{
 "schema_version": "0.2",
 "name": "gap-167-8-4",
 "code_type": "CSS",
 "n": 167,
 "k": 8,
 "checks": {
  "X": [
   [
    1,
    2
   ],
   [
    4,
    5
   ],
   [
    6,
    7
   ],
   [
    9,
    10
   ],
   [
    11,
    12
   ],
   [
    0,
    1,
    15,
    16
   ],
   [
    2,
    3,
    17,
    18
   ],
   [
    5,
    6,
    20,
    21
   ],
   [
    7,
    8,
    22,
    23
   ],
   [
    10,
    11,
    25,
    26
   ],
   [
    12,
    13,
    27,
    28
   ],
   [
    14,
    15,
    29,
    30
   ],
   [
    16,
    17,
    31,
    32
   ],
   [
    19,
    20,
    34,
    35
   ],
   [
    21,
    22,
    36,
    37
   ],
   [
    24,
    25,
    39,
    40
   ],
   [
    26,
    27,
    41,
    42
   ],
   [
    30,
    31,
    45,
    46
   ],
   [
    32,
    33,
    47,
    48
   ],
   [
    35,
    36,
    51,
    52
   ],
   [
    37,
    38,
    53,
    54
   ],
   [
    40,
    41,
    57,
    58
   ],
   [
    42,
    43,
    59,
    60
   ],
   [
    44,
    45,
    61,
    62
   ],
   [
    46,
    47,
    63,
    64
   ],
   [
    48,
    49,
    65,
    66
   ],
   [
    50,
    51,
    67,
    68
   ],
   [
    52,
    53,
    69,
    70
   ],
   [
    54,
    55,
    71,
    72
   ],
   [
    56,
    57,
    73,
    74
   ],
   [
    58,
    59,
    75,
    76
   ],
   [
    62,
    63
   ],
   [
    64,
    65,
    78,
    79
   ],
   [
    66,
    67,
    80,
    81
   ],
   [
    68,
    69,
    82
   ],
   [
    70,
    71,
    83,
    84
   ],
   [
    72,
    73,
    85,
    86
   ],
   [
    74,
    75,
    87
   ],
   [
    76,
    77
   ],
   [
    88,
    89
   ],
   [
    78,
    90,
    91
   ],
   [
    79,
    80,
    92,
    93
   ],
   [
    81,
    82,
    94,
    95
   ],
   [
    83,
    96,
    97
   ],
   [
    84,
    85,
    98,
    99
   ],
   [
    86,
    87,
    100,
    101
   ],
   [
    102,
    103
   ],
   [
    89,
    90,
    106,
    107
   ],
   [
    91,
    92,
    108,
    109
   ],
   [
    93,
    94,
    110,
    111
   ],
   [
    95,
    96,
    112,
    113
   ],
   [
    97,
    98,
    114,
    115
   ],
   [
    99,
    100,
    116,
    117
   ],
   [
    101,
    102,
    118,
    119
   ],
   [
    103,
    104,
    120,
    121
   ],
   [
    105,
    106,
    122,
    123
   ],
   [
    107,
    108,
    124,
    125
   ],
   [
    111,
    112,
    127,
    128
   ],
   [
    113,
    114,
    129,
    130
   ],
   [
    117,
    118,
    132,
    133
   ],
   [
    119,
    120,
    134,
    135
   ],
   [
    123,
    124,
    138,
    139
   ],
   [
    125,
    126,
    140,
    141
   ],
   [
    128,
    129,
    143,
    144
   ],
   [
    130,
    131,
    145,
    146
   ],
   [
    133,
    134,
    148,
    149
   ],
   [
    135,
    136,
    150,
    151
   ],
   [
    137,
    138,
    152,
    153
   ],
   [
    139,
    140,
    154,
    155
   ],
   [
    142,
    143,
    157,
    158
   ],
   [
    144,
    145,
    159,
    160
   ],
   [
    147,
    148,
    162,
    163
   ],
   [
    149,
    150,
    164,
    165
   ],
   [
    153,
    154
   ],
   [
    155,
    156
   ],
   [
    158,
    159
   ],
   [
    160,
    161
   ],
   [
    163,
    164
   ],
   [
    165,
    166
   ]
  ],
  "Z": [
   [
    0,
    14,
    15
   ],
   [
    1,
    2,
    16,
    17
   ],
   [
    3,
    18
   ],
   [
    4,
    5,
    19,
    20
   ],
   [
    6,
    7,
    21,
    22
   ],
   [
    8,
    23
   ],
   [
    9,
    10,
    24,
    25
   ],
   [
    11,
    12,
    26,
    27
   ],
   [
    13,
    28
   ],
   [
    14,
    29
   ],
   [
    15,
    16,
    30,
    31
   ],
   [
    17,
    18,
    32,
    33
   ],
   [
    19,
    34
   ],
   [
    20,
    21,
    35,
    36
   ],
   [
    22,
    23,
    37,
    38
   ],
   [
    24,
    39
   ],
   [
    25,
    26,
    40,
    41
   ],
   [
    27,
    28,
    42,
    43
   ],
   [
    29,
    30,
    44,
    45
   ],
   [
    31,
    32,
    46,
    47
   ],
   [
    33,
    48,
    49
   ],
   [
    34,
    35,
    50,
    51
   ],
   [
    36,
    37,
    52,
    53
   ],
   [
    38,
    54,
    55
   ],
   [
    39,
    40,
    56,
    57
   ],
   [
    41,
    42,
    58,
    59
   ],
   [
    43,
    60
   ],
   [
    44,
    61
   ],
   [
    45,
    46,
    62,
    63
   ],
   [
    47,
    48,
    64,
    65
   ],
   [
    49,
    50,
    66,
    67
   ],
   [
    51,
    52,
    68,
    69
   ],
   [
    53,
    54,
    70,
    71
   ],
   [
    55,
    56,
    72,
    73
   ],
   [
    57,
    58,
    74,
    75
   ],
   [
    59,
    60,
    76,
    77
   ],
   [
    65,
    66,
    79,
    80
   ],
   [
    67,
    68,
    81,
    82
   ],
   [
    71,
    72,
    84,
    85
   ],
   [
    73,
    74,
    86,
    87
   ],
   [
    78,
    79,
    91,
    92
   ],
   [
    80,
    81,
    93,
    94
   ],
   [
    83,
    84,
    97,
    98
   ],
   [
    85,
    86,
    99,
    100
   ],
   [
    88,
    89,
    105,
    106
   ],
   [
    90,
    91,
    107,
    108
   ],
   [
    92,
    93,
    109,
    110
   ],
   [
    94,
    95,
    111,
    112
   ],
   [
    96,
    97,
    113,
    114
   ],
   [
    98,
    99,
    115,
    116
   ],
   [
    100,
    101,
    117,
    118
   ],
   [
    102,
    103,
    119,
    120
   ],
   [
    104,
    121
   ],
   [
    105,
    122
   ],
   [
    106,
    107,
    123,
    124
   ],
   [
    108,
    109,
    125,
    126
   ],
   [
    110,
    111,
    127
   ],
   [
    112,
    113,
    128,
    129
   ],
   [
    114,
    115,
    130,
    131
   ],
   [
    116,
    117,
    132
   ],
   [
    118,
    119,
    133,
    134
   ],
   [
    120,
    121,
    135,
    136
   ],
   [
    122,
    123,
    137,
    138
   ],
   [
    124,
    125,
    139,
    140
   ],
   [
    126,
    141
   ],
   [
    127,
    128,
    142,
    143
   ],
   [
    129,
    130,
    144,
    145
   ],
   [
    131,
    146
   ],
   [
    132,
    133,
    147,
    148
   ],
   [
    134,
    135,
    149,
    150
   ],
   [
    136,
    151
   ],
   [
    137,
    152
   ],
   [
    138,
    139,
    153,
    154
   ],
   [
    140,
    141,
    155,
    156
   ],
   [
    142,
    157
   ],
   [
    143,
    144,
    158,
    159
   ],
   [
    145,
    146,
    160,
    161
   ],
   [
    147,
    162
   ],
   [
    148,
    149,
    163,
    164
   ],
   [
    150,
    151,
    165,
    166
   ]
  ]
 },
 "distance": {
  "d": 4,
  "X": {
   "value": 5,
   "confidence": "upper_bound",
   "witness": [
    96,
    113,
    128,
    142,
    157
   ],
   "witness_provenance": {
    "found_by": [
     "@mathys"
    ],
    "date": "2026-11-02",
    "found_at_samples": 1000,
    "survived_samples": 1000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     0
    ]
   }
  },
  "Z": {
   "value": 4,
   "confidence": "upper_bound",
   "witness": [
    0,
    16,
    32,
    33
   ],
   "witness_provenance": {
    "found_by": [
     "@mathys"
    ],
    "date": "2026-11-02",
    "found_at_samples": 1000,
    "survived_samples": 1000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "@mathysrennela"
  ],
  "construction": "priced calculus E-PEEL transform of codes/168-8-5.json",
  "references": [],
  "date": "2026-11-02",
  "notes": "",
  "model": "Beam 1.0"
 },
 "locality": {
  "coordinates": [
   [
    1.5,
    0.5
   ],
   [
    2.5,
    0.5
   ],
   [
    3.5,
    0.5
   ],
   [
    4.5,
    0.5
   ],
   [
    6.5,
    0.5
   ],
   [
    7.5,
    0.5
   ],
   [
    8.5,
    0.5
   ],
   [
    9.5,
    0.5
   ],
   [
    10.5,
    0.5
   ],
   [
    12.5,
    0.5
   ],
   [
    13.5,
    0.5
   ],
   [
    14.5,
    0.5
   ],
   [
    15.5,
    0.5
   ],
   [
    16.5,
    0.5
   ],
   [
    0.5,
    1.5
   ],
   [
    1.5,
    1.5
   ],
   [
    2.5,
    1.5
   ],
   [
    3.5,
    1.5
   ],
   [
    4.5,
    1.5
   ],
   [
    6.5,
    1.5
   ],
   [
    7.5,
    1.5
   ],
   [
    8.5,
    1.5
   ],
   [
    9.5,
    1.5
   ],
   [
    10.5,
    1.5
   ],
   [
    12.5,
    1.5
   ],
   [
    13.5,
    1.5
   ],
   [
    14.5,
    1.5
   ],
   [
    15.5,
    1.5
   ],
   [
    16.5,
    1.5
   ],
   [
    0.5,
    2.5
   ],
   [
    1.5,
    2.5
   ],
   [
    2.5,
    2.5
   ],
   [
    3.5,
    2.5
   ],
   [
    4.5,
    2.5
   ],
   [
    6.5,
    2.5
   ],
   [
    7.5,
    2.5
   ],
   [
    8.5,
    2.5
   ],
   [
    9.5,
    2.5
   ],
   [
    10.5,
    2.5
   ],
   [
    12.5,
    2.5
   ],
   [
    13.5,
    2.5
   ],
   [
    14.5,
    2.5
   ],
   [
    15.5,
    2.5
   ],
   [
    16.5,
    2.5
   ],
   [
    0.5,
    3.5
   ],
   [
    1.5,
    3.5
   ],
   [
    2.5,
    3.5
   ],
   [
    3.5,
    3.5
   ],
   [
    4.5,
    3.5
   ],
   [
    5.5,
    3.5
   ],
   [
    6.5,
    3.5
   ],
   [
    7.5,
    3.5
   ],
   [
    8.5,
    3.5
   ],
   [
    9.5,
    3.5
   ],
   [
    10.5,
    3.5
   ],
   [
    11.5,
    3.5
   ],
   [
    12.5,
    3.5
   ],
   [
    13.5,
    3.5
   ],
   [
    14.5,
    3.5
   ],
   [
    15.5,
    3.5
   ],
   [
    16.5,
    3.5
   ],
   [
    0.5,
    4.5
   ],
   [
    1.5,
    4.5
   ],
   [
    2.5,
    4.5
   ],
   [
    3.5,
    4.5
   ],
   [
    4.5,
    4.5
   ],
   [
    5.5,
    4.5
   ],
   [
    6.5,
    4.5
   ],
   [
    7.5,
    4.5
   ],
   [
    8.5,
    4.5
   ],
   [
    9.5,
    4.5
   ],
   [
    10.5,
    4.5
   ],
   [
    11.5,
    4.5
   ],
   [
    12.5,
    4.5
   ],
   [
    13.5,
    4.5
   ],
   [
    14.5,
    4.5
   ],
   [
    15.5,
    4.5
   ],
   [
    16.5,
    4.5
   ],
   [
    3.5,
    5.5
   ],
   [
    4.5,
    5.5
   ],
   [
    5.5,
    5.5
   ],
   [
    6.5,
    5.5
   ],
   [
    7.5,
    5.5
   ],
   [
    9.5,
    5.5
   ],
   [
    10.5,
    5.5
   ],
   [
    11.5,
    5.5
   ],
   [
    12.5,
    5.5
   ],
   [
    13.5,
    5.5
   ],
   [
    0.5,
    6.5
   ],
   [
    1.5,
    6.5
   ],
   [
    2.5,
    6.5
   ],
   [
    3.5,
    6.5
   ],
   [
    4.5,
    6.5
   ],
   [
    5.5,
    6.5
   ],
   [
    6.5,
    6.5
   ],
   [
    7.5,
    6.5
   ],
   [
    8.5,
    6.5
   ],
   [
    9.5,
    6.5
   ],
   [
    10.5,
    6.5
   ],
   [
    11.5,
    6.5
   ],
   [
    12.5,
    6.5
   ],
   [
    13.5,
    6.5
   ],
   [
    14.5,
    6.5
   ],
   [
    15.5,
    6.5
   ],
   [
    16.5,
    6.5
   ],
   [
    0.5,
    7.5
   ],
   [
    1.5,
    7.5
   ],
   [
    2.5,
    7.5
   ],
   [
    3.5,
    7.5
   ],
   [
    4.5,
    7.5
   ],
   [
    5.5,
    7.5
   ],
   [
    6.5,
    7.5
   ],
   [
    7.5,
    7.5
   ],
   [
    8.5,
    7.5
   ],
   [
    9.5,
    7.5
   ],
   [
    10.5,
    7.5
   ],
   [
    11.5,
    7.5
   ],
   [
    12.5,
    7.5
   ],
   [
    13.5,
    7.5
   ],
   [
    14.5,
    7.5
   ],
   [
    15.5,
    7.5
   ],
   [
    16.5,
    7.5
   ],
   [
    0.5,
    8.5
   ],
   [
    1.5,
    8.5
   ],
   [
    2.5,
    8.5
   ],
   [
    3.5,
    8.5
   ],
   [
    4.5,
    8.5
   ],
   [
    6.5,
    8.5
   ],
   [
    7.5,
    8.5
   ],
   [
    8.5,
    8.5
   ],
   [
    9.5,
    8.5
   ],
   [
    10.5,
    8.5
   ],
   [
    12.5,
    8.5
   ],
   [
    13.5,
    8.5
   ],
   [
    14.5,
    8.5
   ],
   [
    15.5,
    8.5
   ],
   [
    16.5,
    8.5
   ],
   [
    0.5,
    9.5
   ],
   [
    1.5,
    9.5
   ],
   [
    2.5,
    9.5
   ],
   [
    3.5,
    9.5
   ],
   [
    4.5,
    9.5
   ],
   [
    6.5,
    9.5
   ],
   [
    7.5,
    9.5
   ],
   [
    8.5,
    9.5
   ],
   [
    9.5,
    9.5
   ],
   [
    10.5,
    9.5
   ],
   [
    12.5,
    9.5
   ],
   [
    13.5,
    9.5
   ],
   [
    14.5,
    9.5
   ],
   [
    15.5,
    9.5
   ],
   [
    16.5,
    9.5
   ],
   [
    0.5,
    10.5
   ],
   [
    1.5,
    10.5
   ],
   [
    2.5,
    10.5
   ],
   [
    3.5,
    10.5
   ],
   [
    4.5,
    10.5
   ],
   [
    6.5,
    10.5
   ],
   [
    7.5,
    10.5
   ],
   [
    8.5,
    10.5
   ],
   [
    9.5,
    10.5
   ],
   [
    10.5,
    10.5
   ],
   [
    12.5,
    10.5
   ],
   [
    13.5,
    10.5
   ],
   [
    14.5,
    10.5
   ],
   [
    15.5,
    10.5
   ],
   [
    16.5,
    10.5
   ]
  ],
  "layers": 1,
  "contributed_by": {
   "by": [
    "@vprusso"
   ],
   "date": "2026-11-04",
   "method": "Inherited from the laid-out parent codes/168-8-5.json: the parent's coordinates with the entry of the removed qubit (parent index 0) dropped, since this peel child keeps the parent's qubit order. Radius, layer count, and class re-measured by the verifier."
  }
 }
}