FAILURE MAP
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FA-81471 / MIDI event timing / Open access

Tick to microsecond conversion through a tempo map: each tempo segment floored separately · case 01

Long files with many tempo changes drift early: fractional microseconds are discarded at every segment boundary.

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

ROOT CAUSE

Each completed segment is integer-divided before being added instead of flooring the exact total once.

VERIFIED REPAIR

Restore the rounding stage step so that it reads `total += Fraction((t - tick) * tempo, ppq)`.

Unsuccessful approach: Rounding each segment to nearest still quantises per segment, drifting in the other direction.

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 += (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), ([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)]]
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 417500001750000Passed
oracle 5547618547618Passed
oracle 6171428171430Failed
oracle 7554993554994Failed

SHA-256 / ede5c610270e2d5e38d4408e3208e22fe4531e46daec4637599e0fd490caaebc

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 += round(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), ([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)]]
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 417500001750000Passed
oracle 5547619547618Failed
oracle 6171430171430Passed
oracle 7554994554994Passed

SHA-256 / 09f2a5ea579bc88ce18301db9cf02a5d257d1b57e049d39c188beb7f2f1ab2ec

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), ([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)]]
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 417500001750000Passed
oracle 5547618547618Passed
oracle 6171430171430Passed
oracle 7554994554994Passed

SHA-256 / 15236f05ab34005e7a482f2287f8c0550017a5ff5718e2df14ccf9e49b21ffba

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 2026-09-29T14:50:03.196471+00:00.

Case digest / 7ffc9bdeb2cc9b970d985a51d54198111f18a044906d31ce4e9d34de5d639467