{
 "schema_version": "0.1",
 "name": "[[169,10,3]]",
 "code_type": "CSS",
 "n": 169,
 "k": 10,
 "checks": {
  "X": [
   [
    0,
    1,
    13,
    14
   ],
   [
    2,
    3,
    15,
    16
   ],
   [
    4,
    5,
    17,
    18
   ],
   [
    6,
    7,
    19,
    20
   ],
   [
    8,
    9,
    21,
    22
   ],
   [
    10,
    11,
    23,
    24
   ],
   [
    14,
    15,
    27,
    28
   ],
   [
    16,
    17,
    29,
    30
   ],
   [
    18,
    19,
    31,
    32
   ],
   [
    20,
    21,
    33,
    34
   ],
   [
    22,
    23,
    35,
    36
   ],
   [
    24,
    25,
    37,
    38
   ],
   [
    26,
    27,
    39,
    40
   ],
   [
    28,
    29,
    41,
    42
   ],
   [
    30,
    31,
    43,
    44
   ],
   [
    32,
    33,
    45,
    46
   ],
   [
    34,
    35,
    47,
    48
   ],
   [
    36,
    37,
    49,
    50
   ],
   [
    40,
    41,
    53,
    54
   ],
   [
    44,
    45,
    57,
    58
   ],
   [
    46,
    47,
    59,
    60
   ],
   [
    50,
    51,
    63,
    64
   ],
   [
    52,
    53,
    65,
    66
   ],
   [
    54,
    55,
    67,
    68
   ],
   [
    56,
    57,
    69,
    70
   ],
   [
    58,
    59,
    71,
    72
   ],
   [
    60,
    61,
    73,
    74
   ],
   [
    62,
    63,
    75,
    76
   ],
   [
    66,
    67,
    79,
    80
   ],
   [
    68,
    69,
    81,
    82
   ],
   [
    70,
    71,
    83,
    84
   ],
   [
    72,
    73,
    85,
    86
   ],
   [
    74,
    75,
    87,
    88
   ],
   [
    76,
    77,
    89,
    90
   ],
   [
    78,
    79,
    91,
    92
   ],
   [
    80,
    81,
    93,
    94
   ],
   [
    82,
    83,
    95,
    96
   ],
   [
    86,
    87,
    99,
    100
   ],
   [
    88,
    89,
    101,
    102
   ],
   [
    92,
    93,
    105,
    106
   ],
   [
    94,
    95,
    107,
    108
   ],
   [
    96,
    97,
    109,
    110
   ],
   [
    98,
    99,
    111,
    112
   ],
   [
    100,
    101,
    113,
    114
   ],
   [
    102,
    103,
    115,
    116
   ],
   [
    104,
    105,
    117,
    118
   ],
   [
    106,
    107,
    119,
    120
   ],
   [
    108,
    109,
    121,
    122
   ],
   [
    110,
    111,
    123,
    124
   ],
   [
    112,
    113,
    125,
    126
   ],
   [
    114,
    115,
    127,
    128
   ],
   [
    118,
    119,
    131,
    132
   ],
   [
    122,
    123,
    135,
    136
   ],
   [
    124,
    125,
    137,
    138
   ],
   [
    128,
    129,
    141,
    142
   ],
   [
    130,
    131,
    143,
    144
   ],
   [
    132,
    133,
    145,
    146
   ],
   [
    134,
    135,
    147,
    148
   ],
   [
    136,
    137,
    149,
    150
   ],
   [
    138,
    139,
    151,
    152
   ],
   [
    140,
    141,
    153,
    154
   ],
   [
    144,
    145,
    157,
    158
   ],
   [
    146,
    147,
    159,
    160
   ],
   [
    148,
    149,
    161,
    162
   ],
   [
    150,
    151,
    163,
    164
   ],
   [
    152,
    153,
    165,
    166
   ],
   [
    154,
    155,
    167,
    168
   ],
   [
    13,
    26
   ],
   [
    39,
    52
   ],
   [
    65,
    78
   ],
   [
    91,
    104
   ],
   [
    117,
    130
   ],
   [
    143,
    156
   ],
   [
    12,
    25
   ],
   [
    38,
    51
   ],
   [
    64,
    77
   ],
   [
    90,
    103
   ],
   [
    116,
    129
   ],
   [
    142,
    155
   ]
  ],
  "Z": [
   [
    1,
    2,
    14,
    15
   ],
   [
    3,
    4,
    16,
    17
   ],
   [
    5,
    6,
    18,
    19
   ],
   [
    7,
    8,
    20,
    21
   ],
   [
    9,
    10,
    22,
    23
   ],
   [
    11,
    12,
    24,
    25
   ],
   [
    13,
    14,
    26,
    27
   ],
   [
    15,
    16,
    28,
    29
   ],
   [
    17,
    18,
    30,
    31
   ],
   [
    19,
    20,
    32,
    33
   ],
   [
    21,
    22,
    34,
    35
   ],
   [
    23,
    24,
    36,
    37
   ],
   [
    27,
    28,
    40,
    41
   ],
   [
    29,
    30,
    42,
    43
   ],
   [
    31,
    32,
    44,
    45
   ],
   [
    33,
    34,
    46,
    47
   ],
   [
    35,
    36,
    48,
    49
   ],
   [
    37,
    38,
    50,
    51
   ],
   [
    39,
    40,
    52,
    53
   ],
   [
    41,
    42,
    54,
    55
   ],
   [
    43,
    44,
    56,
    57
   ],
   [
    47,
    48,
    60,
    61
   ],
   [
    49,
    50,
    62,
    63
   ],
   [
    53,
    54,
    66,
    67
   ],
   [
    55,
    56,
    68,
    69
   ],
   [
    57,
    58,
    70,
    71
   ],
   [
    59,
    60,
    72,
    73
   ],
   [
    61,
    62,
    74,
    75
   ],
   [
    63,
    64,
    76,
    77
   ],
   [
    65,
    66,
    78,
    79
   ],
   [
    67,
    68,
    80,
    81
   ],
   [
    69,
    70,
    82,
    83
   ],
   [
    71,
    72,
    84,
    85
   ],
   [
    73,
    74,
    86,
    87
   ],
   [
    75,
    76,
    88,
    89
   ],
   [
    79,
    80,
    92,
    93
   ],
   [
    83,
    84,
    96,
    97
   ],
   [
    85,
    86,
    98,
    99
   ],
   [
    89,
    90,
    102,
    103
   ],
   [
    91,
    92,
    104,
    105
   ],
   [
    93,
    94,
    106,
    107
   ],
   [
    95,
    96,
    108,
    109
   ],
   [
    97,
    98,
    110,
    111
   ],
   [
    99,
    100,
    112,
    113
   ],
   [
    101,
    102,
    114,
    115
   ],
   [
    105,
    106,
    118,
    119
   ],
   [
    107,
    108,
    120,
    121
   ],
   [
    109,
    110,
    122,
    123
   ],
   [
    111,
    112,
    124,
    125
   ],
   [
    113,
    114,
    126,
    127
   ],
   [
    115,
    116,
    128,
    129
   ],
   [
    117,
    118,
    130,
    131
   ],
   [
    119,
    120,
    132,
    133
   ],
   [
    121,
    122,
    134,
    135
   ],
   [
    125,
    126,
    138,
    139
   ],
   [
    127,
    128,
    140,
    141
   ],
   [
    131,
    132,
    144,
    145
   ],
   [
    133,
    134,
    146,
    147
   ],
   [
    135,
    136,
    148,
    149
   ],
   [
    137,
    138,
    150,
    151
   ],
   [
    139,
    140,
    152,
    153
   ],
   [
    141,
    142,
    154,
    155
   ],
   [
    143,
    144,
    156,
    157
   ],
   [
    145,
    146,
    158,
    159
   ],
   [
    147,
    148,
    160,
    161
   ],
   [
    149,
    150,
    162,
    163
   ],
   [
    151,
    152,
    164,
    165
   ],
   [
    153,
    154,
    166,
    167
   ],
   [
    0,
    1
   ],
   [
    2,
    3
   ],
   [
    4,
    5
   ],
   [
    6,
    7
   ],
   [
    8,
    9
   ],
   [
    10,
    11
   ],
   [
    157,
    158
   ],
   [
    159,
    160
   ],
   [
    161,
    162
   ],
   [
    163,
    164
   ],
   [
    165,
    166
   ],
   [
    167,
    168
   ]
  ]
 },
 "distance": {
  "d": 3,
  "X": {
   "value": 3,
   "confidence": "upper_bound",
   "witness": [
    59,
    73,
    87
   ]
  },
  "Z": {
   "value": 3,
   "confidence": "upper_bound",
   "witness": [
    134,
    147,
    159
   ]
  }
 },
 "provenance": {
  "authors": [
   "@mathysrennela"
  ],
  "construction": "Holey rotated surface code on integer grid L=13, period-3 hole sublattice: X plaquettes on even-parity cells, Z on odd-parity cells, X-holes at (3a,3b) even parity, Z-holes at (3a,3b) odd parity, margin 3 from boundaries (smallest size of the family generalizing codes/625-50-3.json); standard rotated-surface boundary pairs (X chains vertical, Z chains horizontal).",
  "origin": "submission",
  "date": "2026-08-09",
  "model": "DeepSeek V4 Flash 0731"
 },
 "family": "topological",
 "locality": {
  "coordinates": [
   [
    0.0,
    0.0
   ],
   [
    0.0,
    1.0
   ],
   [
    0.0,
    2.0
   ],
   [
    0.0,
    3.0
   ],
   [
    0.0,
    4.0
   ],
   [
    0.0,
    5.0
   ],
   [
    0.0,
    6.0
   ],
   [
    0.0,
    7.0
   ],
   [
    0.0,
    8.0
   ],
   [
    0.0,
    9.0
   ],
   [
    0.0,
    10.0
   ],
   [
    0.0,
    11.0
   ],
   [
    0.0,
    12.0
   ],
   [
    1.0,
    0.0
   ],
   [
    1.0,
    1.0
   ],
   [
    1.0,
    2.0
   ],
   [
    1.0,
    3.0
   ],
   [
    1.0,
    4.0
   ],
   [
    1.0,
    5.0
   ],
   [
    1.0,
    6.0
   ],
   [
    1.0,
    7.0
   ],
   [
    1.0,
    8.0
   ],
   [
    1.0,
    9.0
   ],
   [
    1.0,
    10.0
   ],
   [
    1.0,
    11.0
   ],
   [
    1.0,
    12.0
   ],
   [
    2.0,
    0.0
   ],
   [
    2.0,
    1.0
   ],
   [
    2.0,
    2.0
   ],
   [
    2.0,
    3.0
   ],
   [
    2.0,
    4.0
   ],
   [
    2.0,
    5.0
   ],
   [
    2.0,
    6.0
   ],
   [
    2.0,
    7.0
   ],
   [
    2.0,
    8.0
   ],
   [
    2.0,
    9.0
   ],
   [
    2.0,
    10.0
   ],
   [
    2.0,
    11.0
   ],
   [
    2.0,
    12.0
   ],
   [
    3.0,
    0.0
   ],
   [
    3.0,
    1.0
   ],
   [
    3.0,
    2.0
   ],
   [
    3.0,
    3.0
   ],
   [
    3.0,
    4.0
   ],
   [
    3.0,
    5.0
   ],
   [
    3.0,
    6.0
   ],
   [
    3.0,
    7.0
   ],
   [
    3.0,
    8.0
   ],
   [
    3.0,
    9.0
   ],
   [
    3.0,
    10.0
   ],
   [
    3.0,
    11.0
   ],
   [
    3.0,
    12.0
   ],
   [
    4.0,
    0.0
   ],
   [
    4.0,
    1.0
   ],
   [
    4.0,
    2.0
   ],
   [
    4.0,
    3.0
   ],
   [
    4.0,
    4.0
   ],
   [
    4.0,
    5.0
   ],
   [
    4.0,
    6.0
   ],
   [
    4.0,
    7.0
   ],
   [
    4.0,
    8.0
   ],
   [
    4.0,
    9.0
   ],
   [
    4.0,
    10.0
   ],
   [
    4.0,
    11.0
   ],
   [
    4.0,
    12.0
   ],
   [
    5.0,
    0.0
   ],
   [
    5.0,
    1.0
   ],
   [
    5.0,
    2.0
   ],
   [
    5.0,
    3.0
   ],
   [
    5.0,
    4.0
   ],
   [
    5.0,
    5.0
   ],
   [
    5.0,
    6.0
   ],
   [
    5.0,
    7.0
   ],
   [
    5.0,
    8.0
   ],
   [
    5.0,
    9.0
   ],
   [
    5.0,
    10.0
   ],
   [
    5.0,
    11.0
   ],
   [
    5.0,
    12.0
   ],
   [
    6.0,
    0.0
   ],
   [
    6.0,
    1.0
   ],
   [
    6.0,
    2.0
   ],
   [
    6.0,
    3.0
   ],
   [
    6.0,
    4.0
   ],
   [
    6.0,
    5.0
   ],
   [
    6.0,
    6.0
   ],
   [
    6.0,
    7.0
   ],
   [
    6.0,
    8.0
   ],
   [
    6.0,
    9.0
   ],
   [
    6.0,
    10.0
   ],
   [
    6.0,
    11.0
   ],
   [
    6.0,
    12.0
   ],
   [
    7.0,
    0.0
   ],
   [
    7.0,
    1.0
   ],
   [
    7.0,
    2.0
   ],
   [
    7.0,
    3.0
   ],
   [
    7.0,
    4.0
   ],
   [
    7.0,
    5.0
   ],
   [
    7.0,
    6.0
   ],
   [
    7.0,
    7.0
   ],
   [
    7.0,
    8.0
   ],
   [
    7.0,
    9.0
   ],
   [
    7.0,
    10.0
   ],
   [
    7.0,
    11.0
   ],
   [
    7.0,
    12.0
   ],
   [
    8.0,
    0.0
   ],
   [
    8.0,
    1.0
   ],
   [
    8.0,
    2.0
   ],
   [
    8.0,
    3.0
   ],
   [
    8.0,
    4.0
   ],
   [
    8.0,
    5.0
   ],
   [
    8.0,
    6.0
   ],
   [
    8.0,
    7.0
   ],
   [
    8.0,
    8.0
   ],
   [
    8.0,
    9.0
   ],
   [
    8.0,
    10.0
   ],
   [
    8.0,
    11.0
   ],
   [
    8.0,
    12.0
   ],
   [
    9.0,
    0.0
   ],
   [
    9.0,
    1.0
   ],
   [
    9.0,
    2.0
   ],
   [
    9.0,
    3.0
   ],
   [
    9.0,
    4.0
   ],
   [
    9.0,
    5.0
   ],
   [
    9.0,
    6.0
   ],
   [
    9.0,
    7.0
   ],
   [
    9.0,
    8.0
   ],
   [
    9.0,
    9.0
   ],
   [
    9.0,
    10.0
   ],
   [
    9.0,
    11.0
   ],
   [
    9.0,
    12.0
   ],
   [
    10.0,
    0.0
   ],
   [
    10.0,
    1.0
   ],
   [
    10.0,
    2.0
   ],
   [
    10.0,
    3.0
   ],
   [
    10.0,
    4.0
   ],
   [
    10.0,
    5.0
   ],
   [
    10.0,
    6.0
   ],
   [
    10.0,
    7.0
   ],
   [
    10.0,
    8.0
   ],
   [
    10.0,
    9.0
   ],
   [
    10.0,
    10.0
   ],
   [
    10.0,
    11.0
   ],
   [
    10.0,
    12.0
   ],
   [
    11.0,
    0.0
   ],
   [
    11.0,
    1.0
   ],
   [
    11.0,
    2.0
   ],
   [
    11.0,
    3.0
   ],
   [
    11.0,
    4.0
   ],
   [
    11.0,
    5.0
   ],
   [
    11.0,
    6.0
   ],
   [
    11.0,
    7.0
   ],
   [
    11.0,
    8.0
   ],
   [
    11.0,
    9.0
   ],
   [
    11.0,
    10.0
   ],
   [
    11.0,
    11.0
   ],
   [
    11.0,
    12.0
   ],
   [
    12.0,
    0.0
   ],
   [
    12.0,
    1.0
   ],
   [
    12.0,
    2.0
   ],
   [
    12.0,
    3.0
   ],
   [
    12.0,
    4.0
   ],
   [
    12.0,
    5.0
   ],
   [
    12.0,
    6.0
   ],
   [
    12.0,
    7.0
   ],
   [
    12.0,
    8.0
   ],
   [
    12.0,
    9.0
   ],
   [
    12.0,
    10.0
   ],
   [
    12.0,
    11.0
   ],
   [
    12.0,
    12.0
   ]
  ],
  "layers": 1
 }
}
