{"abstract":"Long files with many tempo changes drift early: fractional microseconds are discarded at every segment boundary.","category":"MIDI event timing","checks":8,"contract":"Input [ppq, changes, tick] where changes are [tick, microseconds_per_quarter] in any order (a later entry at the same tick overrides an earlier one). Before the first change the tempo is 500000. Each tempo applies from its tick onward. Sum the exact time of each segment and floor once at the end. Invalid ppq or negative tick returns None.","contract_signature":"x","evaluation_group":"w2-midi-event-timing-tempo-map-time","failed_approach":"Rounding each segment to nearest still quantises per segment, drifting in the other direction.","family":"w2-midi-event-timing-tempo-map-time-rounding-stage","id":"FA-81471","implementations":{"attempt":{"sha256":"09f2a5ea579bc88ce18301db9cf02a5d257d1b57e049d39c188beb7f2f1ab2ec","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    if not isinstance(x, list) or len(x) != 3:\n        return None\n    ppq, changes, target = x\n    if ppq <= 0 or target < 0:\n        return None\n    tempo_at = {}\n    for t, us in changes:\n        tempo_at[t] = us\n    points = sorted(tempo_at.items())\n    total = Fraction(0)\n    tick = 0\n    tempo = 500000\n    for t, us in points:\n        if t >= target:\n            break\n        total += round(Fraction((t - tick) * tempo, ppq))\n        tick = t\n        tempo = us\n    total += Fraction((target - tick) * tempo, ppq)\n    return int(total)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([480, [], 480], 500000), ([480, [], 1], 1041), ([96, [[0, 600000]], 96], 600000), ([480, [[480, 250000]], 960], 750000), ([480, [[960, 1000000], [480, 250000]], 1440], 1750000), ([7, [[3, 333333]], 10], 547618), ([7, [[1, 100001], [2, 200003]], 5], 171430), ([11, [[5, 777777], [9, 123457]], 13], 554994)], [([480, [[480, 250000]], 960], 750000), ([480, [[960, 1000000], [480, 250000]], 1440], 1750000), ([7, [[3, 333333]], 10], 547618), ([480, [[0, 400000], [0, 300000]], 480], 300000), ([480, [[240, 300000], [240, 200000]], 480], 350000), ([3, [[1, 1000]], 2], 167000), ([480, [[480, 250000]], 480], 500000), ([13, [[4, 499999], [8, 333337]], 12], 410257)], [([7, [[3, 333333]], 10], 547618), ([7, [[1, 100001], [2, 200003]], 5], 171430), ([480, [[240, 300000], [240, 200000]], 480], 350000), ([480, [[480, 250000]], 480], 500000), ([0, [], 10], None), ([480, [], -1], None), ([480, [[100, 100000]], 50], 52083), ([11, [[5, 777777], [9, 123457]], 13], 554994)], [([7, [[3, 333333]], 10], 547618), ([3, [[1, 1000]], 2], 167000), ([480, [], -1], None), ([480, [[100, 100000]], 50], 52083), ([480, [[0, 1000000], [480, 500000]], 720], 1250000), ([480, [[0, 300000], [0, 400000]], 480], 400000), ([7, [[2, 300001], [2, 400003]], 6], 371430), ([13, [[4, 499999], [8, 333337]], 12], 410257)], [([480, [], 480], 500000), ([7, [[3, 333333]], 10], 547618), ([7, [[1, 100001], [2, 200003]], 5], 171430), ([3, [[1, 1000]], 2], 167000), ([11, [[5, 777777], [9, 123457]], 13], 554994), ([480, [[0, 300000], [0, 400000]], 480], 400000), ([7, [[2, 300001], [2, 400003]], 6], 371430), ([13, [[4, 499999], [8, 333337]], 12], 410257)]]\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":"ede5c610270e2d5e38d4408e3208e22fe4531e46daec4637599e0fd490caaebc","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\nfrom fractions import Fraction\nN = 1\nobservations = []\ndef solve(x):\n    if not isinstance(x, list) or len(x) != 3:\n        return None\n    ppq, changes, target = x\n    if ppq <= 0 or target < 0:\n        return None\n    tempo_at = {}\n    for t, us in changes:\n        tempo_at[t] = us\n    points = sorted(tempo_at.items())\n    total = Fraction(0)\n    tick = 0\n    tempo = 500000\n    for t, us in points:\n        if t >= target:\n            break\n        total += (t - tick) * tempo // ppq\n        tick = t\n        tempo = us\n    total += Fraction((target - tick) * tempo, ppq)\n    return int(total)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[([480, [], 480], 500000), ([480, [], 1], 1041), ([96, [[0, 600000]], 96], 600000), ([480, [[480, 250000]], 960], 750000), ([480, [[960, 1000000], [480, 250000]], 1440], 1750000), ([7, [[3, 333333]], 10], 547618), ([7, [[1, 100001], [2, 200003]], 5], 171430), ([11, [[5, 777777], [9, 123457]], 13], 554994)], [([480, [[480, 250000]], 960], 750000), ([480, [[960, 1000000], [480, 250000]], 1440], 1750000), ([7, [[3, 333333]], 10], 547618), ([480, [[0, 400000], [0, 300000]], 480], 300000), ([480, [[240, 300000], [240, 200000]], 480], 350000), ([3, [[1, 1000]], 2], 167000), ([480, [[480, 250000]], 480], 500000), ([13, [[4, 499999], [8, 333337]], 12], 410257)], [([7, [[3, 333333]], 10], 547618), ([7, [[1, 100001], [2, 200003]], 5], 171430), ([480, [[240, 300000], [240, 200000]], 480], 350000), ([480, [[480, 250000]], 480], 500000), ([0, [], 10], None), ([480, [], -1], None), ([480, [[100, 100000]], 50], 52083), ([11, [[5, 777777], [9, 123457]], 13], 554994)], [([7, [[3, 333333]], 10], 547618), ([3, [[1, 1000]], 2], 167000), ([480, [], -1], None), ([480, [[100, 100000]], 50], 52083), ([480, [[0, 1000000], [480, 500000]], 720], 1250000), ([480, [[0, 300000], [0, 400000]], 480], 400000), ([7, [[2, 300001], [2, 400003]], 6], 371430), ([13, [[4, 499999], [8, 333337]], 12], 410257)], [([480, [], 480], 500000), ([7, [[3, 333333]], 10], 547618), ([7, [[1, 100001], [2, 200003]], 5], 171430), ([3, [[1, 1000]], 2], 167000), ([11, [[5, 777777], [9, 123457]], 13], 554994), ([480, [[0, 300000], [0, 400000]], 480], 400000), ([7, [[2, 300001], [2, 400003]], 6], 371430), ([13, [[4, 499999], [8, 333337]], 12], 410257)]]\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-tempo-map-time-rounding-stage","generated_at":"2026-09-29T14:50:03.196471+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":"Each completed segment is integer-divided before being added instead of flooring the exact total once.","sha256":"5dc848ec88befc6ac17cf4a6648bfc756b34502dfc98e0f212eb95e8febe86f6","title":"Tick to microsecond conversion through a tempo map: each tempo segment floored separately · 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":42.757,"exit_code":1,"observations":[{"actual":500000,"check":"oracle 0","expected":500000,"passed":true},{"actual":1041,"check":"oracle 1","expected":1041,"passed":true},{"actual":600000,"check":"oracle 2","expected":600000,"passed":true},{"actual":750000,"check":"oracle 3","expected":750000,"passed":true},{"actual":1750000,"check":"oracle 4","expected":1750000,"passed":true},{"actual":547619,"check":"oracle 5","expected":547618,"passed":false},{"actual":171430,"check":"oracle 6","expected":171430,"passed":true},{"actual":554994,"check":"oracle 7","expected":554994,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 0\", \"actual\": 500000, \"expected\": 500000, \"passed\": true}, {\"check\": \"oracle 1\", \"actual\": 1041, \"expected\": 1041, \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": 600000, \"expected\": 600000, \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": 750000, \"expected\": 750000, \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": 1750000, \"expected\": 1750000, \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": 547619, \"expected\": 547618, \"passed\": false}, {\"check\": \"oracle 6\", \"actual\": 171430, \"expected\": 171430, \"passed\": true}, {\"check\": \"oracle 7\", \"actual\": 554994, \"expected\": 554994, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":41.719,"exit_code":1,"observations":[{"actual":500000,"check":"oracle 0","expected":500000,"passed":true},{"actual":1041,"check":"oracle 1","expected":1041,"passed":true},{"actual":600000,"check":"oracle 2","expected":600000,"passed":true},{"actual":750000,"check":"oracle 3","expected":750000,"passed":true},{"actual":1750000,"check":"oracle 4","expected":1750000,"passed":true},{"actual":547618,"check":"oracle 5","expected":547618,"passed":true},{"actual":171428,"check":"oracle 6","expected":171430,"passed":false},{"actual":554993,"check":"oracle 7","expected":554994,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"oracle 0\", \"actual\": 500000, \"expected\": 500000, \"passed\": true}, {\"check\": \"oracle 1\", \"actual\": 1041, \"expected\": 1041, \"passed\": true}, {\"check\": \"oracle 2\", \"actual\": 600000, \"expected\": 600000, \"passed\": true}, {\"check\": \"oracle 3\", \"actual\": 750000, \"expected\": 750000, \"passed\": true}, {\"check\": \"oracle 4\", \"actual\": 1750000, \"expected\": 1750000, \"passed\": true}, {\"check\": \"oracle 5\", \"actual\": 547618, \"expected\": 547618, \"passed\": true}, {\"check\": \"oracle 6\", \"actual\": 171428, \"expected\": 171430, \"passed\": false}, {\"check\": \"oracle 7\", \"actual\": 554993, \"expected\": 554994, \"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."}}