{"abstract":"Heavily corrupted words are decoded instead of flagged.","category":"Error-correcting codes","checks":8,"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].","contract_signature":"codebook, r, radius","evaluation_group":"w2-error_correcting_codes-bounded-distance-decode","failed_approach":"Rejecting at the radius itself refuses words exactly radius errors away.","family":"w2-error_correcting_codes-bounded-distance-decode-decoding-radius","id":"FA-72336","implementations":{"attempt":{"sha256":"7c7f641c9b92966c1929ae2ecfef10c055e68a41cac9f63893f7f2f6d283d17b","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(codebook, r, radius):\n    best, bd, tie = None, None, False\n    for cwd in codebook:\n        d = sum(a != b for a, b in zip(cwd, r))\n        if bd is None or d < bd:\n            best, bd, tie = cwd, d, False\n        elif d == bd and cwd != best:\n            tie = True\n    if bd is None or bd >= radius or tie:\n        return None\n    return [list(best), bd]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['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]]]\nfor label, args, expected in fixtures[N - 1]:\n    check(label, solve(*args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"25c3ca54dd0928276351de59d1ad5b6263d9f7ae68ec09fcfd312c1029fb77eb","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(codebook, r, radius):\n    best, bd, tie = None, None, False\n    for cwd in codebook:\n        d = sum(a != b for a, b in zip(cwd, r))\n        if bd is None or d < bd:\n            best, bd, tie = cwd, d, False\n        elif d == bd and cwd != best:\n            tie = True\n    if bd is None or tie:\n        return None\n    return [list(best), bd]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\nfixtures = [[['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]]]\nfor label, args, expected in fixtures[N - 1]:\n    check(label, solve(*args), expected)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"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.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"w2-error_correcting_codes-bounded-distance-decode-decoding-radius","generated_at":"2026-09-29T14:48:37.640301+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Short control-channel codes are decoded against small codebooks; ties must be reported as failures, not guessed.","root_cause":"The radius check is missing.","sha256":"6f109598246ece3e2c60393f0a6337e27c0bf3a0c78f507d7c6a0e3f4268638d","title":"Bounded-distance decoder accepts any distance · case 01","variant":1,"variant_policy":"Five numbered records share a model and may reuse boundary fixtures.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":41.84,"exit_code":1,"observations":[{"actual":null,"check":"regression [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...","expected":null,"passed":true},{"actual":null,"check":"regression [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...","expected":null,"passed":true},{"actual":null,"check":"partial-repair [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...","expected":[[1,1,0,1,1],1],"passed":false},{"actual":null,"check":"partial-repair [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...","expected":[[1,1,0,1,1],1],"passed":false},{"actual":[[0,0,1,1,1],0],"check":"control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...","expected":[[0,0,1,1,1],0],"passed":true},{"actual":[[1,1,0,1,1],1],"check":"control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...","expected":[[1,1,0,1,1],1],"passed":true},{"actual":null,"check":"control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...","expected":null,"passed":true},{"actual":[[0,0,0,0,0],0],"check":"control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...","expected":[[0,0,0,0,0],0],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"regression [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"partial-repair [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...\", \"actual\": null, \"expected\": [[1, 1, 0, 1, 1], 1], \"passed\": false}, {\"check\": \"partial-repair [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...\", \"actual\": null, \"expected\": [[1, 1, 0, 1, 1], 1], \"passed\": false}, {\"check\": \"control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...\", \"actual\": [[0, 0, 1, 1, 1], 0], \"expected\": [[0, 0, 1, 1, 1], 0], \"passed\": true}, {\"check\": \"control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...\", \"actual\": [[1, 1, 0, 1, 1], 1], \"expected\": [[1, 1, 0, 1, 1], 1], \"passed\": true}, {\"check\": \"control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...\", \"actual\": [[0, 0, 0, 0, 0], 0], \"expected\": [[0, 0, 0, 0, 0], 0], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":39.888,"exit_code":1,"observations":[{"actual":[[0,0,1,1,1],1],"check":"regression [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...","expected":null,"passed":false},{"actual":[[1,1,0,1,1],1],"check":"regression [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...","expected":null,"passed":false},{"actual":[[1,1,0,1,1],1],"check":"partial-repair [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...","expected":[[1,1,0,1,1],1],"passed":true},{"actual":[[1,1,0,1,1],1],"check":"partial-repair [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...","expected":[[1,1,0,1,1],1],"passed":true},{"actual":[[0,0,1,1,1],0],"check":"control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...","expected":[[0,0,1,1,1],0],"passed":true},{"actual":[[1,1,0,1,1],1],"check":"control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...","expected":[[1,1,0,1,1],1],"passed":true},{"actual":null,"check":"control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...","expected":null,"passed":true},{"actual":[[0,0,0,0,0],0],"check":"control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...","expected":[[0,0,0,0,0],0],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"regression [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...\", \"actual\": [[0, 0, 1, 1, 1], 1], \"expected\": null, \"passed\": false}, {\"check\": \"regression [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...\", \"actual\": [[1, 1, 0, 1, 1], 1], \"expected\": null, \"passed\": false}, {\"check\": \"partial-repair [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...\", \"actual\": [[1, 1, 0, 1, 1], 1], \"expected\": [[1, 1, 0, 1, 1], 1], \"passed\": true}, {\"check\": \"partial-repair [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...\", \"actual\": [[1, 1, 0, 1, 1], 1], \"expected\": [[1, 1, 0, 1, 1], 1], \"passed\": true}, {\"check\": \"control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...\", \"actual\": [[0, 0, 1, 1, 1], 0], \"expected\": [[0, 0, 1, 1, 1], 0], \"passed\": true}, {\"check\": \"control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...\", \"actual\": [[1, 1, 0, 1, 1], 1], \"expected\": [[1, 1, 0, 1, 1], 1], \"passed\": true}, {\"check\": \"control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...\", \"actual\": null, \"expected\": null, \"passed\": true}, {\"check\": \"control [[[0, 0, 0, 0, 0], [1, 1, 1, 0, 0], [0, 0, 1, 1, 1], [1, 1, 0, 1, 1...\", \"actual\": [[0, 0, 0, 0, 0], 0], \"expected\": [[0, 0, 0, 0, 0], 0], \"passed\": true}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}