{"abstract":"A major triad on D returns [2,6,9]-shaped values rather than [0,3,7].","category":"Music interval and transposition theory","checks":8,"contract":"Input a list of integers. Compute the right-packed normal form of the set and of its inversion (p -> -p mod 12), transpose each to start on 0, and return whichever is more packed: compare the last value, then the penultimate, and so on toward the second (the original wins ties). Empty input returns []; non-integers return None.","contract_signature":"x","evaluation_group":"w2-music-interval-prime-form","failed_approach":"Subtracting the lowest pitch class rather than the first member of the chosen rotation mis-transposes wrapped forms.","family":"w2-music-interval-prime-form-transposition-to-zero","id":"FA-81051","implementations":{"attempt":{"sha256":"143ea1fcedd153cccd640ca887f3130bff1175296d46fba993273516594563a8","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    def normal(values):\n        pcs = sorted(set(p % 12 for p in values))\n        n = len(pcs)\n        best = None\n        for r in range(n):\n            rot = pcs[r:] + [p + 12 for p in pcs[:r]]\n            key = [rot[-1] - rot[0]] + [rot[j] - rot[0] for j in range(n - 2, 0, -1)]\n            if best is None or (key, rot[0]) < best[0]:\n                best = ((key, rot[0]), rot)\n        return [p - pcs[0] for p in best[1]]\n    if not x:\n        return []\n    a = normal(x)\n    b = normal([(-p) % 12 for p in x])\n    ka = [a[-1]] + a[-2:0:-1]\n    kb = [b[-1]] + b[-2:0:-1]\n    return a if ka <= kb else b\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([0, 4, 7], [0, 3, 7]), ([0, 3, 7], [0, 3, 7]), ([2, 6, 9], [0, 3, 7]), ([0, 1, 5, 6, 8], [0, 1, 5, 6, 8]), ([0, 4, 8], [0, 4, 8]), ([0, 3, 6, 9], [0, 3, 6, 9]), ([0, 5, 7], [0, 2, 7]), ([], [])], [([0, 4, 7], [0, 3, 7]), ([0, 3, 7], [0, 3, 7]), ([2, 6, 9], [0, 3, 7]), ([0, 1, 5, 6, 8], [0, 1, 5, 6, 8]), ([0, 1, 3, 5, 8, 9], [0, 1, 4, 5, 7, 9]), ([0, 2, 3, 6, 7, 9], [0, 2, 3, 6, 7, 9]), ([0, 1, 4], [0, 1, 4]), ([7, 11, 2, 5], [0, 2, 5, 8])], [([2, 6, 9], [0, 3, 7]), ([0, 1, 5, 6, 8], [0, 1, 5, 6, 8]), ([0, 1, 3, 5, 8, 9], [0, 1, 4, 5, 7, 9]), ([0, 2, 3, 6, 7, 9], [0, 2, 3, 6, 7, 9]), ([0, 1, 4], [0, 1, 4]), ([0, 3, 4], [0, 1, 4]), ([4, 5, 8], [0, 1, 4]), ([10, 1, 5], [0, 3, 7])], [([0, 1, 5, 6, 8], [0, 1, 5, 6, 8]), ([0, 2, 3, 6, 7, 9], [0, 2, 3, 6, 7, 9]), ([0, 1, 4], [0, 1, 4]), ([0, 3, 4], [0, 1, 4]), ([4, 5, 8], [0, 1, 4]), ([0, 2, 7], [0, 2, 7]), ([0, 5, 7], [0, 2, 7]), ([0, 3, 6, 10], [0, 2, 5, 8])], [([0, 1, 3, 5, 8, 9], [0, 1, 4, 5, 7, 9]), ([0, 1, 4], [0, 1, 4]), ([0, 2, 7], [0, 2, 7]), ([0, 5, 7], [0, 2, 7]), ([1, 2, 4, 8], [0, 1, 3, 7]), ([0, 1, 5], [0, 1, 5]), ([7, 11, 2, 5], [0, 2, 5, 8]), ([0, 2, 6, 7], [0, 1, 5, 7])]]\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":"5737bbe166ffa5c4d7570e148f029de4f07b00e68ab5b075548da84a5bf84817","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    def normal(values):\n        pcs = sorted(set(p % 12 for p in values))\n        n = len(pcs)\n        best = None\n        for r in range(n):\n            rot = pcs[r:] + [p + 12 for p in pcs[:r]]\n            key = [rot[-1] - rot[0]] + [rot[j] - rot[0] for j in range(n - 2, 0, -1)]\n            if best is None or (key, rot[0]) < best[0]:\n                best = ((key, rot[0]), rot)\n        return [p % 12 for p in best[1]]\n    if not x:\n        return []\n    a = normal(x)\n    b = normal([(-p) % 12 for p in x])\n    ka = [a[-1]] + a[-2:0:-1]\n    kb = [b[-1]] + b[-2:0:-1]\n    return a if ka <= kb else b\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([0, 4, 7], [0, 3, 7]), ([0, 3, 7], [0, 3, 7]), ([2, 6, 9], [0, 3, 7]), ([0, 1, 5, 6, 8], [0, 1, 5, 6, 8]), ([0, 4, 8], [0, 4, 8]), ([0, 3, 6, 9], [0, 3, 6, 9]), ([0, 5, 7], [0, 2, 7]), ([], [])], [([0, 4, 7], [0, 3, 7]), ([0, 3, 7], [0, 3, 7]), ([2, 6, 9], [0, 3, 7]), ([0, 1, 5, 6, 8], [0, 1, 5, 6, 8]), ([0, 1, 3, 5, 8, 9], [0, 1, 4, 5, 7, 9]), ([0, 2, 3, 6, 7, 9], [0, 2, 3, 6, 7, 9]), ([0, 1, 4], [0, 1, 4]), ([7, 11, 2, 5], [0, 2, 5, 8])], [([2, 6, 9], [0, 3, 7]), ([0, 1, 5, 6, 8], [0, 1, 5, 6, 8]), ([0, 1, 3, 5, 8, 9], [0, 1, 4, 5, 7, 9]), ([0, 2, 3, 6, 7, 9], [0, 2, 3, 6, 7, 9]), ([0, 1, 4], [0, 1, 4]), ([0, 3, 4], [0, 1, 4]), ([4, 5, 8], [0, 1, 4]), ([10, 1, 5], [0, 3, 7])], [([0, 1, 5, 6, 8], [0, 1, 5, 6, 8]), ([0, 2, 3, 6, 7, 9], [0, 2, 3, 6, 7, 9]), ([0, 1, 4], [0, 1, 4]), ([0, 3, 4], [0, 1, 4]), ([4, 5, 8], [0, 1, 4]), ([0, 2, 7], [0, 2, 7]), ([0, 5, 7], [0, 2, 7]), ([0, 3, 6, 10], [0, 2, 5, 8])], [([0, 1, 3, 5, 8, 9], [0, 1, 4, 5, 7, 9]), ([0, 1, 4], [0, 1, 4]), ([0, 2, 7], [0, 2, 7]), ([0, 5, 7], [0, 2, 7]), ([1, 2, 4, 8], [0, 1, 3, 7]), ([0, 1, 5], [0, 1, 5]), ([7, 11, 2, 5], [0, 2, 5, 8]), ([0, 2, 6, 7], [0, 1, 5, 7])]]\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-prime-form-transposition-to-zero","generated_at":"2026-09-29T14:49:59.345534+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Set-class labelling depends on prime forms being computed identically for every member of a class.","root_cause":"The normal form is reduced mod 12 but never transposed so that its first member is 0.","sha256":"fe176bc470766143ce3267359323d46eda1c184f7ec5cc85a82bbcf8df2ed4ee","title":"Pitch-class set prime form (right-packed): normal form not transposed to zero · 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":42.031,"exit_code":1,"observations":[{"actual":[0,4,7],"check":"oracle 0","expected":[0,3,7],"passed":false},{"actual":[0,3,7],"check":"oracle 1","expected":[0,3,7],"passed":true},{"actual":[0,3,7],"check":"oracle 2","expected":[0,3,7],"passed":true},{"actual":[0,1,5,6,8],"check":"oracle 3","expected":[0,1,5,6,8],"passed":true},{"actual":[0,4,8],"check":"oracle 4","expected":[0,4,8],"passed":true},{"actual":[0,3,6,9],"check":"oracle 5","expected":[0,3,6,9],"passed":true},{"actual":[5,7,12],"check":"oracle 6","expected":[0,2,7],"passed":false},{"actual":[],"check":"oracle 7","expected":[],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 0\", \"actual\": [0, 4, 7], \"expected\": [0, 3, 7], \"passed\": false}, {\"check\": \"oracle 1\", \"actual\": [0, 3, 7], \"expected\": [0, 3, 7], \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": [0, 3, 7], \"expected\": [0, 3, 7], \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": [0, 1, 5, 6, 8], \"expected\": [0, 1, 5, 6, 8], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [0, 4, 8], \"expected\": [0, 4, 8], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [0, 3, 6, 9], \"expected\": [0, 3, 6, 9], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [5, 7, 12], \"expected\": [0, 2, 7], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [], \"expected\": [], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":38.175,"exit_code":1,"observations":[{"actual":[5,8,0],"check":"oracle 0","expected":[0,3,7],"passed":false},{"actual":[5,9,0],"check":"oracle 1","expected":[0,3,7],"passed":false},{"actual":[2,6,9],"check":"oracle 2","expected":[0,3,7],"passed":false},{"actual":[4,6,7,11,0],"check":"oracle 3","expected":[0,1,5,6,8],"passed":false},{"actual":[0,4,8],"check":"oracle 4","expected":[0,4,8],"passed":true},{"actual":[0,3,6,9],"check":"oracle 5","expected":[0,3,6,9],"passed":true},{"actual":[5,7,0],"check":"oracle 6","expected":[0,2,7],"passed":false},{"actual":[],"check":"oracle 7","expected":[],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 0\", \"actual\": [5, 8, 0], \"expected\": [0, 3, 7], \"passed\": false}, {\"check\": \"oracle 1\", \"actual\": [5, 9, 0], \"expected\": [0, 3, 7], \"passed\": false}, {\"check\": \"oracle 2\", \"actual\": [2, 6, 9], \"expected\": [0, 3, 7], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [4, 6, 7, 11, 0], \"expected\": [0, 1, 5, 6, 8], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [0, 4, 8], \"expected\": [0, 4, 8], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [0, 3, 6, 9], \"expected\": [0, 3, 6, 9], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [5, 7, 0], \"expected\": [0, 2, 7], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [], \"expected\": [], \"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."}}