{"abstract":"With three meters, the middle segment is treated as starting from bar 0, so positions after the last change land in the wrong bar.","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.","evaluation_group":"w2-midi-event-timing-bar-beat-tick","failed_approach":"Counting segment bars inclusively extends each segment by one bar.","family":"w2-midi-event-timing-bar-beat-tick-segment-span","id":"FA-81536","implementations":{"attempt":{"sha256":"b408297fd7d772559627e5e6cd18e63d749c64f5e4dc03810bbc69d4ef76024a","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 * 4 // den\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 + 1) * 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, 6, 8]], 1440], [2, 1, 0]), ([480, [[0, 4, 4], [2, 3, 4]], 5280], [4, 1, 0]), ([480, [[0, 4, 4], [1, 5, 8], [3, 4, 4]], 4320], [4, 1, 0]), ([480, [[0, 4, 4], [1, 5, 8], [3, 4, 4]], 5000], [4, 2, 200])], [([480, [[0, 6, 8]], 720], [1, 4, 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]], 5300], [4, 1, 20]), ([480, [[0, 2, 2]], 1000], [1, 2, 40]), ([120, [[0, 4, 4], [4, 6, 8], [6, 4, 4]], 2000], [5, 2, 20]), ([120, [[0, 4, 4], [4, 6, 8], [6, 4, 4]], 3000], [7, 4, 0])], [([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]), ([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, [[1, 4, 4]], 0], None), ([480, [[0, 4, 4]], -5], None), ([480, [[0, 4, 4], [1, 5, 8], [3, 4, 4]], 5000], [4, 2, 200])], [([480, [[0, 4, 4], [2, 3, 4]], 5280], [4, 1, 0]), ([480, [[0, 4, 4], [2, 3, 4]], 5300], [4, 1, 20]), ([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, 3, 16]], 700], [2, 3, 100]), ([120, [[0, 4, 4], [4, 6, 8], [6, 4, 4]], 3000], [7, 4, 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]], 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":"845b14286f55d3282b7874b48bae2141ff16f80ead62ed43b6c01987b0704873","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 * 4 // den\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 * 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, 6, 8]], 1440], [2, 1, 0]), ([480, [[0, 4, 4], [2, 3, 4]], 5280], [4, 1, 0]), ([480, [[0, 4, 4], [1, 5, 8], [3, 4, 4]], 4320], [4, 1, 0]), ([480, [[0, 4, 4], [1, 5, 8], [3, 4, 4]], 5000], [4, 2, 200])], [([480, [[0, 6, 8]], 720], [1, 4, 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]], 5300], [4, 1, 20]), ([480, [[0, 2, 2]], 1000], [1, 2, 40]), ([120, [[0, 4, 4], [4, 6, 8], [6, 4, 4]], 2000], [5, 2, 20]), ([120, [[0, 4, 4], [4, 6, 8], [6, 4, 4]], 3000], [7, 4, 0])], [([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]), ([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, [[1, 4, 4]], 0], None), ([480, [[0, 4, 4]], -5], None), ([480, [[0, 4, 4], [1, 5, 8], [3, 4, 4]], 5000], [4, 2, 200])], [([480, [[0, 4, 4], [2, 3, 4]], 5280], [4, 1, 0]), ([480, [[0, 4, 4], [2, 3, 4]], 5300], [4, 1, 20]), ([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, 3, 16]], 700], [2, 3, 100]), ([120, [[0, 4, 4], [4, 6, 8], [6, 4, 4]], 3000], [7, 4, 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]], 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"},"fixed":{"sha256":"4dc0f4579feb86297c14e7e613e764f0059d677df83e6a51239a68c0a976b5e5","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 * 4 // den\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, 6, 8]], 1440], [2, 1, 0]), ([480, [[0, 4, 4], [2, 3, 4]], 5280], [4, 1, 0]), ([480, [[0, 4, 4], [1, 5, 8], [3, 4, 4]], 4320], [4, 1, 0]), ([480, [[0, 4, 4], [1, 5, 8], [3, 4, 4]], 5000], [4, 2, 200])], [([480, [[0, 6, 8]], 720], [1, 4, 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]], 5300], [4, 1, 20]), ([480, [[0, 2, 2]], 1000], [1, 2, 40]), ([120, [[0, 4, 4], [4, 6, 8], [6, 4, 4]], 2000], [5, 2, 20]), ([120, [[0, 4, 4], [4, 6, 8], [6, 4, 4]], 3000], [7, 4, 0])], [([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]), ([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, [[1, 4, 4]], 0], None), ([480, [[0, 4, 4]], -5], None), ([480, [[0, 4, 4], [1, 5, 8], [3, 4, 4]], 5000], [4, 2, 200])], [([480, [[0, 4, 4], [2, 3, 4]], 5280], [4, 1, 0]), ([480, [[0, 4, 4], [2, 3, 4]], 5300], [4, 1, 20]), ([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, 3, 16]], 700], [2, 3, 100]), ([120, [[0, 4, 4], [4, 6, 8], [6, 4, 4]], 3000], [7, 4, 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]], 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-segment-span","generated_at":"2026-09-29T14:50:03.838703+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.","repair":"Restore the segment span step so that it reads `(next_bar - b) * bar_len`.","root_cause":"The length of a signature segment multiplies the next change's absolute bar index instead of the bar count in the segment.","sha256":"8fce7efa8238bb4b92ed399674c47ac1bb45c3bea944057fbc268b225d7ecc5d","title":"Bar, beat and tick position with meter changes: segment length measured from bar zero · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":41.749,"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":[1,4,0],"check":"oracle 3","expected":[1,4,0],"passed":true},{"actual":[2,1,0],"check":"oracle 4","expected":[2,1,0],"passed":true},{"actual":[3,4,0],"check":"oracle 5","expected":[4,1,0],"passed":false},{"actual":[2,3,0],"check":"oracle 6","expected":[4,1,0],"passed":false},{"actual":[2,5,200],"check":"oracle 7","expected":[4,2,200],"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, 4, 0], \"expected\": [1, 4, 0], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [2, 1, 0], \"expected\": [2, 1, 0], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [3, 4, 0], \"expected\": [4, 1, 0], \"passed\": false}, {\"check\": \"oracle 6\", \"actual\": [2, 3, 0], \"expected\": [4, 1, 0], \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": [2, 5, 200], \"expected\": [4, 2, 200], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":39.662,"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":[1,4,0],"check":"oracle 3","expected":[1,4,0],"passed":true},{"actual":[2,1,0],"check":"oracle 4","expected":[2,1,0],"passed":true},{"actual":[4,1,0],"check":"oracle 5","expected":[4,1,0],"passed":true},{"actual":[4,1,0],"check":"oracle 6","expected":[4,1,0],"passed":true},{"actual":[4,3,200],"check":"oracle 7","expected":[4,2,200],"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, 4, 0], \"expected\": [1, 4, 0], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [2, 1, 0], \"expected\": [2, 1, 0], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [4, 1, 0], \"expected\": [4, 1, 0], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [4, 1, 0], \"expected\": [4, 1, 0], \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": [4, 3, 200], \"expected\": [4, 2, 200], \"passed\": false}], \"passed\": false}\n"},"fixed":{"elapsed_ms":41.783,"exit_code":0,"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":[1,4,0],"check":"oracle 3","expected":[1,4,0],"passed":true},{"actual":[2,1,0],"check":"oracle 4","expected":[2,1,0],"passed":true},{"actual":[4,1,0],"check":"oracle 5","expected":[4,1,0],"passed":true},{"actual":[4,1,0],"check":"oracle 6","expected":[4,1,0],"passed":true},{"actual":[4,2,200],"check":"oracle 7","expected":[4,2,200],"passed":true}],"passed":true,"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, 4, 0], \"expected\": [1, 4, 0], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [2, 1, 0], \"expected\": [2, 1, 0], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": [4, 1, 0], \"expected\": [4, 1, 0], \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": [4, 1, 0], \"expected\": [4, 1, 0], \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": [4, 2, 200], \"expected\": [4, 2, 200], \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}