{"abstract":"In 6/8 the fourth eighth-note beat is reported as beat 2 because beats are measured in quarters.","category":"MIDI event timing","checks":8,"contract":"Input [ppq, signatures, tick]. signatures is a list of [bar_index, numerator, denominator] sorted by bar, the first at bar 0; each takes effect at the start of its bar. A beat lasts ppq*4/denominator ticks. Return [bar (1-based), beat (1-based), tick within beat]; invalid input returns None.","contract_signature":"x","evaluation_group":"w2-midi-event-timing-bar-beat-tick","failed_approach":"Scaling by den/4 instead of 4/den makes eighth-note beats twice a quarter instead of half.","family":"w2-midi-event-timing-bar-beat-tick-beat-length-unit","id":"FA-81521","implementations":{"attempt":{"sha256":"420d43e2fd4078a347717f75befb6fa45faa3cf30d70ab878b83a5252feb7684","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 len(x) != 3:\n        return None\n    ppq, sigs, tick = x\n    if tick < 0 or not sigs or sigs[0][0] != 0:\n        return None\n    start = 0\n    for k, (b, num, den) in enumerate(sigs):\n        beat = ppq * den // 4\n        bar_len = beat * num\n        next_bar = sigs[k + 1][0] if k + 1 < len(sigs) else None\n        if next_bar is not None:\n            span = (next_bar - b) * bar_len\n            if tick >= start + span:\n                start += span\n                continue\n        offset = tick - start\n        return [b + offset // bar_len + 1, offset % bar_len // beat + 1, offset % beat]\n    return None\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([480, [[0, 4, 4]], 0], [1, 1, 0]), ([480, [[0, 4, 4]], 1920], [2, 1, 0]), ([480, [[0, 4, 4]], 2400], [2, 2, 0]), ([480, [[0, 6, 8]], 720], [1, 4, 0]), ([480, [[0, 3, 4]], 1450], [2, 1, 10]), ([480, [[0, 4, 4], [2, 3, 4]], 3840], [3, 1, 0]), ([480, [[0, 2, 2]], 1000], [1, 2, 40]), ([96, [[0, 7, 8], [1, 4, 4]], 336], [2, 1, 0])], [([480, [[0, 6, 8]], 1440], [2, 1, 0]), ([480, [[0, 3, 4]], 1450], [2, 1, 10]), ([480, [[0, 4, 4], [2, 3, 4]], 3840], [3, 1, 0]), ([480, [[0, 4, 4], [2, 3, 4]], 5280], [4, 1, 0]), ([480, [[0, 4, 4], [2, 3, 4]], 5300], [4, 1, 20]), ([96, [[0, 7, 8], [1, 4, 4]], 336], [2, 1, 0]), ([96, [[0, 7, 8], [1, 4, 4]], 400], [2, 1, 64]), ([480, [[0, 4, 4], [1, 5, 8], [3, 4, 4]], 1920], [2, 1, 0])], [([480, [[0, 6, 8]], 720], [1, 4, 0]), ([480, [[0, 4, 4], [2, 3, 4]], 5300], [4, 1, 20]), ([480, [[0, 2, 2]], 1000], [1, 2, 40]), ([96, [[0, 7, 8], [1, 4, 4]], 400], [2, 1, 64]), ([480, [[0, 4, 4], [1, 5, 8], [3, 4, 4]], 1920], [2, 1, 0]), ([480, [[0, 4, 4], [1, 5, 8], [3, 4, 4]], 4320], [4, 1, 0]), ([480, [[1, 4, 4]], 0], None), ([480, [[0, 4, 4]], -5], None)], [([480, [[0, 6, 8]], 720], [1, 4, 0]), ([480, [[0, 6, 8]], 1440], [2, 1, 0]), ([480, [[0, 2, 2]], 1000], [1, 2, 40]), ([96, [[0, 7, 8], [1, 4, 4]], 336], [2, 1, 0]), ([96, [[0, 7, 8], [1, 4, 4]], 400], [2, 1, 64]), ([480, [[0, 4, 4], [1, 5, 8], [3, 4, 4]], 4320], [4, 1, 0]), ([480, [[0, 4, 4]], -5], None), ([480, [[0, 3, 16]], 700], [2, 3, 100])], [([480, [[0, 2, 2]], 1000], [1, 2, 40]), ([96, [[0, 7, 8], [1, 4, 4]], 336], [2, 1, 0]), ([96, [[0, 7, 8], [1, 4, 4]], 400], [2, 1, 64]), ([480, [[0, 4, 4], [1, 5, 8], [3, 4, 4]], 4320], [4, 1, 0]), ([480, [[0, 3, 16]], 700], [2, 3, 100]), ([120, [[0, 4, 4], [4, 6, 8], [6, 4, 4]], 2000], [5, 2, 20]), ([480, [[0, 4, 4], [1, 5, 8], [3, 4, 4]], 5000], [4, 2, 200]), ([120, [[0, 4, 4], [4, 6, 8], [6, 4, 4]], 3000], [7, 4, 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":"4f77f001ad3b340d5a5a9ef97b3625464d1d07a02d6ea33bc09e027812ecb9e7","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 len(x) != 3:\n        return None\n    ppq, sigs, tick = x\n    if tick < 0 or not sigs or sigs[0][0] != 0:\n        return None\n    start = 0\n    for k, (b, num, den) in enumerate(sigs):\n        beat = ppq\n        bar_len = beat * num\n        next_bar = sigs[k + 1][0] if k + 1 < len(sigs) else None\n        if next_bar is not None:\n            span = (next_bar - b) * bar_len\n            if tick >= start + span:\n                start += span\n                continue\n        offset = tick - start\n        return [b + offset // bar_len + 1, offset % bar_len // beat + 1, offset % beat]\n    return None\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([480, [[0, 4, 4]], 0], [1, 1, 0]), ([480, [[0, 4, 4]], 1920], [2, 1, 0]), ([480, [[0, 4, 4]], 2400], [2, 2, 0]), ([480, [[0, 6, 8]], 720], [1, 4, 0]), ([480, [[0, 3, 4]], 1450], [2, 1, 10]), ([480, [[0, 4, 4], [2, 3, 4]], 3840], [3, 1, 0]), ([480, [[0, 2, 2]], 1000], [1, 2, 40]), ([96, [[0, 7, 8], [1, 4, 4]], 336], [2, 1, 0])], [([480, [[0, 6, 8]], 1440], [2, 1, 0]), ([480, [[0, 3, 4]], 1450], [2, 1, 10]), ([480, [[0, 4, 4], [2, 3, 4]], 3840], [3, 1, 0]), ([480, [[0, 4, 4], [2, 3, 4]], 5280], [4, 1, 0]), ([480, [[0, 4, 4], [2, 3, 4]], 5300], [4, 1, 20]), ([96, [[0, 7, 8], [1, 4, 4]], 336], [2, 1, 0]), ([96, [[0, 7, 8], [1, 4, 4]], 400], [2, 1, 64]), ([480, [[0, 4, 4], [1, 5, 8], [3, 4, 4]], 1920], [2, 1, 0])], [([480, [[0, 6, 8]], 720], [1, 4, 0]), ([480, [[0, 4, 4], [2, 3, 4]], 5300], [4, 1, 20]), ([480, [[0, 2, 2]], 1000], [1, 2, 40]), ([96, [[0, 7, 8], [1, 4, 4]], 400], [2, 1, 64]), ([480, [[0, 4, 4], [1, 5, 8], [3, 4, 4]], 1920], [2, 1, 0]), ([480, [[0, 4, 4], [1, 5, 8], [3, 4, 4]], 4320], [4, 1, 0]), ([480, [[1, 4, 4]], 0], None), ([480, [[0, 4, 4]], -5], None)], [([480, [[0, 6, 8]], 720], [1, 4, 0]), ([480, [[0, 6, 8]], 1440], [2, 1, 0]), ([480, [[0, 2, 2]], 1000], [1, 2, 40]), ([96, [[0, 7, 8], [1, 4, 4]], 336], [2, 1, 0]), ([96, [[0, 7, 8], [1, 4, 4]], 400], [2, 1, 64]), ([480, [[0, 4, 4], [1, 5, 8], [3, 4, 4]], 4320], [4, 1, 0]), ([480, [[0, 4, 4]], -5], None), ([480, [[0, 3, 16]], 700], [2, 3, 100])], [([480, [[0, 2, 2]], 1000], [1, 2, 40]), ([96, [[0, 7, 8], [1, 4, 4]], 336], [2, 1, 0]), ([96, [[0, 7, 8], [1, 4, 4]], 400], [2, 1, 64]), ([480, [[0, 4, 4], [1, 5, 8], [3, 4, 4]], 4320], [4, 1, 0]), ([480, [[0, 3, 16]], 700], [2, 3, 100]), ([120, [[0, 4, 4], [4, 6, 8], [6, 4, 4]], 2000], [5, 2, 20]), ([480, [[0, 4, 4], [1, 5, 8], [3, 4, 4]], 5000], [4, 2, 200]), ([120, [[0, 4, 4], [4, 6, 8], [6, 4, 4]], 3000], [7, 4, 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 Standard MIDI File or MIDI 1.0/2.0 implementation. 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-midi-event-timing-bar-beat-tick-beat-length-unit","generated_at":"2026-09-29T14:50:03.777031+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"MIDI sequencers, file readers and synth drivers depend on exact event ordering and tick/time arithmetic.","root_cause":"The beat length ignores the time-signature denominator.","sha256":"836312e4e549078d7f36246ca7569c90c51e97e089eeca5944449320a4cf03bc","title":"Bar, beat and tick position with meter changes: every beat treated as a quarter note · 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":40.376,"exit_code":1,"observations":[{"actual":[1,1,0],"check":"oracle 0","expected":[1,1,0],"passed":true},{"actual":[2,1,0],"check":"oracle 1","expected":[2,1,0],"passed":true},{"actual":[2,2,0],"check":"oracle 2","expected":[2,2,0],"passed":true},{"actual":[1,1,720],"check":"oracle 3","expected":[1,4,0],"passed":false},{"actual":[2,1,10],"check":"oracle 4","expected":[2,1,10],"passed":true},{"actual":[3,1,0],"check":"oracle 5","expected":[3,1,0],"passed":true},{"actual":[3,1,40],"check":"oracle 6","expected":[1,2,40],"passed":false},{"actual":[1,2,144],"check":"oracle 7","expected":[2,1,0],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 0\", \"actual\": [1, 1, 0], \"expected\": [1, 1, 0], \"passed\": true}, {\"check\": \"oracle 1\", \"actual\": [2, 1, 0], \"expected\": [2, 1, 0], \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": [2, 2, 0], \"expected\": [2, 2, 0], \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": [1, 1, 720], \"expected\": [1, 4, 0], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [2, 1, 10], \"expected\": [2, 1, 10], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [3, 1, 0], \"expected\": [3, 1, 0], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [3, 1, 40], \"expected\": [1, 2, 40], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [1, 2, 144], \"expected\": [2, 1, 0], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":38.886,"exit_code":1,"observations":[{"actual":[1,1,0],"check":"oracle 0","expected":[1,1,0],"passed":true},{"actual":[2,1,0],"check":"oracle 1","expected":[2,1,0],"passed":true},{"actual":[2,2,0],"check":"oracle 2","expected":[2,2,0],"passed":true},{"actual":[1,2,240],"check":"oracle 3","expected":[1,4,0],"passed":false},{"actual":[2,1,10],"check":"oracle 4","expected":[2,1,10],"passed":true},{"actual":[3,1,0],"check":"oracle 5","expected":[3,1,0],"passed":true},{"actual":[2,1,40],"check":"oracle 6","expected":[1,2,40],"passed":false},{"actual":[1,4,48],"check":"oracle 7","expected":[2,1,0],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 0\", \"actual\": [1, 1, 0], \"expected\": [1, 1, 0], \"passed\": true}, {\"check\": \"oracle 1\", \"actual\": [2, 1, 0], \"expected\": [2, 1, 0], \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": [2, 2, 0], \"expected\": [2, 2, 0], \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": [1, 2, 240], \"expected\": [1, 4, 0], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [2, 1, 10], \"expected\": [2, 1, 10], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [3, 1, 0], \"expected\": [3, 1, 0], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [2, 1, 40], \"expected\": [1, 2, 40], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [1, 4, 48], \"expected\": [2, 1, 0], \"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."}}