), ([0, 1], [1, 0, 0, 0, 0, 0]), ([0, 6], [0, 0, 0, 0, 0, 1]), ([0, 7], [0, 0, 0, 0, 1, 0]), ([0, 1, 4, 6], [1, 1, 1, 1, 1, 1]), ([11, -1], [0, 0, 0, 0, 0, 0]), ([-13, 2], [0, 0, 1, 0, 0, 0]), ([-13, 11], [0, 0, 0, 0, 0, 0])], [([0, 7], [0, 0, 0, 0, 1, 0]), ([0, 1, 4, 6], [1, 1, 1, 1, 1, 1]), ([0, 1, 3, 7], [1, 1, 1, 1, 1, 1]), ([0, 2, 4, 6, 8, 10], [0, 6, 0, 6, 0, 3]), ([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [12, 12, 12, 12, 12, 6]), ([-1, 0, 4], [1, 0, 0, 1, 1, 0]), ([4, -3, 9], [0, 0, 0, 0, 1, 0]), ([-14, 10, 3], [0, 0, 0, 0, 1, 0])], [([0, 2, 4, 6, 8, 10], [0, 6, 0, 6, 0, 3]), ([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [12, 12, 12, 12, 12, 6]), ([0, 3, 6, 9], [0, 0, 4, 0, 0, 2]), ([0, 4, 8], [0, 0, 0, 3, 0, 0]), ([-13, 2], [0, 0, 1, 0, 0, 0]), ([0, 5, 7], [0, 1, 0, 0, 2, 0]), ([-13, 11], [0, 0, 0, 0, 0, 0]), ([-25, 1, 11], [0, 1, 0, 0, 0, 0])], [([0, 4, 8], [0, 0, 0, 3, 0, 0]), ([0, 5, 7], [0, 1, 0, 0, 2, 0]), ([1, 8], [0, 0, 0, 0, 1, 0]), ([0, 2, 7], [0, 1, 0, 0, 2, 0]), ([2, 11], [0, 0, 1, 0, 0, 0]), ([4, -3, 9], [0, 0, 0, 0, 1, 0]), ([-13, 11], [0, 0, 0, 0, 0, 0]), ([-14, 10, 3], [0, 0, 0, 0, 1, 0])], [([11, -1], [0, 0, 0, 0, 0, 0]), ([0, 2, 7], [0, 1, 0, 0, 2, 0]), ([2, 11], [0, 0, 1, 0, 0, 0]), ([], [0, 0, 0, 0, 0, 0]), ([5], [0, 0, 0, 0, 0, 0]), ([0, 12, 24], [0, 0, 0, 0, 0, 0]), ([-13, 11], [0, 0, 0, 0, 0, 0]), ([-14, 10, 3], [0, 0, 0, 0, 1, 0])]]\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":"c2b32158d57a63b279a8b05fdfe383d1aeeeae6cd5741120db9ff5ba06151626","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 all(isinstance(v, int) for v in x):\n        return None\n    pcs = sorted(set(abs(v) % 12 for v in x))\n    vec = [0] * 6\n    for i in range(len(pcs)):\n        for j in range(i + 1, len(pcs)):\n            d = (pcs[j] - pcs[i]) % 12\n            ic = min(d, 12 - d)\n            vec[ic - 1] += 1\n    return vec\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([0, 4, 7], [0, 0, 1, 1, 1, 0]), ([0, 1], [1, 0, 0, 0, 0, 0]), ([0, 6], [0, 0, 0, 0, 0, 1]), ([0, 7], [0, 0, 0, 0, 1, 0]), ([0, 1, 4, 6], [1, 1, 1, 1, 1, 1]), ([11, -1], [0, 0, 0, 0, 0, 0]), ([-13, 2], [0, 0, 1, 0, 0, 0]), ([-13, 11], [0, 0, 0, 0, 0, 0])], [([0, 7], [0, 0, 0, 0, 1, 0]), ([0, 1, 4, 6], [1, 1, 1, 1, 1, 1]), ([0, 1, 3, 7], [1, 1, 1, 1, 1, 1]), ([0, 2, 4, 6, 8, 10], [0, 6, 0, 6, 0, 3]), ([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [12, 12, 12, 12, 12, 6]), ([-1, 0, 4], [1, 0, 0, 1, 1, 0]), ([4, -3, 9], [0, 0, 0, 0, 1, 0]), ([-14, 10, 3], [0, 0, 0, 0, 1, 0])], [([0, 2, 4, 6, 8, 10], [0, 6, 0, 6, 0, 3]), ([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [12, 12, 12, 12, 12, 6]), ([0, 3, 6, 9], [0, 0, 4, 0, 0, 2]), ([0, 4, 8], [0, 0, 0, 3, 0, 0]), ([-13, 2], [0, 0, 1, 0, 0, 0]), ([0, 5, 7], [0, 1, 0, 0, 2, 0]), ([-13, 11], [0, 0, 0, 0, 0, 0]), ([-25, 1, 11], [0, 1, 0, 0, 0, 0])], [([0, 4, 8], [0, 0, 0, 3, 0, 0]), ([0, 5, 7], [0, 1, 0, 0, 2, 0]), ([1, 8], [0, 0, 0, 0, 1, 0]), ([0, 2, 7], [0, 1, 0, 0, 2, 0]), ([2, 11], [0, 0, 1, 0, 0, 0]), ([4, -3, 9], [0, 0, 0, 0, 1, 0]), ([-13, 11], [0, 0, 0, 0, 0, 0]), ([-14, 10, 3], [0, 0, 0, 0, 1, 0])], [([11, -1], [0, 0, 0, 0, 0, 0]), ([0, 2, 7], [0, 1, 0, 0, 2, 0]), ([2, 11], [0, 0, 1, 0, 0, 0]), ([], [0, 0, 0, 0, 0, 0]), ([5], [0, 0, 0, 0, 0, 0]), ([0, 12, 24], [0, 0, 0, 0, 0, 0]), ([-13, 11], [0, 0, 0, 0, 0, 0]), ([-14, 10, 3], [0, 0, 0, 0, 1, 0])]]\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"},"fixed":{"sha256":"0f8f6d7a89356f5b376d4c481fcdda1c80384e39cdd8f2e7a0ddf147e667bec8","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 all(isinstance(v, int) for v in x):\n        return None\n    pcs = sorted(set(v % 12 for v in x))\n    vec = [0] * 6\n    for i in range(len(pcs)):\n        for j in range(i + 1, len(pcs)):\n            d = (pcs[j] - pcs[i]) % 12\n            ic = min(d, 12 - d)\n            vec[ic - 1] += 1\n    return vec\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([0, 4, 7], [0, 0, 1, 1, 1, 0]), ([0, 1], [1, 0, 0, 0, 0, 0]), ([0, 6], [0, 0, 0, 0, 0, 1]), ([0, 7], [0, 0, 0, 0, 1, 0]), ([0, 1, 4, 6], [1, 1, 1, 1, 1, 1]), ([11, -1], [0, 0, 0, 0, 0, 0]), ([-13, 2], [0, 0, 1, 0, 0, 0]), ([-13, 11], [0, 0, 0, 0, 0, 0])], [([0, 7], [0, 0, 0, 0, 1, 0]), ([0, 1, 4, 6], [1, 1, 1, 1, 1, 1]), ([0, 1, 3, 7], [1, 1, 1, 1, 1, 1]), ([0, 2, 4, 6, 8, 10], [0, 6, 0, 6, 0, 3]), ([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [12, 12, 12, 12, 12, 6]), ([-1, 0, 4], [1, 0, 0, 1, 1, 0]), ([4, -3, 9], [0, 0, 0, 0, 1, 0]), ([-14, 10, 3], [0, 0, 0, 0, 1, 0])], [([0, 2, 4, 6, 8, 10], [0, 6, 0, 6, 0, 3]), ([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [12, 12, 12, 12, 12, 6]), ([0, 3, 6, 9], [0, 0, 4, 0, 0, 2]), ([0, 4, 8], [0, 0, 0, 3, 0, 0]), ([-13, 2], [0, 0, 1, 0, 0, 0]), ([0, 5, 7], [0, 1, 0, 0, 2, 0]), ([-13, 11], [0, 0, 0, 0, 0, 0]), ([-25, 1, 11], [0, 1, 0, 0, 0, 0])], [([0, 4, 8], [0, 0, 0, 3, 0, 0]), ([0, 5, 7], [0, 1, 0, 0, 2, 0]), ([1, 8], [0, 0, 0, 0, 1, 0]), ([0, 2, 7], [0, 1, 0, 0, 2, 0]), ([2, 11], [0, 0, 1, 0, 0, 0]), ([4, -3, 9], [0, 0, 0, 0, 1, 0]), ([-13, 11], [0, 0, 0, 0, 0, 0]), ([-14, 10, 3], [0, 0, 0, 0, 1, 0])], [([11, -1], [0, 0, 0, 0, 0, 0]), ([0, 2, 7], [0, 1, 0, 0, 2, 0]), ([2, 11], [0, 0, 1, 0, 0, 0]), ([], [0, 0, 0, 0, 0, 0]), ([5], [0, 0, 0, 0, 0, 0]), ([0, 12, 24], [0, 0, 0, 0, 0, 0]), ([-13, 11], [0, 0, 0, 0, 0, 0]), ([-14, 10, 3], [0, 0, 0, 0, 1, 0])]]\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-class-vector-negative-reduction","generated_at":"2026-09-29T14:49:59.864123+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Interval vectors drive set-class similarity measures and Z-relation detection.","repair":"Restore the negative reduction step so that it reads `sorted(set(v % 12 for v in x))`.","root_cause":"Negative inputs are reduced via their absolute value, which reflects them around zero.","sha256":"b1d48bc3bc879b21aaf3ba362574a237af9bf4128dcd62ab8024dad8954e38e0","title":"Interval-class vector of a pitch-class set: negative pitch numbers reflected instead of reduced · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":42.13,"exit_code":1,"observations":[{"actual":[0,0,1,1,1,0],"check":"oracle 0","expected":[0,0,1,1,1,0],"passed":true},{"actual":[1,0,0,0,0,0],"check":"oracle 1","expected":[1,0,0,0,0,0],"passed":true},{"actual":[0,0,0,0,0,1],"check":"oracle 2","expected":[0,0,0,0,0,1],"passed":true},{"actual":[0,0,0,0,1,0],"check":"oracle 3","expected":[0,0,0,0,1,0],"passed":true},{"actual":[1,1,1,1,1,1],"check":"oracle 4","expected":[1,1,1,1,1,1],"passed":true},{"actual":[0,0,0,0,0,0],"check":"oracle 5","expected":[0,0,0,0,0,0],"passed":true},{"actual":[0,0,1,0,0,0],"check":"oracle 6","expected":[0,0,1,0,0,0],"passed":true},{"actual":[0,0,0,0,0,1],"check":"oracle 7","expected":[0,0,0,0,0,0],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 0\", \"actual\": [0, 0, 1, 1, 1, 0], \"expected\": [0, 0, 1, 1, 1, 0], \"passed\": true}, {\"check\": \"oracle 1\", \"actual\": [1, 0, 0, 0, 0, 0], \"expected\": [1, 0, 0, 0, 0, 0], \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": [0, 0, 0, 0, 0, 1], \"expected\": [0, 0, 0, 0, 0, 1], \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": [0, 0, 0, 0, 1, 0], \"expected\": [0, 0, 0, 0, 1, 0], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [1, 1, 1, 1, 1, 1], \"expected\": [1, 1, 1, 1, 1, 1], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [0, 0, 0, 0, 0, 0], \"expected\": [0, 0, 0, 0, 0, 0], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [0, 0, 1, 0, 0, 0], \"expected\": [0, 0, 1, 0, 0, 0], \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": [0, 0, 0, 0, 0, 1], \"expected\": [0, 0, 0, 0, 0, 0], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":41.137,"exit_code":1,"observations":[{"actual":[0,0,1,1,1,0],"check":"oracle 0","expected":[0,0,1,1,1,0],"passed":true},{"actual":[1,0,0,0,0,0],"check":"oracle 1","expected":[1,0,0,0,0,0],"passed":true},{"actual":[0,0,0,0,0,1],"check":"oracle 2","expected":[0,0,0,0,0,1],"passed":true},{"actual":[0,0,0,0,1,0],"check":"oracle 3","expected":[0,0,0,0,1,0],"passed":true},{"actual":[1,1,1,1,1,1],"check":"oracle 4","expected":[1,1,1,1,1,1],"passed":true},{"actual":[0,1,0,0,0,0],"check":"oracle 5","expected":[0,0,0,0,0,0],"passed":false},{"actual":[1,0,0,0,0,0],"check":"oracle 6","expected":[0,0,1,0,0,0],"passed":false},{"actual":[0,1,0,0,0,0],"check":"oracle 7","expected":[0,0,0,0,0,0],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 0\", \"actual\": [0, 0, 1, 1, 1, 0], \"expected\": [0, 0, 1, 1, 1, 0], \"passed\": true}, {\"check\": \"oracle 1\", \"actual\": [1, 0, 0, 0, 0, 0], \"expected\": [1, 0, 0, 0, 0, 0], \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": [0, 0, 0, 0, 0, 1], \"expected\": [0, 0, 0, 0, 0, 1], \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": [0, 0, 0, 0, 1, 0], \"expected\": [0, 0, 0, 0, 1, 0], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [1, 1, 1, 1, 1, 1], \"expected\": [1, 1, 1, 1, 1, 1], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [0, 1, 0, 0, 0, 0], \"expected\": [0, 0, 0, 0, 0, 0], \"passed\": false}, {\"check\": \"oracle 6\", \"actual\": [1, 0, 0, 0, 0, 0], \"expected\": [0, 0, 1, 0, 0, 0], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [0, 1, 0, 0, 0, 0], \"expected\": [0, 0, 0, 0, 0, 0], \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":43.495,"exit_code":0,"observations":[{"actual":[0,0,1,1,1,0],"check":"oracle 0","expected":[0,0,1,1,1,0],"passed":true},{"actual":[1,0,0,0,0,0],"check":"oracle 1","expected":[1,0,0,0,0,0],"passed":true},{"actual":[0,0,0,0,0,1],"check":"oracle 2","expected":[0,0,0,0,0,1],"passed":true},{"actual":[0,0,0,0,1,0],"check":"oracle 3","expected":[0,0,0,0,1,0],"passed":true},{"actual":[1,1,1,1,1,1],"check":"oracle 4","expected":[1,1,1,1,1,1],"passed":true},{"actual":[0,0,0,0,0,0],"check":"oracle 5","expected":[0,0,0,0,0,0],"passed":true},{"actual":[0,0,1,0,0,0],"check":"oracle 6","expected":[0,0,1,0,0,0],"passed":true},{"actual":[0,0,0,0,0,0],"check":"oracle 7","expected":[0,0,0,0,0,0],"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 0\", \"actual\": [0, 0, 1, 1, 1, 0], \"expected\": [0, 0, 1, 1, 1, 0], \"passed\": true}, {\"check\": \"oracle 1\", \"actual\": [1, 0, 0, 0, 0, 0], \"expected\": [1, 0, 0, 0, 0, 0], \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": [0, 0, 0, 0, 0, 1], \"expected\": [0, 0, 0, 0, 0, 1], \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": [0, 0, 0, 0, 1, 0], \"expected\": [0, 0, 0, 0, 1, 0], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [1, 1, 1, 1, 1, 1], \"expected\": [1, 1, 1, 1, 1, 1], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [0, 0, 0, 0, 0, 0], \"expected\": [0, 0, 0, 0, 0, 0], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [0, 0, 1, 0, 0, 0], \"expected\": [0, 0, 1, 0, 0, 0], \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": [0, 0, 0, 0, 0, 0], \"expected\": [0, 0, 0, 0, 0, 0], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}