FA-81481 / MIDI event timing / Open access

Tick to microsecond conversion through a tempo map: first of duplicate tempo events wins · case 01

When two tempo events share a tick, the earlier-listed one is kept instead of the later override.

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

ROOT CAUSE

Duplicate ticks keep the first value seen.

THE FAILURE

Duplicate ticks keep the first value seen.

Unsuccessful approach: Keeping the smaller tempo value picks by speed, not by event order.

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.setdefault(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), ([480, [[0, 400000], [0, 300000]], 480], 300000), ([480, [[0, 300000], [0, 400000]], 480], 400000), ([7, [[2, 300001], [2, 400003]], 6], 371430)], [([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, [[240, 300000], [240, 200000]], 480], 350000), ([3, [[1, 1000]], 2], 167000), ([480, [[0, 300000], [0, 400000]], 480], 400000), ([7, [[2, 300001], [2, 400003]], 6], 371430)], [([7, [[1, 100001], [2, 200003]], 5], 171430), ([480, [[0, 400000], [0, 300000]], 480], 300000), ([3, [[1, 1000]], 2], 167000), ([480, [[480, 250000]], 480], 500000), ([0, [], 10], None), ([480, [], -1], None), ([480, [[0, 300000], [0, 400000]], 480], 400000), ([7, [[2, 300001], [2, 400003]], 6], 371430)], [([480, [[240, 300000], [240, 200000]], 480], 350000), ([0, [], 10], None), ([480, [], -1], None), ([480, [[100, 100000]], 50], 52083), ([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)], [([480, [], 480], 500000), ([480, [[0, 400000], [0, 300000]], 480], 300000), ([480, [[240, 300000], [240, 200000]], 480], 350000), ([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 fixture	Actual	Expected	Outcome
oracle 0	`500000`	`500000`	Passed
oracle 1	`1041`	`1041`	Passed
oracle 2	`600000`	`600000`	Passed
oracle 3	`750000`	`750000`	Passed
oracle 4	`1750000`	`1750000`	Passed
oracle 5	`400000`	`300000`	Failed
oracle 6	`300000`	`400000`	Failed
oracle 7	`314286`	`371430`	Failed

SHA-256 / 036bd64eb33a16395124b58ce778b0260e5db3817056d20d2374331b21c75e5c

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] = min(tempo_at.get(t, us), 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), ([480, [[0, 400000], [0, 300000]], 480], 300000), ([480, [[0, 300000], [0, 400000]], 480], 400000), ([7, [[2, 300001], [2, 400003]], 6], 371430)], [([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, [[240, 300000], [240, 200000]], 480], 350000), ([3, [[1, 1000]], 2], 167000), ([480, [[0, 300000], [0, 400000]], 480], 400000), ([7, [[2, 300001], [2, 400003]], 6], 371430)], [([7, [[1, 100001], [2, 200003]], 5], 171430), ([480, [[0, 400000], [0, 300000]], 480], 300000), ([3, [[1, 1000]], 2], 167000), ([480, [[480, 250000]], 480], 500000), ([0, [], 10], None), ([480, [], -1], None), ([480, [[0, 300000], [0, 400000]], 480], 400000), ([7, [[2, 300001], [2, 400003]], 6], 371430)], [([480, [[240, 300000], [240, 200000]], 480], 350000), ([0, [], 10], None), ([480, [], -1], None), ([480, [[100, 100000]], 50], 52083), ([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)], [([480, [], 480], 500000), ([480, [[0, 400000], [0, 300000]], 480], 300000), ([480, [[240, 300000], [240, 200000]], 480], 350000), ([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 fixture	Actual	Expected	Outcome
oracle 0	`500000`	`500000`	Passed
oracle 1	`1041`	`1041`	Passed
oracle 2	`600000`	`600000`	Passed
oracle 3	`750000`	`750000`	Passed
oracle 4	`1750000`	`1750000`	Passed
oracle 5	`300000`	`300000`	Passed
oracle 6	`300000`	`400000`	Failed
oracle 7	`314286`	`371430`	Failed

SHA-256 / 00310a663c43ca1046a0874ba02f1f53c7d8d82af98f98be43a3f12126985837

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 8 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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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 2026-09-29T14:50:03.321569+00:00.

Case digest / 98f6e65c2a2b0f9ca2a94650205d8c5e0f29c0f973ac2507970e9185f1bc7180