FAILURE MAP
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FA-81486 / MIDI event timing / Open access

Tick to microsecond conversion through a tempo map: segment start not advanced at a tempo change · case 01

After a tempo change the time before the change is counted again at the new tempo.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The segment origin stays at the previous change when a new tempo takes effect.

VERIFIED REPAIR

Restore the segment bookkeeping step so that it reads `tick = t tempo = us`.

Unsuccessful approach: Starting the next segment one tick after the change drops a tick from the timeline.

Case 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.

Why this case matters

MIDI sequencers, file readers and synth drivers depend on exact event ordering and tick/time arithmetic.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(x):
    if not isinstance(x, list) or len(x) != 3:
        return None
    ppq, changes, target = x
    if ppq <= 0 or target < 0:
        return None
    tempo_at = {}
    for t, us in changes:
        tempo_at[t] = us
    points = sorted(tempo_at.items())
    total = Fraction(0)
    tick = 0
    tempo = 500000
    for t, us in points:
        if t >= target:
            break
        total += Fraction((t - tick) * tempo, ppq)
        tempo = us
    total += Fraction((target - tick) * tempo, ppq)
    return int(total)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[([480, [], 480], 500000), ([480, [], 1], 1041), ([96, [[0, 600000]], 96], 600000), ([480, [[480, 250000]], 960], 750000), ([7, [[3, 333333]], 10], 547618), ([480, [[480, 250000]], 480], 500000), ([0, [], 10], None), ([480, [], -1], None)], [([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), ([0, [], 10], None), ([480, [], -1], None), ([480, [[100, 100000]], 50], 52083)], [([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), ([480, [[0, 400000], [0, 300000]], 480], 300000), ([480, [[240, 300000], [240, 200000]], 480], 350000), ([3, [[1, 1000]], 2], 167000)], [([7, [[3, 333333]], 10], 547618), ([7, [[1, 100001], [2, 200003]], 5], 171430), ([480, [[0, 400000], [0, 300000]], 480], 300000), ([480, [[240, 300000], [240, 200000]], 480], 350000), ([3, [[1, 1000]], 2], 167000), ([11, [[5, 777777], [9, 123457]], 13], 554994), ([480, [[0, 1000000], [480, 500000]], 720], 1250000), ([480, [[0, 300000], [0, 400000]], 480], 400000)], [([7, [[1, 100001], [2, 200003]], 5], 171430), ([480, [[240, 300000], [240, 200000]], 480], 350000), ([3, [[1, 1000]], 2], 167000), ([11, [[5, 777777], [9, 123457]], 13], 554994), ([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)]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("oracle %d" % i, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
oracle 0500000500000Passed
oracle 110411041Passed
oracle 2600000600000Passed
oracle 31000000750000Failed
oracle 4690475547618Failed
oracle 5500000500000Passed
oracle 6NoneNonePassed
oracle 7NoneNonePassed

SHA-256 / 623616d25ef03b24954ad023bf34f2a0478f82e9df19da7543f43f5b626a8063

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(x):
    if not isinstance(x, list) or len(x) != 3:
        return None
    ppq, changes, target = x
    if ppq <= 0 or target < 0:
        return None
    tempo_at = {}
    for t, us in changes:
        tempo_at[t] = us
    points = sorted(tempo_at.items())
    total = Fraction(0)
    tick = 0
    tempo = 500000
    for t, us in points:
        if t >= target:
            break
        total += Fraction((t - tick) * tempo, ppq)
        tick = t + 1
        tempo = us
    total += Fraction((target - tick) * tempo, ppq)
    return int(total)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[([480, [], 480], 500000), ([480, [], 1], 1041), ([96, [[0, 600000]], 96], 600000), ([480, [[480, 250000]], 960], 750000), ([7, [[3, 333333]], 10], 547618), ([480, [[480, 250000]], 480], 500000), ([0, [], 10], None), ([480, [], -1], None)], [([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), ([0, [], 10], None), ([480, [], -1], None), ([480, [[100, 100000]], 50], 52083)], [([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), ([480, [[0, 400000], [0, 300000]], 480], 300000), ([480, [[240, 300000], [240, 200000]], 480], 350000), ([3, [[1, 1000]], 2], 167000)], [([7, [[3, 333333]], 10], 547618), ([7, [[1, 100001], [2, 200003]], 5], 171430), ([480, [[0, 400000], [0, 300000]], 480], 300000), ([480, [[240, 300000], [240, 200000]], 480], 350000), ([3, [[1, 1000]], 2], 167000), ([11, [[5, 777777], [9, 123457]], 13], 554994), ([480, [[0, 1000000], [480, 500000]], 720], 1250000), ([480, [[0, 300000], [0, 400000]], 480], 400000)], [([7, [[1, 100001], [2, 200003]], 5], 171430), ([480, [[240, 300000], [240, 200000]], 480], 350000), ([3, [[1, 1000]], 2], 167000), ([11, [[5, 777777], [9, 123457]], 13], 554994), ([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)]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("oracle %d" % i, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
oracle 0500000500000Passed
oracle 110411041Passed
oracle 2593750600000Failed
oracle 3749479750000Failed
oracle 4499999547618Failed
oracle 5500000500000Passed
oracle 6NoneNonePassed
oracle 7NoneNonePassed

SHA-256 / 950ec481079b9248792987467707c6c53fec204f94ce0b5655d9a090904eb2e3

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
N = 1
observations = []
def solve(x):
    if not isinstance(x, list) or len(x) != 3:
        return None
    ppq, changes, target = x
    if ppq <= 0 or target < 0:
        return None
    tempo_at = {}
    for t, us in changes:
        tempo_at[t] = us
    points = sorted(tempo_at.items())
    total = Fraction(0)
    tick = 0
    tempo = 500000
    for t, us in points:
        if t >= target:
            break
        total += Fraction((t - tick) * tempo, ppq)
        tick = t
        tempo = us
    total += Fraction((target - tick) * tempo, ppq)
    return int(total)
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[([480, [], 480], 500000), ([480, [], 1], 1041), ([96, [[0, 600000]], 96], 600000), ([480, [[480, 250000]], 960], 750000), ([7, [[3, 333333]], 10], 547618), ([480, [[480, 250000]], 480], 500000), ([0, [], 10], None), ([480, [], -1], None)], [([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), ([0, [], 10], None), ([480, [], -1], None), ([480, [[100, 100000]], 50], 52083)], [([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), ([480, [[0, 400000], [0, 300000]], 480], 300000), ([480, [[240, 300000], [240, 200000]], 480], 350000), ([3, [[1, 1000]], 2], 167000)], [([7, [[3, 333333]], 10], 547618), ([7, [[1, 100001], [2, 200003]], 5], 171430), ([480, [[0, 400000], [0, 300000]], 480], 300000), ([480, [[240, 300000], [240, 200000]], 480], 350000), ([3, [[1, 1000]], 2], 167000), ([11, [[5, 777777], [9, 123457]], 13], 554994), ([480, [[0, 1000000], [480, 500000]], 720], 1250000), ([480, [[0, 300000], [0, 400000]], 480], 400000)], [([7, [[1, 100001], [2, 200003]], 5], 171430), ([480, [[240, 300000], [240, 200000]], 480], 350000), ([3, [[1, 1000]], 2], 167000), ([11, [[5, 777777], [9, 123457]], 13], 554994), ([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)]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("oracle %d" % i, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
oracle 0500000500000Passed
oracle 110411041Passed
oracle 2600000600000Passed
oracle 3750000750000Passed
oracle 4547618547618Passed
oracle 5500000500000Passed
oracle 6NoneNonePassed
oracle 7NoneNonePassed

SHA-256 / 98147817d483b3171441fe596b32d2c3cbd336c5abc268af07297dcd5ae7806d

Verification & scope

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.

Observations recorded using Python 3.12.14 at 2026-09-29T14:50:03.412326+00:00.

Case digest / c8ec487741723889bcb05f09912aec04cf7c2af4ba660c31f319cba9a23f29b0