{"abstract":"A semitone is recorded in the ic2 slot and a major third in the ic4 slot.","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.","contract_signature":"x","evaluation_group":"w2-music-interval-interval-class-vector","failed_approach":"Wrapping the index modulo six moves the tritone into the ic1 slot and still shifts every other class.","family":"w2-music-interval-interval-class-vector-vector-slot","id":"FA-81076","implementations":{"attempt":{"sha256":"30fa58d7b65a88b033804ce759cd16c3f36d4a70946d196ba91aae1521095f64","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 % 6] += 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, 7], [0, 0, 0, 0, 1, 0]), ([0, 4, 8], [0, 0, 0, 3, 0, 0]), ([11, -1], [0, 0, 0, 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])], [([0, 4, 7], [0, 0, 1, 1, 1, 0]), ([0, 1], [1, 0, 0, 0, 0, 0]), ([0, 7], [0, 0, 0, 0, 1, 0]), ([0, 4, 8], [0, 0, 0, 3, 0, 0]), ([-1, 0, 4], [1, 0, 0, 1, 1, 0]), ([-13, 2], [0, 0, 1, 0, 0, 0]), ([0, 12, 24], [0, 0, 0, 0, 0, 0]), ([-13, 11], [0, 0, 0, 0, 0, 0])], [([0, 1], [1, 0, 0, 0, 0, 0]), ([0, 7], [0, 0, 0, 0, 1, 0]), ([0, 4, 8], [0, 0, 0, 3, 0, 0]), ([-1, 0, 4], [1, 0, 0, 1, 1, 0]), ([-13, 2], [0, 0, 1, 0, 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])], [([0, 4, 8], [0, 0, 0, 3, 0, 0]), ([-1, 0, 4], [1, 0, 0, 1, 1, 0]), ([-13, 2], [0, 0, 1, 0, 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]), ([3, 10], [0, 0, 0, 0, 1, 0])], [([-1, 0, 4], [1, 0, 0, 1, 1, 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]), ([3, 10], [0, 0, 0, 0, 1, 0]), ([4, -3, 9], [0, 0, 0, 0, 1, 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":"4db9b13d7cdf73b3a2799418ad7de5c674e3f23ec9493373cdc18695f9fbc73b","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\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, 7], [0, 0, 0, 0, 1, 0]), ([0, 4, 8], [0, 0, 0, 3, 0, 0]), ([11, -1], [0, 0, 0, 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])], [([0, 4, 7], [0, 0, 1, 1, 1, 0]), ([0, 1], [1, 0, 0, 0, 0, 0]), ([0, 7], [0, 0, 0, 0, 1, 0]), ([0, 4, 8], [0, 0, 0, 3, 0, 0]), ([-1, 0, 4], [1, 0, 0, 1, 1, 0]), ([-13, 2], [0, 0, 1, 0, 0, 0]), ([0, 12, 24], [0, 0, 0, 0, 0, 0]), ([-13, 11], [0, 0, 0, 0, 0, 0])], [([0, 1], [1, 0, 0, 0, 0, 0]), ([0, 7], [0, 0, 0, 0, 1, 0]), ([0, 4, 8], [0, 0, 0, 3, 0, 0]), ([-1, 0, 4], [1, 0, 0, 1, 1, 0]), ([-13, 2], [0, 0, 1, 0, 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])], [([0, 4, 8], [0, 0, 0, 3, 0, 0]), ([-1, 0, 4], [1, 0, 0, 1, 1, 0]), ([-13, 2], [0, 0, 1, 0, 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]), ([3, 10], [0, 0, 0, 0, 1, 0])], [([-1, 0, 4], [1, 0, 0, 1, 1, 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]), ([3, 10], [0, 0, 0, 0, 1, 0]), ([4, -3, 9], [0, 0, 0, 0, 1, 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-vector-slot","generated_at":"2026-09-29T14:49:59.841688+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.","root_cause":"Interval classes 1..6 are used directly as zero-based list indices.","sha256":"8e950be3b3e76f6faa3464a28bf10e12151614624d19bedf660273401b1b2930","title":"Interval-class vector of a pitch-class set: interval class stored one slot high · 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":40.064,"exit_code":1,"observations":[{"actual":[0,0,0,1,1,1],"check":"oracle 0","expected":[0,0,1,1,1,0],"passed":false},{"actual":[0,0,0,0,0,1],"check":"oracle 1","expected":[0,0,0,0,1,0],"passed":false},{"actual":[0,0,0,0,3,0],"check":"oracle 2","expected":[0,0,0,3,0,0],"passed":false},{"actual":[0,0,0,0,0,0],"check":"oracle 3","expected":[0,0,0,0,0,0],"passed":true},{"actual":[0,0,0,0,0,0],"check":"oracle 4","expected":[0,0,0,0,0,0],"passed":true},{"actual":[0,0,0,0,0,0],"check":"oracle 5","expected":[0,0,0,0,0,0],"passed":true},{"actual":[0,0,0,0,0,0],"check":"oracle 6","expected":[0,0,0,0,0,0],"passed":true},{"actual":[0,0,0,0,0,0],"check":"oracle 7","expected":[0,0,0,0,0,0],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 0\", \"actual\": [0, 0, 0, 1, 1, 1], \"expected\": [0, 0, 1, 1, 1, 0], \"passed\": false}, {\"check\": \"oracle 1\", \"actual\": [0, 0, 0, 0, 0, 1], \"expected\": [0, 0, 0, 0, 1, 0], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [0, 0, 0, 0, 3, 0], \"expected\": [0, 0, 0, 3, 0, 0], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [0, 0, 0, 0, 0, 0], \"expected\": [0, 0, 0, 0, 0, 0], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [0, 0, 0, 0, 0, 0], \"expected\": [0, 0, 0, 0, 0, 0], \"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, 0, 0, 0, 0], \"expected\": [0, 0, 0, 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\": false}\n"},"broken":{"elapsed_ms":38.504,"exit_code":1,"observations":[{"actual":[0,0,0,1,1,1],"check":"oracle 0","expected":[0,0,1,1,1,0],"passed":false},{"actual":[0,0,0,0,0,1],"check":"oracle 1","expected":[0,0,0,0,1,0],"passed":false},{"actual":[0,0,0,0,3,0],"check":"oracle 2","expected":[0,0,0,3,0,0],"passed":false},{"actual":[0,0,0,0,0,0],"check":"oracle 3","expected":[0,0,0,0,0,0],"passed":true},{"actual":[0,0,0,0,0,0],"check":"oracle 4","expected":[0,0,0,0,0,0],"passed":true},{"actual":[0,0,0,0,0,0],"check":"oracle 5","expected":[0,0,0,0,0,0],"passed":true},{"actual":[0,0,0,0,0,0],"check":"oracle 6","expected":[0,0,0,0,0,0],"passed":true},{"actual":[0,0,0,0,0,0],"check":"oracle 7","expected":[0,0,0,0,0,0],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 0\", \"actual\": [0, 0, 0, 1, 1, 1], \"expected\": [0, 0, 1, 1, 1, 0], \"passed\": false}, {\"check\": \"oracle 1\", \"actual\": [0, 0, 0, 0, 0, 1], \"expected\": [0, 0, 0, 0, 1, 0], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [0, 0, 0, 0, 3, 0], \"expected\": [0, 0, 0, 3, 0, 0], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [0, 0, 0, 0, 0, 0], \"expected\": [0, 0, 0, 0, 0, 0], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [0, 0, 0, 0, 0, 0], \"expected\": [0, 0, 0, 0, 0, 0], \"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, 0, 0, 0, 0], \"expected\": [0, 0, 0, 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\": 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."}}