FA-81621 / MIDI event timing / Open access
Lookahead scheduler dispatch windows: event on the window edge dispatched early · case 01
An event exactly at now + lookahead is sent in the current window and the next window misses nothing, so it fires one window early.
ROOT CAUSE
The dispatch window is closed at its end instead of half-open.
VERIFIED REPAIR
Restore the window end step so that it reads `t < now + ahead`.
Unsuccessful approach: Shrinking the window by one millisecond defers events that are inside the half-open window.
Case contract
Input [events, windows]: events are [time_ms, id]; windows are [now, lookahead] processed in order. In each window, walk not-yet-handled events in time order: an event more than 20 ms late (time < now - 20) is dropped (reported once); an event with time < now + lookahead is dispatched in that window (late events within tolerance included). Return {"batches": ids per window, "dropped": ids}.
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
N = 1
observations = []
def solve(x):
if not isinstance(x, list) or len(x) != 2:
return None
events, windows = x
sent = set()
batches = []
dropped = []
for now, ahead in windows:
batch = []
for t, eid in sorted(events):
if eid in sent:
continue
if t < now - 20:
sent.add(eid)
dropped.append(eid)
elif t <= now + ahead:
sent.add(eid)
batch.append(eid)
batches.append(batch)
return {'batches': batches, 'dropped': dropped}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[([[[0, 'a'], [25, 'b'], [50, 'c']], [[0, 25], [25, 25], [50, 25]]], {'batches': [['a'], ['b'], ['c']], 'dropped': []}), ([[[5, 'a']], [[30, 10]]], {'batches': [[]], 'dropped': ['a']}), ([[[9, 'a']], [[30, 10], [40, 10]]], {'batches': [[], []], 'dropped': ['a']}), ([[[10, 'a']], [[30, 10]]], {'batches': [['a']], 'dropped': []}), ([[[100, 'x'], [0, 'y']], [[0, 50], [50, 100]]], {'batches': [['y'], ['x']], 'dropped': []}), ([[[30, 'b'], [20, 'a']], [[0, 40]]], {'batches': [['a', 'b']], 'dropped': []}), ([[[49, 'a'], [50, 'b']], [[0, 50]]], {'batches': [['a']], 'dropped': []}), ([[[60, 'm'], [61, 'n']], [[0, 60], [60, 1]]], {'batches': [[], ['m']], 'dropped': []})], [([[[10, 'a'], [30, 'b']], [[0, 30], [30, 30]]], {'batches': [['a'], ['b']], 'dropped': []}), ([[[100, 'x'], [0, 'y']], [[0, 50], [50, 100]]], {'batches': [['y'], ['x']], 'dropped': []}), ([[[30, 'b'], [20, 'a']], [[0, 40]]], {'batches': [['a', 'b']], 'dropped': []}), ([[[3, 'z'], [3, 'y']], [[0, 10]]], {'batches': [['y', 'z']], 'dropped': []}), ([[[0, 'a'], [100, 'b']], [[200, 10], [210, 10]]], {'batches': [[], []], 'dropped': ['a', 'b']}), ([[[49, 'a'], [50, 'b']], [[0, 50]]], {'batches': [['a']], 'dropped': []}), ([[[15, 'q'], [70, 'r']], [[40, 20], [60, 20], [80, 20]]], {'batches': [[], ['r'], []], 'dropped': ['q']}), ([[[60, 'm'], [61, 'n']], [[0, 60], [60, 1]]], {'batches': [[], ['m']], 'dropped': []})], [([[[0, 'a'], [25, 'b'], [50, 'c']], [[0, 25], [25, 25], [50, 25]]], {'batches': [['a'], ['b'], ['c']], 'dropped': []}), ([[[0, 'a'], [100, 'b']], [[200, 10], [210, 10]]], {'batches': [[], []], 'dropped': ['a', 'b']}), ([[[49, 'a'], [50, 'b']], [[0, 50]]], {'batches': [['a']], 'dropped': []}), ([[[15, 'q'], [70, 'r']], [[40, 20], [60, 20], [80, 20]]], {'batches': [[], ['r'], []], 'dropped': ['q']}), ([[], [[0, 10]]], {'batches': [[]], 'dropped': []}), ([[[5, 'late']], [[25, 5], [26, 5]]], {'batches': [['late'], []], 'dropped': []}), ([[[60, 'm'], [61, 'n']], [[0, 60], [60, 1]]], {'batches': [[], ['m']], 'dropped': []}), ([[[30, 'a'], [20, 'b']], [[0, 40]]], {'batches': [['b', 'a']], 'dropped': []})], [([[[0, 'a'], [25, 'b'], [50, 'c']], [[0, 25], [25, 25], [50, 25]]], {'batches': [['a'], ['b'], ['c']], 'dropped': []}), ([[[10, 'a'], [30, 'b']], [[0, 30], [30, 30]]], {'batches': [['a'], ['b']], 'dropped': []}), ([[[5, 'a']], [[30, 10]]], {'batches': [[]], 'dropped': ['a']}), ([[[49, 'a'], [50, 'b']], [[0, 50]]], {'batches': [['a']], 'dropped': []}), ([[[5, 'late']], [[25, 5], [26, 5]]], {'batches': [['late'], []], 'dropped': []}), ([[[60, 'm'], [61, 'n']], [[0, 60], [60, 1]]], {'batches': [[], ['m']], 'dropped': []}), ([[[30, 'a'], [20, 'b']], [[0, 40]]], {'batches': [['b', 'a']], 'dropped': []}), ([[[5, 'z'], [1, 'y'], [3, 'x']], [[0, 10]]], {'batches': [['y', 'x', 'z']], 'dropped': []})], [([[[0, 'a'], [25, 'b'], [50, 'c']], [[0, 25], [25, 25], [50, 25]]], {'batches': [['a'], ['b'], ['c']], 'dropped': []}), ([[[10, 'a'], [30, 'b']], [[0, 30], [30, 30]]], {'batches': [['a'], ['b']], 'dropped': []}), ([[[5, 'a']], [[30, 10]]], {'batches': [[]], 'dropped': ['a']}), ([[[9, 'a']], [[30, 10], [40, 10]]], {'batches': [[], []], 'dropped': ['a']}), ([[[10, 'a']], [[30, 10]]], {'batches': [['a']], 'dropped': []}), ([[[100, 'x'], [0, 'y']], [[0, 50], [50, 100]]], {'batches': [['y'], ['x']], 'dropped': []}), ([[[49, 'a'], [50, 'b']], [[0, 50]]], {'batches': [['a']], 'dropped': []}), ([[[60, 'm'], [61, 'n']], [[0, 60], [60, 1]]], {'batches': [[], ['m']], 'dropped': []})]]
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 | {'batches': [['a', 'b'], ['c'], []], 'dropped': []} | {'batches': [['a'], ['b'], ['c']], 'dropped': []} | Failed |
| oracle 1 | {'batches': [[]], 'dropped': ['a']} | {'batches': [[]], 'dropped': ['a']} | Passed |
| oracle 2 | {'batches': [[], []], 'dropped': ['a']} | {'batches': [[], []], 'dropped': ['a']} | Passed |
| oracle 3 | {'batches': [['a']], 'dropped': []} | {'batches': [['a']], 'dropped': []} | Passed |
| oracle 4 | {'batches': [['y'], ['x']], 'dropped': []} | {'batches': [['y'], ['x']], 'dropped': []} | Passed |
| oracle 5 | {'batches': [['a', 'b']], 'dropped': []} | {'batches': [['a', 'b']], 'dropped': []} | Passed |
| oracle 6 | {'batches': [['a', 'b']], 'dropped': []} | {'batches': [['a']], 'dropped': []} | Failed |
| oracle 7 | {'batches': [['m'], ['n']], 'dropped': []} | {'batches': [[], ['m']], 'dropped': []} | Failed |
SHA-256 / e60459939fa7fd9931440311479cb62640365688629929151333374e7b583c31
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
if not isinstance(x, list) or len(x) != 2:
return None
events, windows = x
sent = set()
batches = []
dropped = []
for now, ahead in windows:
batch = []
for t, eid in sorted(events):
if eid in sent:
continue
if t < now - 20:
sent.add(eid)
dropped.append(eid)
elif t < now + ahead - 1:
sent.add(eid)
batch.append(eid)
batches.append(batch)
return {'batches': batches, 'dropped': dropped}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[([[[0, 'a'], [25, 'b'], [50, 'c']], [[0, 25], [25, 25], [50, 25]]], {'batches': [['a'], ['b'], ['c']], 'dropped': []}), ([[[5, 'a']], [[30, 10]]], {'batches': [[]], 'dropped': ['a']}), ([[[9, 'a']], [[30, 10], [40, 10]]], {'batches': [[], []], 'dropped': ['a']}), ([[[10, 'a']], [[30, 10]]], {'batches': [['a']], 'dropped': []}), ([[[100, 'x'], [0, 'y']], [[0, 50], [50, 100]]], {'batches': [['y'], ['x']], 'dropped': []}), ([[[30, 'b'], [20, 'a']], [[0, 40]]], {'batches': [['a', 'b']], 'dropped': []}), ([[[49, 'a'], [50, 'b']], [[0, 50]]], {'batches': [['a']], 'dropped': []}), ([[[60, 'm'], [61, 'n']], [[0, 60], [60, 1]]], {'batches': [[], ['m']], 'dropped': []})], [([[[10, 'a'], [30, 'b']], [[0, 30], [30, 30]]], {'batches': [['a'], ['b']], 'dropped': []}), ([[[100, 'x'], [0, 'y']], [[0, 50], [50, 100]]], {'batches': [['y'], ['x']], 'dropped': []}), ([[[30, 'b'], [20, 'a']], [[0, 40]]], {'batches': [['a', 'b']], 'dropped': []}), ([[[3, 'z'], [3, 'y']], [[0, 10]]], {'batches': [['y', 'z']], 'dropped': []}), ([[[0, 'a'], [100, 'b']], [[200, 10], [210, 10]]], {'batches': [[], []], 'dropped': ['a', 'b']}), ([[[49, 'a'], [50, 'b']], [[0, 50]]], {'batches': [['a']], 'dropped': []}), ([[[15, 'q'], [70, 'r']], [[40, 20], [60, 20], [80, 20]]], {'batches': [[], ['r'], []], 'dropped': ['q']}), ([[[60, 'm'], [61, 'n']], [[0, 60], [60, 1]]], {'batches': [[], ['m']], 'dropped': []})], [([[[0, 'a'], [25, 'b'], [50, 'c']], [[0, 25], [25, 25], [50, 25]]], {'batches': [['a'], ['b'], ['c']], 'dropped': []}), ([[[0, 'a'], [100, 'b']], [[200, 10], [210, 10]]], {'batches': [[], []], 'dropped': ['a', 'b']}), ([[[49, 'a'], [50, 'b']], [[0, 50]]], {'batches': [['a']], 'dropped': []}), ([[[15, 'q'], [70, 'r']], [[40, 20], [60, 20], [80, 20]]], {'batches': [[], ['r'], []], 'dropped': ['q']}), ([[], [[0, 10]]], {'batches': [[]], 'dropped': []}), ([[[5, 'late']], [[25, 5], [26, 5]]], {'batches': [['late'], []], 'dropped': []}), ([[[60, 'm'], [61, 'n']], [[0, 60], [60, 1]]], {'batches': [[], ['m']], 'dropped': []}), ([[[30, 'a'], [20, 'b']], [[0, 40]]], {'batches': [['b', 'a']], 'dropped': []})], [([[[0, 'a'], [25, 'b'], [50, 'c']], [[0, 25], [25, 25], [50, 25]]], {'batches': [['a'], ['b'], ['c']], 'dropped': []}), ([[[10, 'a'], [30, 'b']], [[0, 30], [30, 30]]], {'batches': [['a'], ['b']], 'dropped': []}), ([[[5, 'a']], [[30, 10]]], {'batches': [[]], 'dropped': ['a']}), ([[[49, 'a'], [50, 'b']], [[0, 50]]], {'batches': [['a']], 'dropped': []}), ([[[5, 'late']], [[25, 5], [26, 5]]], {'batches': [['late'], []], 'dropped': []}), ([[[60, 'm'], [61, 'n']], [[0, 60], [60, 1]]], {'batches': [[], ['m']], 'dropped': []}), ([[[30, 'a'], [20, 'b']], [[0, 40]]], {'batches': [['b', 'a']], 'dropped': []}), ([[[5, 'z'], [1, 'y'], [3, 'x']], [[0, 10]]], {'batches': [['y', 'x', 'z']], 'dropped': []})], [([[[0, 'a'], [25, 'b'], [50, 'c']], [[0, 25], [25, 25], [50, 25]]], {'batches': [['a'], ['b'], ['c']], 'dropped': []}), ([[[10, 'a'], [30, 'b']], [[0, 30], [30, 30]]], {'batches': [['a'], ['b']], 'dropped': []}), ([[[5, 'a']], [[30, 10]]], {'batches': [[]], 'dropped': ['a']}), ([[[9, 'a']], [[30, 10], [40, 10]]], {'batches': [[], []], 'dropped': ['a']}), ([[[10, 'a']], [[30, 10]]], {'batches': [['a']], 'dropped': []}), ([[[100, 'x'], [0, 'y']], [[0, 50], [50, 100]]], {'batches': [['y'], ['x']], 'dropped': []}), ([[[49, 'a'], [50, 'b']], [[0, 50]]], {'batches': [['a']], 'dropped': []}), ([[[60, 'm'], [61, 'n']], [[0, 60], [60, 1]]], {'batches': [[], ['m']], 'dropped': []})]]
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 | {'batches': [['a'], ['b'], ['c']], 'dropped': []} | {'batches': [['a'], ['b'], ['c']], 'dropped': []} | Passed |
| oracle 1 | {'batches': [[]], 'dropped': ['a']} | {'batches': [[]], 'dropped': ['a']} | Passed |
| oracle 2 | {'batches': [[], []], 'dropped': ['a']} | {'batches': [[], []], 'dropped': ['a']} | Passed |
| oracle 3 | {'batches': [['a']], 'dropped': []} | {'batches': [['a']], 'dropped': []} | Passed |
| oracle 4 | {'batches': [['y'], ['x']], 'dropped': []} | {'batches': [['y'], ['x']], 'dropped': []} | Passed |
| oracle 5 | {'batches': [['a', 'b']], 'dropped': []} | {'batches': [['a', 'b']], 'dropped': []} | Passed |
| oracle 6 | {'batches': [[]], 'dropped': []} | {'batches': [['a']], 'dropped': []} | Failed |
| oracle 7 | {'batches': [[], []], 'dropped': []} | {'batches': [[], ['m']], 'dropped': []} | Failed |
SHA-256 / ad37356de955797d55365deef1309fc5f9fce06f7e54324258057dc0ecfa9999
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
if not isinstance(x, list) or len(x) != 2:
return None
events, windows = x
sent = set()
batches = []
dropped = []
for now, ahead in windows:
batch = []
for t, eid in sorted(events):
if eid in sent:
continue
if t < now - 20:
sent.add(eid)
dropped.append(eid)
elif t < now + ahead:
sent.add(eid)
batch.append(eid)
batches.append(batch)
return {'batches': batches, 'dropped': dropped}
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[([[[0, 'a'], [25, 'b'], [50, 'c']], [[0, 25], [25, 25], [50, 25]]], {'batches': [['a'], ['b'], ['c']], 'dropped': []}), ([[[5, 'a']], [[30, 10]]], {'batches': [[]], 'dropped': ['a']}), ([[[9, 'a']], [[30, 10], [40, 10]]], {'batches': [[], []], 'dropped': ['a']}), ([[[10, 'a']], [[30, 10]]], {'batches': [['a']], 'dropped': []}), ([[[100, 'x'], [0, 'y']], [[0, 50], [50, 100]]], {'batches': [['y'], ['x']], 'dropped': []}), ([[[30, 'b'], [20, 'a']], [[0, 40]]], {'batches': [['a', 'b']], 'dropped': []}), ([[[49, 'a'], [50, 'b']], [[0, 50]]], {'batches': [['a']], 'dropped': []}), ([[[60, 'm'], [61, 'n']], [[0, 60], [60, 1]]], {'batches': [[], ['m']], 'dropped': []})], [([[[10, 'a'], [30, 'b']], [[0, 30], [30, 30]]], {'batches': [['a'], ['b']], 'dropped': []}), ([[[100, 'x'], [0, 'y']], [[0, 50], [50, 100]]], {'batches': [['y'], ['x']], 'dropped': []}), ([[[30, 'b'], [20, 'a']], [[0, 40]]], {'batches': [['a', 'b']], 'dropped': []}), ([[[3, 'z'], [3, 'y']], [[0, 10]]], {'batches': [['y', 'z']], 'dropped': []}), ([[[0, 'a'], [100, 'b']], [[200, 10], [210, 10]]], {'batches': [[], []], 'dropped': ['a', 'b']}), ([[[49, 'a'], [50, 'b']], [[0, 50]]], {'batches': [['a']], 'dropped': []}), ([[[15, 'q'], [70, 'r']], [[40, 20], [60, 20], [80, 20]]], {'batches': [[], ['r'], []], 'dropped': ['q']}), ([[[60, 'm'], [61, 'n']], [[0, 60], [60, 1]]], {'batches': [[], ['m']], 'dropped': []})], [([[[0, 'a'], [25, 'b'], [50, 'c']], [[0, 25], [25, 25], [50, 25]]], {'batches': [['a'], ['b'], ['c']], 'dropped': []}), ([[[0, 'a'], [100, 'b']], [[200, 10], [210, 10]]], {'batches': [[], []], 'dropped': ['a', 'b']}), ([[[49, 'a'], [50, 'b']], [[0, 50]]], {'batches': [['a']], 'dropped': []}), ([[[15, 'q'], [70, 'r']], [[40, 20], [60, 20], [80, 20]]], {'batches': [[], ['r'], []], 'dropped': ['q']}), ([[], [[0, 10]]], {'batches': [[]], 'dropped': []}), ([[[5, 'late']], [[25, 5], [26, 5]]], {'batches': [['late'], []], 'dropped': []}), ([[[60, 'm'], [61, 'n']], [[0, 60], [60, 1]]], {'batches': [[], ['m']], 'dropped': []}), ([[[30, 'a'], [20, 'b']], [[0, 40]]], {'batches': [['b', 'a']], 'dropped': []})], [([[[0, 'a'], [25, 'b'], [50, 'c']], [[0, 25], [25, 25], [50, 25]]], {'batches': [['a'], ['b'], ['c']], 'dropped': []}), ([[[10, 'a'], [30, 'b']], [[0, 30], [30, 30]]], {'batches': [['a'], ['b']], 'dropped': []}), ([[[5, 'a']], [[30, 10]]], {'batches': [[]], 'dropped': ['a']}), ([[[49, 'a'], [50, 'b']], [[0, 50]]], {'batches': [['a']], 'dropped': []}), ([[[5, 'late']], [[25, 5], [26, 5]]], {'batches': [['late'], []], 'dropped': []}), ([[[60, 'm'], [61, 'n']], [[0, 60], [60, 1]]], {'batches': [[], ['m']], 'dropped': []}), ([[[30, 'a'], [20, 'b']], [[0, 40]]], {'batches': [['b', 'a']], 'dropped': []}), ([[[5, 'z'], [1, 'y'], [3, 'x']], [[0, 10]]], {'batches': [['y', 'x', 'z']], 'dropped': []})], [([[[0, 'a'], [25, 'b'], [50, 'c']], [[0, 25], [25, 25], [50, 25]]], {'batches': [['a'], ['b'], ['c']], 'dropped': []}), ([[[10, 'a'], [30, 'b']], [[0, 30], [30, 30]]], {'batches': [['a'], ['b']], 'dropped': []}), ([[[5, 'a']], [[30, 10]]], {'batches': [[]], 'dropped': ['a']}), ([[[9, 'a']], [[30, 10], [40, 10]]], {'batches': [[], []], 'dropped': ['a']}), ([[[10, 'a']], [[30, 10]]], {'batches': [['a']], 'dropped': []}), ([[[100, 'x'], [0, 'y']], [[0, 50], [50, 100]]], {'batches': [['y'], ['x']], 'dropped': []}), ([[[49, 'a'], [50, 'b']], [[0, 50]]], {'batches': [['a']], 'dropped': []}), ([[[60, 'm'], [61, 'n']], [[0, 60], [60, 1]]], {'batches': [[], ['m']], 'dropped': []})]]
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 | {'batches': [['a'], ['b'], ['c']], 'dropped': []} | {'batches': [['a'], ['b'], ['c']], 'dropped': []} | Passed |
| oracle 1 | {'batches': [[]], 'dropped': ['a']} | {'batches': [[]], 'dropped': ['a']} | Passed |
| oracle 2 | {'batches': [[], []], 'dropped': ['a']} | {'batches': [[], []], 'dropped': ['a']} | Passed |
| oracle 3 | {'batches': [['a']], 'dropped': []} | {'batches': [['a']], 'dropped': []} | Passed |
| oracle 4 | {'batches': [['y'], ['x']], 'dropped': []} | {'batches': [['y'], ['x']], 'dropped': []} | Passed |
| oracle 5 | {'batches': [['a', 'b']], 'dropped': []} | {'batches': [['a', 'b']], 'dropped': []} | Passed |
| oracle 6 | {'batches': [['a']], 'dropped': []} | {'batches': [['a']], 'dropped': []} | Passed |
| oracle 7 | {'batches': [[], ['m']], 'dropped': []} | {'batches': [[], ['m']], 'dropped': []} | Passed |
SHA-256 / 1da32f9ab57292f36d7019b258e6fe2e0e95ff97c31ba4865b831ec0021d3aa4
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 2026-09-29T14:50:04.612586+00:00.
Case digest / eccd32d47cd20235e8e6e782a93fd0e5afb46b93480e6a6d57e4270dc58f1ccf