FA-81351 / MIDI event timing / Open access

Variable-length quantity delta encoder: five-byte deltas produced · case 01

Delta 0x10000000 is encoded as five bytes instead of being rejected.

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

ROOT CAUSE

The range check uses the 32-bit maximum rather than the 28-bit maximum representable in four groups.

THE FAILURE

The range check uses the 32-bit maximum rather than the 28-bit maximum representable in four groups.

Unsuccessful approach: A non-strict bound rejects 0x0FFFFFFF, the largest encodable delta.

Case contract

Input a delta-time integer 0..0x0FFFFFFF (booleans rejected). Encode as 7-bit groups, most significant group first, with bit 7 set on every byte except the last. Zero encodes as [0]. Out-of-range or non-integer input 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

N = 1
observations = []
def solve(x):
    if not isinstance(x, int) or isinstance(x, bool) or x < 0 or x > 0xFFFFFFFF:
        return None
    out = [x & 0x7F]
    x >>= 7
    while x:
        out.append((x & 0x7F) | 0x80)
        x >>= 7
    return out[::-1]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[(0, [0]), (1, [1]), (64, [64]), (127, [127]), (128, [129, 0]), (129, [129, 1]), (268435455, [255, 255, 255, 127]), (268435456, None)], [(127, [127]), (128, [129, 0]), (129, [129, 1]), (255, [129, 127]), (8192, [192, 0]), (16383, [255, 127]), (268435455, [255, 255, 255, 127]), (268435456, None)], [(255, [129, 127]), (8192, [192, 0]), (16383, [255, 127]), (16384, [129, 128, 0]), (100000, [134, 141, 32]), (2097151, [255, 255, 127]), (268435455, [255, 255, 255, 127]), (268435456, None)], [(16384, [129, 128, 0]), (100000, [134, 141, 32]), (2097151, [255, 255, 127]), (2097152, [129, 128, 128, 0]), (268435455, [255, 255, 255, 127]), (268435456, None), (-1, None), (True, None)], [(2097152, [129, 128, 128, 0]), (268435455, [255, 255, 255, 127]), (268435456, None), (-1, None), (True, None), ('7', None), (480, [131, 96]), (960, [135, 64])]]
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	`[0]`	`[0]`	Passed
oracle 1	`[1]`	`[1]`	Passed
oracle 2	`[64]`	`[64]`	Passed
oracle 3	`[127]`	`[127]`	Passed
oracle 4	`[129, 0]`	`[129, 0]`	Passed
oracle 5	`[129, 1]`	`[129, 1]`	Passed
oracle 6	`[255, 255, 255, 127]`	`[255, 255, 255, 127]`	Passed
oracle 7	`[129, 128, 128, 128, 0]`	`None`	Failed

SHA-256 / d82e3e36c21aad4bde37ac235c54d91202fb37c4e8564d381f473abddb1c3cbc

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, int) or isinstance(x, bool) or x < 0 or x >= 0x0FFFFFFF:
        return None
    out = [x & 0x7F]
    x >>= 7
    while x:
        out.append((x & 0x7F) | 0x80)
        x >>= 7
    return out[::-1]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[(0, [0]), (1, [1]), (64, [64]), (127, [127]), (128, [129, 0]), (129, [129, 1]), (268435455, [255, 255, 255, 127]), (268435456, None)], [(127, [127]), (128, [129, 0]), (129, [129, 1]), (255, [129, 127]), (8192, [192, 0]), (16383, [255, 127]), (268435455, [255, 255, 255, 127]), (268435456, None)], [(255, [129, 127]), (8192, [192, 0]), (16383, [255, 127]), (16384, [129, 128, 0]), (100000, [134, 141, 32]), (2097151, [255, 255, 127]), (268435455, [255, 255, 255, 127]), (268435456, None)], [(16384, [129, 128, 0]), (100000, [134, 141, 32]), (2097151, [255, 255, 127]), (2097152, [129, 128, 128, 0]), (268435455, [255, 255, 255, 127]), (268435456, None), (-1, None), (True, None)], [(2097152, [129, 128, 128, 0]), (268435455, [255, 255, 255, 127]), (268435456, None), (-1, None), (True, None), ('7', None), (480, [131, 96]), (960, [135, 64])]]
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	`[0]`	`[0]`	Passed
oracle 1	`[1]`	`[1]`	Passed
oracle 2	`[64]`	`[64]`	Passed
oracle 3	`[127]`	`[127]`	Passed
oracle 4	`[129, 0]`	`[129, 0]`	Passed
oracle 5	`[129, 1]`	`[129, 1]`	Passed
oracle 6	`None`	`[255, 255, 255, 127]`	Failed
oracle 7	`None`	`None`	Passed

SHA-256 / 58f456b7b798de56fa549fcda86033a19692f8aaf4242bd99025d09972d60cb4

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.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

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 2026-09-29T14:50:02.189847+00:00.

Case digest / 222073cb449025de2d4837ee654395fa0ee0b47370718beeffdaeac62f7a0131