{"abstract":"A tempo of 3840000 microseconds reports 15.62 BPM instead of 15.63.","category":"MIDI event timing","checks":8,"contract":"Input the bytes of a Set Tempo meta event: FF 51 03 followed by a 24-bit big-endian microseconds-per-quarter value (nonzero). Return [microseconds, bpm_x100] where bpm_x100 = 6000000000 / microseconds rounded half up. Anything else returns None.","evaluation_group":"w2-midi-event-timing-set-tempo-meta","failed_approach":"Python round uses round-half-even, so exact halves like 1562.5 still round down.","family":"w2-midi-event-timing-set-tempo-meta-bpm-rounding","id":"FA-81501","implementations":{"attempt":{"sha256":"3e3e9013323d98c0cc844b82097c2a2226ec16e86b82901383b95727e9ce4d60","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) != 6 or x[0] != 0xFF or x[1] != 0x51 or x[2] != 3:\n        return None\n    us = (x[3] << 16) | (x[4] << 8) | x[5]\n    if us == 0:\n        return None\n    centi = round(6000000000 / us)\n    return [us, centi]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([255, 81, 3, 7, 161, 32], [500000, 12000]), ([255, 81, 3, 9, 39, 192], [600000, 10000]), ([255, 81, 3, 58, 152, 0], [3840000, 1563]), ([255, 81, 3, 2, 88, 0], [153600, 39063]), ([255, 81, 3, 0, 0, 1], [1, 6000000000]), ([255, 81, 4, 7, 161, 32], None), ([255, 81, 2, 7, 161, 32], None), ([255, 81, 3, 0, 0, 0], None)], [([255, 81, 3, 11, 184, 0], [768000, 7813]), ([255, 81, 3, 255, 255, 255], [16777215, 358]), ([255, 81, 4, 7, 161, 32], None), ([255, 81, 2, 7, 161, 32], None), ([255, 81, 3, 0, 0, 0], None), ([255, 82, 3, 7, 161, 32], None), ([255, 81, 3, 7, 161], None), ([255, 81, 3, 6, 26, 128], [400000, 15000])], [([255, 81, 3, 58, 152, 0], [3840000, 1563]), ([255, 81, 3, 2, 88, 0], [153600, 39063]), ([255, 82, 3, 7, 161, 32], None), ([255, 81, 3, 7, 161], None), ([255, 81, 3, 6, 26, 128], [400000, 15000]), ([255, 81, 3, 3, 13, 64], [200000, 30000]), ([255, 81, 3, 0, 3, 232], [1000, 6000000]), ([255, 81, 3, 15, 66, 64], [1000000, 6000])], [([255, 81, 3, 7, 161, 32], [500000, 12000]), ([255, 81, 3, 58, 152, 0], [3840000, 1563]), ([255, 81, 3, 11, 184, 0], [768000, 7813]), ([255, 81, 3, 2, 88, 0], [153600, 39063]), ([255, 81, 3, 255, 255, 255], [16777215, 358]), ([255, 81, 3, 3, 13, 64], [200000, 30000]), ([255, 81, 3, 0, 3, 232], [1000, 6000000]), ([255, 81, 3, 15, 66, 64], [1000000, 6000])], [([255, 81, 3, 7, 161, 32], [500000, 12000]), ([255, 81, 3, 9, 39, 192], [600000, 10000]), ([255, 81, 3, 58, 152, 0], [3840000, 1563]), ([255, 81, 3, 11, 184, 0], [768000, 7813]), ([255, 81, 3, 2, 88, 0], [153600, 39063]), ([255, 81, 3, 0, 0, 1], [1, 6000000000]), ([255, 81, 3, 255, 255, 255], [16777215, 358]), ([255, 81, 4, 7, 161, 32], None)]]\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":"3c97905c03af2effccc36ca8191908b24f8f0c670c86d68fcdb1b136ba4a5c6b","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) != 6 or x[0] != 0xFF or x[1] != 0x51 or x[2] != 3:\n        return None\n    us = (x[3] << 16) | (x[4] << 8) | x[5]\n    if us == 0:\n        return None\n    centi = 6000000000 // us\n    return [us, centi]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([255, 81, 3, 7, 161, 32], [500000, 12000]), ([255, 81, 3, 9, 39, 192], [600000, 10000]), ([255, 81, 3, 58, 152, 0], [3840000, 1563]), ([255, 81, 3, 2, 88, 0], [153600, 39063]), ([255, 81, 3, 0, 0, 1], [1, 6000000000]), ([255, 81, 4, 7, 161, 32], None), ([255, 81, 2, 7, 161, 32], None), ([255, 81, 3, 0, 0, 0], None)], [([255, 81, 3, 11, 184, 0], [768000, 7813]), ([255, 81, 3, 255, 255, 255], [16777215, 358]), ([255, 81, 4, 7, 161, 32], None), ([255, 81, 2, 7, 161, 32], None), ([255, 81, 3, 0, 0, 0], None), ([255, 82, 3, 7, 161, 32], None), ([255, 81, 3, 7, 161], None), ([255, 81, 3, 6, 26, 128], [400000, 15000])], [([255, 81, 3, 58, 152, 0], [3840000, 1563]), ([255, 81, 3, 2, 88, 0], [153600, 39063]), ([255, 82, 3, 7, 161, 32], None), ([255, 81, 3, 7, 161], None), ([255, 81, 3, 6, 26, 128], [400000, 15000]), ([255, 81, 3, 3, 13, 64], [200000, 30000]), ([255, 81, 3, 0, 3, 232], [1000, 6000000]), ([255, 81, 3, 15, 66, 64], [1000000, 6000])], [([255, 81, 3, 7, 161, 32], [500000, 12000]), ([255, 81, 3, 58, 152, 0], [3840000, 1563]), ([255, 81, 3, 11, 184, 0], [768000, 7813]), ([255, 81, 3, 2, 88, 0], [153600, 39063]), ([255, 81, 3, 255, 255, 255], [16777215, 358]), ([255, 81, 3, 3, 13, 64], [200000, 30000]), ([255, 81, 3, 0, 3, 232], [1000, 6000000]), ([255, 81, 3, 15, 66, 64], [1000000, 6000])], [([255, 81, 3, 7, 161, 32], [500000, 12000]), ([255, 81, 3, 9, 39, 192], [600000, 10000]), ([255, 81, 3, 58, 152, 0], [3840000, 1563]), ([255, 81, 3, 11, 184, 0], [768000, 7813]), ([255, 81, 3, 2, 88, 0], [153600, 39063]), ([255, 81, 3, 0, 0, 1], [1, 6000000000]), ([255, 81, 3, 255, 255, 255], [16777215, 358]), ([255, 81, 4, 7, 161, 32], None)]]\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":"02d8de02aed83c046e812b7176345c2232a226d542bbb08a29c07efb5d700745","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) != 6 or x[0] != 0xFF or x[1] != 0x51 or x[2] != 3:\n        return None\n    us = (x[3] << 16) | (x[4] << 8) | x[5]\n    if us == 0:\n        return None\n    centi = (12000000000 + us) // (2 * us)\n    return [us, centi]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([255, 81, 3, 7, 161, 32], [500000, 12000]), ([255, 81, 3, 9, 39, 192], [600000, 10000]), ([255, 81, 3, 58, 152, 0], [3840000, 1563]), ([255, 81, 3, 2, 88, 0], [153600, 39063]), ([255, 81, 3, 0, 0, 1], [1, 6000000000]), ([255, 81, 4, 7, 161, 32], None), ([255, 81, 2, 7, 161, 32], None), ([255, 81, 3, 0, 0, 0], None)], [([255, 81, 3, 11, 184, 0], [768000, 7813]), ([255, 81, 3, 255, 255, 255], [16777215, 358]), ([255, 81, 4, 7, 161, 32], None), ([255, 81, 2, 7, 161, 32], None), ([255, 81, 3, 0, 0, 0], None), ([255, 82, 3, 7, 161, 32], None), ([255, 81, 3, 7, 161], None), ([255, 81, 3, 6, 26, 128], [400000, 15000])], [([255, 81, 3, 58, 152, 0], [3840000, 1563]), ([255, 81, 3, 2, 88, 0], [153600, 39063]), ([255, 82, 3, 7, 161, 32], None), ([255, 81, 3, 7, 161], None), ([255, 81, 3, 6, 26, 128], [400000, 15000]), ([255, 81, 3, 3, 13, 64], [200000, 30000]), ([255, 81, 3, 0, 3, 232], [1000, 6000000]), ([255, 81, 3, 15, 66, 64], [1000000, 6000])], [([255, 81, 3, 7, 161, 32], [500000, 12000]), ([255, 81, 3, 58, 152, 0], [3840000, 1563]), ([255, 81, 3, 11, 184, 0], [768000, 7813]), ([255, 81, 3, 2, 88, 0], [153600, 39063]), ([255, 81, 3, 255, 255, 255], [16777215, 358]), ([255, 81, 3, 3, 13, 64], [200000, 30000]), ([255, 81, 3, 0, 3, 232], [1000, 6000000]), ([255, 81, 3, 15, 66, 64], [1000000, 6000])], [([255, 81, 3, 7, 161, 32], [500000, 12000]), ([255, 81, 3, 9, 39, 192], [600000, 10000]), ([255, 81, 3, 58, 152, 0], [3840000, 1563]), ([255, 81, 3, 11, 184, 0], [768000, 7813]), ([255, 81, 3, 2, 88, 0], [153600, 39063]), ([255, 81, 3, 0, 0, 1], [1, 6000000000]), ([255, 81, 3, 255, 255, 255], [16777215, 358]), ([255, 81, 4, 7, 161, 32], None)]]\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-set-tempo-meta-bpm-rounding","generated_at":"2026-09-29T14:50:03.709797+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 BPM rounding step so that it reads `(12000000000 + us) // (2 * us)`.","root_cause":"The scaled BPM is floor-divided with no half adjustment.","sha256":"bc221b6fa58ea402433d73fd095c20602a960980cb8ff1f7697436c6a817a8b2","title":"Set Tempo meta event to BPM: BPM truncated instead of rounded · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verification":{"attempt":{"elapsed_ms":41.207,"exit_code":1,"observations":[{"actual":[500000,12000],"check":"oracle 0","expected":[500000,12000],"passed":true},{"actual":[600000,10000],"check":"oracle 1","expected":[600000,10000],"passed":true},{"actual":[3840000,1562],"check":"oracle 2","expected":[3840000,1563],"passed":false},{"actual":[153600,39062],"check":"oracle 3","expected":[153600,39063],"passed":false},{"actual":[1,6000000000],"check":"oracle 4","expected":[1,6000000000],"passed":true},{"actual":null,"check":"oracle 5","expected":null,"passed":true},{"actual":null,"check":"oracle 6","expected":null,"passed":true},{"actual":null,"check":"oracle 7","expected":null,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 0\", \"actual\": [500000, 12000], \"expected\": [500000, 12000], \"passed\": true}, {\"check\": \"oracle 1\", \"actual\": [600000, 10000], \"expected\": [600000, 10000], \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": [3840000, 1562], \"expected\": [3840000, 1563], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [153600, 39062], \"expected\": [153600, 39063], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [1, 6000000000], \"expected\": [1, 6000000000], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": null, \"expected\": null, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":42.741,"exit_code":1,"observations":[{"actual":[500000,12000],"check":"oracle 0","expected":[500000,12000],"passed":true},{"actual":[600000,10000],"check":"oracle 1","expected":[600000,10000],"passed":true},{"actual":[3840000,1562],"check":"oracle 2","expected":[3840000,1563],"passed":false},{"actual":[153600,39062],"check":"oracle 3","expected":[153600,39063],"passed":false},{"actual":[1,6000000000],"check":"oracle 4","expected":[1,6000000000],"passed":true},{"actual":null,"check":"oracle 5","expected":null,"passed":true},{"actual":null,"check":"oracle 6","expected":null,"passed":true},{"actual":null,"check":"oracle 7","expected":null,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 0\", \"actual\": [500000, 12000], \"expected\": [500000, 12000], \"passed\": true}, {\"check\": \"oracle 1\", \"actual\": [600000, 10000], \"expected\": [600000, 10000], \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": [3840000, 1562], \"expected\": [3840000, 1563], \"passed\": false}, {\"check\": \"oracle 3\", \"actual\": [153600, 39062], \"expected\": [153600, 39063], \"passed\": false}, {\"check\": \"oracle 4\", \"actual\": [1, 6000000000], \"expected\": [1, 6000000000], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": null, \"expected\": null, \"passed\": true}], \"passed\": false}\n"},"fixed":{"elapsed_ms":39.732,"exit_code":0,"observations":[{"actual":[500000,12000],"check":"oracle 0","expected":[500000,12000],"passed":true},{"actual":[600000,10000],"check":"oracle 1","expected":[600000,10000],"passed":true},{"actual":[3840000,1563],"check":"oracle 2","expected":[3840000,1563],"passed":true},{"actual":[153600,39063],"check":"oracle 3","expected":[153600,39063],"passed":true},{"actual":[1,6000000000],"check":"oracle 4","expected":[1,6000000000],"passed":true},{"actual":null,"check":"oracle 5","expected":null,"passed":true},{"actual":null,"check":"oracle 6","expected":null,"passed":true},{"actual":null,"check":"oracle 7","expected":null,"passed":true}],"passed":true,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 0\", \"actual\": [500000, 12000], \"expected\": [500000, 12000], \"passed\": true}, {\"check\": \"oracle 1\", \"actual\": [600000, 10000], \"expected\": [600000, 10000], \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": [3840000, 1563], \"expected\": [3840000, 1563], \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": [153600, 39063], \"expected\": [153600, 39063], \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": [1, 6000000000], \"expected\": [1, 6000000000], \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": null, \"expected\": null, \"passed\": true}], \"passed\": true}\n"}},"verified":true,"visibility":"public"}