FA-81346 / MIDI event timing / Open access

Variable-length quantity delta encoder: groups emitted least significant first · case 01

Delta 128 is written as [0, 129]; the terminating byte comes first and the stream desynchronises.

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

ROOT CAUSE

The groups are collected from least significant upward and returned without reversing.

VERIFIED REPAIR

Restore the group order step so that it reads `out[::-1]`.

Unsuccessful approach: Sorting bytes in descending order happens to put flagged bytes first but scrambles their relative order for multi-byte values.

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 > 0x0FFFFFFF:
        return None
    out = [x & 0x7F]
    x >>= 7
    while x:
        out.append((x & 0x7F) | 0x80)
        x >>= 7
    return out
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]), (255, [129, 127]), (100000, [134, 141, 32]), (268435456, None)], [(127, [127]), (129, [129, 1]), (8192, [192, 0]), (100000, [134, 141, 32]), (268435456, None), (-1, None), (True, None), ('7', None)], [(128, [129, 0]), (129, [129, 1]), (255, [129, 127]), (8192, [192, 0]), (16383, [255, 127]), (100000, [134, 141, 32]), (True, None), ('7', None)], [(129, [129, 1]), (255, [129, 127]), (8192, [192, 0]), (16383, [255, 127]), (16384, [129, 128, 0]), (100000, [134, 141, 32]), (2097151, [255, 255, 127]), (2097152, [129, 128, 128, 0])], [(16383, [255, 127]), (16384, [129, 128, 0]), (100000, [134, 141, 32]), (2097151, [255, 255, 127]), (2097152, [129, 128, 128, 0]), (268435455, [255, 255, 255, 127]), (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	`[0, 129]`	`[129, 0]`	Failed
oracle 5	`[127, 129]`	`[129, 127]`	Failed
oracle 6	`[32, 141, 134]`	`[134, 141, 32]`	Failed
oracle 7	`None`	`None`	Passed

SHA-256 / 6ae2928604c9545097e1a3dfebcd522e62e5a3393b669f5d408f240a828a7dbe

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 sorted(out, reverse=True)
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]), (255, [129, 127]), (100000, [134, 141, 32]), (268435456, None)], [(127, [127]), (129, [129, 1]), (8192, [192, 0]), (100000, [134, 141, 32]), (268435456, None), (-1, None), (True, None), ('7', None)], [(128, [129, 0]), (129, [129, 1]), (255, [129, 127]), (8192, [192, 0]), (16383, [255, 127]), (100000, [134, 141, 32]), (True, None), ('7', None)], [(129, [129, 1]), (255, [129, 127]), (8192, [192, 0]), (16383, [255, 127]), (16384, [129, 128, 0]), (100000, [134, 141, 32]), (2097151, [255, 255, 127]), (2097152, [129, 128, 128, 0])], [(16383, [255, 127]), (16384, [129, 128, 0]), (100000, [134, 141, 32]), (2097151, [255, 255, 127]), (2097152, [129, 128, 128, 0]), (268435455, [255, 255, 255, 127]), (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, 127]`	`[129, 127]`	Passed
oracle 6	`[141, 134, 32]`	`[134, 141, 32]`	Failed
oracle 7	`None`	`None`	Passed

SHA-256 / 9925b5117624a922281db4608e24b0b3207d93cf40dcc893a3a32e3d4e700396

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, 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]), (255, [129, 127]), (100000, [134, 141, 32]), (268435456, None)], [(127, [127]), (129, [129, 1]), (8192, [192, 0]), (100000, [134, 141, 32]), (268435456, None), (-1, None), (True, None), ('7', None)], [(128, [129, 0]), (129, [129, 1]), (255, [129, 127]), (8192, [192, 0]), (16383, [255, 127]), (100000, [134, 141, 32]), (True, None), ('7', None)], [(129, [129, 1]), (255, [129, 127]), (8192, [192, 0]), (16383, [255, 127]), (16384, [129, 128, 0]), (100000, [134, 141, 32]), (2097151, [255, 255, 127]), (2097152, [129, 128, 128, 0])], [(16383, [255, 127]), (16384, [129, 128, 0]), (100000, [134, 141, 32]), (2097151, [255, 255, 127]), (2097152, [129, 128, 128, 0]), (268435455, [255, 255, 255, 127]), (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, 127]`	`[129, 127]`	Passed
oracle 6	`[134, 141, 32]`	`[134, 141, 32]`	Passed
oracle 7	`None`	`None`	Passed

SHA-256 / 4d0da1d40a7ab353c4f058fd73fee73b75269a35567eddbf136736a7e1b83fc0

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 2026-09-29T14:50:02.116343+00:00.

Case digest / fa2188ecc44e1ceee376bc8dd19bcee83fa7040cd2d90d1c421199e2fe2575b0