FA-72336 / Error-correcting codes / Open access

Bounded-distance decoder accepts any distance · case 01

Heavily corrupted words are decoded instead of flagged.

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

ROOT CAUSE

The radius check is missing.

THE FAILURE

The radius check is missing.

Unsuccessful approach: Rejecting at the radius itself refuses words exactly radius errors away.

Case contract

Bounded-distance decoding against an explicit codebook (duplicate entries allowed). Find the codeword at minimum Hamming distance from r; if two different codewords tie for the minimum, or the minimum exceeds radius, return None. Otherwise return [codeword, distance].

Why this case matters

Short control-channel codes are decoded against small codebooks; ties must be reported as failures, not guessed.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(codebook, r, radius):
    best, bd, tie = None, None, False
    for cwd in codebook:
        d = sum(a != b for a, b in zip(cwd, r))
        if bd is None or d < bd:
            best, bd, tie = cwd, d, False
        elif d == bd and cwd != best:
            tie = True
    if bd is None or tie:
        return None
    return [list(best), bd]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [0, 0, 1, 1, 0], 0], None], ['regression [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [1, 0, 0, 1, 1], 0], None], ['partial-repair [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [0, 1, 0, 1, 1], 1], [[1, 1, 0, 1, 1], 1]], ['partial-repair [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [1, 1, 1, 1, 1], 1], [[1, 1, 0, 1, 1], 1]], ['control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [0, 0, 1, 1, 1], 1], [[0, 0, 1, 1, 1], 0]], ['control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [0, 1, 0, 1, 1], 2], [[1, 1, 0, 1, 1], 1]], ['control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [1, 0, 1, 1, 0], 1], None], ['control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [0, 0, 0, 0, 0], 1], [[0, 0, 0, 0, 0], 0]]], [['regression [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [1, 1, 0, 0, 1], 0], None], ['regression [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [0, ...', [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [0, 1, 1, 0, 0, 0], 1], None], ['partial-repair [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [0, 0, 1, 0, 1], 1], [[0, 0, 1, 1, 1], 1]], ['partial-repair [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [0, 0, 0, 0, 1], 1], [[0, 0, 0, 0, 0], 1]], ['control [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [0, ...', [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [0, 0, 1, 1, 0, 1], 3], None], ['control [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [0, ...', [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [0, 1, 0, 1, 0, 1], 3], None], ['control [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [1, ...', [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [1, 1, 1, 0, 0, 0], 3], None], ['control [[], [1], 1]', [[], [1], 1], None]], [['regression [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [1, 0, 0, 1, 1], 0], None], ['regression [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [0, 0, 1, 0, 0], 0], None], ['partial-repair [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [0, ...', [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [0, 1, 0, 1, 1, 1], 2], [[1, 1, 1, 1, 1, 1], 2]], ['partial-repair [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [1, ...', [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [1, 0, 0, 1, 0, 0], 2], [[0, 0, 0, 0, 0, 0], 2]], ['control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [0, 1, 0, 1, 1], 2], [[1, 1, 0, 1, 1], 1]], ['control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [1, 0, 1, 1, 0], 1], None], ['control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [0, 0, 0, 0, 0], 1], [[0, 0, 0, 0, 0], 0]], ['control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [0, 1, 1, 1, 0], 1], None]], [['regression [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [0, ...', [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [0, 1, 1, 0, 0, 0], 1], None], ['regression [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [0, 0, 1, 1, 0], 0], None], ['partial-repair [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [1, 1, 1, 0, 0], 0], [[1, 1, 1, 0, 0], 0]], ['partial-repair [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [1, 0, 1, 0, 0], 1], [[1, 1, 1, 0, 0], 1]], ['control [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [0, ...', [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [0, 1, 0, 1, 0, 1], 3], None], ['control [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [1, ...', [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [1, 1, 1, 0, 0, 0], 3], None], ['control [[], [1], 1]', [[], [1], 1], None], ['control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [0, 0, 1, 1, 1], 1], [[0, 0, 1, 1, 1], 0]]], [['regression [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [0, 0, 1, 0, 0], 0], None], ['regression [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [1, 1, 0, 0, 1], 0], None], ['partial-repair [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [0, ...', [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [0, 0, 0, 0, 0, 1], 1], [[0, 0, 0, 0, 0, 0], 1]], ['partial-repair [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [0, 1, 0, 1, 1], 1], [[1, 1, 0, 1, 1], 1]], ['control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [1, 0, 1, 1, 0], 1], None], ['control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [0, 0, 0, 0, 0], 1], [[0, 0, 0, 0, 0], 0]], ['control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [0, 1, 1, 1, 0], 1], None], ['control [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [0, ...', [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [0, 0, 1, 1, 0, 1], 3], None]]]
for label, args, expected in fixtures[N - 1]:
    check(label, 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
regression [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...	`[[0, 0, 1, 1, 1], 1]`	`None`	Failed
regression [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...	`[[1, 1, 0, 1, 1], 1]`	`None`	Failed
partial-repair [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...	`[[1, 1, 0, 1, 1], 1]`	`[[1, 1, 0, 1, 1], 1]`	Passed
partial-repair [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...	`[[1, 1, 0, 1, 1], 1]`	`[[1, 1, 0, 1, 1], 1]`	Passed
control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...	`[[0, 0, 1, 1, 1], 0]`	`[[0, 0, 1, 1, 1], 0]`	Passed
control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...	`[[1, 1, 0, 1, 1], 1]`	`[[1, 1, 0, 1, 1], 1]`	Passed
control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...	`None`	`None`	Passed
control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...	`[[0, 0, 0, 0, 0], 0]`	`[[0, 0, 0, 0, 0], 0]`	Passed

SHA-256 / 25c3ca54dd0928276351de59d1ad5b6263d9f7ae68ec09fcfd312c1029fb77eb

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(codebook, r, radius):
    best, bd, tie = None, None, False
    for cwd in codebook:
        d = sum(a != b for a, b in zip(cwd, r))
        if bd is None or d < bd:
            best, bd, tie = cwd, d, False
        elif d == bd and cwd != best:
            tie = True
    if bd is None or bd >= radius or tie:
        return None
    return [list(best), bd]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [0, 0, 1, 1, 0], 0], None], ['regression [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [1, 0, 0, 1, 1], 0], None], ['partial-repair [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [0, 1, 0, 1, 1], 1], [[1, 1, 0, 1, 1], 1]], ['partial-repair [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [1, 1, 1, 1, 1], 1], [[1, 1, 0, 1, 1], 1]], ['control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [0, 0, 1, 1, 1], 1], [[0, 0, 1, 1, 1], 0]], ['control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [0, 1, 0, 1, 1], 2], [[1, 1, 0, 1, 1], 1]], ['control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [1, 0, 1, 1, 0], 1], None], ['control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [0, 0, 0, 0, 0], 1], [[0, 0, 0, 0, 0], 0]]], [['regression [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [1, 1, 0, 0, 1], 0], None], ['regression [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [0, ...', [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [0, 1, 1, 0, 0, 0], 1], None], ['partial-repair [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [0, 0, 1, 0, 1], 1], [[0, 0, 1, 1, 1], 1]], ['partial-repair [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [0, 0, 0, 0, 1], 1], [[0, 0, 0, 0, 0], 1]], ['control [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [0, ...', [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [0, 0, 1, 1, 0, 1], 3], None], ['control [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [0, ...', [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [0, 1, 0, 1, 0, 1], 3], None], ['control [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [1, ...', [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [1, 1, 1, 0, 0, 0], 3], None], ['control [[], [1], 1]', [[], [1], 1], None]], [['regression [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [1, 0, 0, 1, 1], 0], None], ['regression [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [0, 0, 1, 0, 0], 0], None], ['partial-repair [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [0, ...', [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [0, 1, 0, 1, 1, 1], 2], [[1, 1, 1, 1, 1, 1], 2]], ['partial-repair [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [1, ...', [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [1, 0, 0, 1, 0, 0], 2], [[0, 0, 0, 0, 0, 0], 2]], ['control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [0, 1, 0, 1, 1], 2], [[1, 1, 0, 1, 1], 1]], ['control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [1, 0, 1, 1, 0], 1], None], ['control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [0, 0, 0, 0, 0], 1], [[0, 0, 0, 0, 0], 0]], ['control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [0, 1, 1, 1, 0], 1], None]], [['regression [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [0, ...', [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [0, 1, 1, 0, 0, 0], 1], None], ['regression [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [0, 0, 1, 1, 0], 0], None], ['partial-repair [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [1, 1, 1, 0, 0], 0], [[1, 1, 1, 0, 0], 0]], ['partial-repair [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [1, 0, 1, 0, 0], 1], [[1, 1, 1, 0, 0], 1]], ['control [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [0, ...', [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [0, 1, 0, 1, 0, 1], 3], None], ['control [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [1, ...', [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [1, 1, 1, 0, 0, 0], 3], None], ['control [[], [1], 1]', [[], [1], 1], None], ['control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [0, 0, 1, 1, 1], 1], [[0, 0, 1, 1, 1], 0]]], [['regression [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [0, 0, 1, 0, 0], 0], None], ['regression [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [1, 1, 0, 0, 1], 0], None], ['partial-repair [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [0, ...', [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [0, 0, 0, 0, 0, 1], 1], [[0, 0, 0, 0, 0, 0], 1]], ['partial-repair [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [0, 1, 0, 1, 1], 1], [[1, 1, 0, 1, 1], 1]], ['control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [1, 0, 1, 1, 0], 1], None], ['control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [0, 0, 0, 0, 0], 1], [[0, 0, 0, 0, 0], 0]], ['control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...', [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1]], [0, 1, 1, 1, 0], 1], None], ['control [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [0, ...', [[[0, 0, 0, 0, 0, 0], [1, 1, 1, 1, 1, 1], [0, 0, 0, 0, 0, 0]], [0, 0, 1, 1, 0, 1], 3], None]]]
for label, args, expected in fixtures[N - 1]:
    check(label, 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
regression [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...	`None`	`None`	Passed
regression [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...	`None`	`None`	Passed
partial-repair [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...	`None`	`[[1, 1, 0, 1, 1], 1]`	Failed
partial-repair [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...	`None`	`[[1, 1, 0, 1, 1], 1]`	Failed
control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...	`[[0, 0, 1, 1, 1], 0]`	`[[0, 0, 1, 1, 1], 0]`	Passed
control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...	`[[1, 1, 0, 1, 1], 1]`	`[[1, 1, 0, 1, 1], 1]`	Passed
control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...	`None`	`None`	Passed
control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...	`[[0, 0, 0, 0, 0], 0]`	`[[0, 0, 0, 0, 0], 0]`	Passed

SHA-256 / 7c7f641c9b92966c1929ae2ecfef10c055e68a41cac9f63893f7f2f6d283d17b

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 of the named code under the stated contract; not a production codec. 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 2026-09-29T14:48:37.640301+00:00.

Case digest / 6f109598246ece3e2c60393f0a6337e27c0bf3a0c78f507d7c6a0e3f4268638d