{
 "schema_version": "0.1",
 "name": "[[198,12,7]] weight-6 planar (k=12 leader family)",
 "code_type": "CSS",
 "n": 198,
 "k": 12,
 "checks": {
  "X": [
   [
    2,
    18,
    27,
    99,
    118,
    128
   ],
   [
    3,
    19,
    28,
    100,
    119,
    129
   ],
   [
    4,
    20,
    29,
    101,
    120,
    130
   ],
   [
    5,
    21,
    30,
    102,
    121,
    131
   ],
   [
    6,
    22,
    31,
    103,
    122,
    132
   ],
   [
    7,
    23,
    32,
    104,
    123,
    133
   ],
   [
    8,
    24,
    33,
    105,
    124,
    134
   ],
   [
    11,
    27,
    36,
    108,
    127,
    137
   ],
   [
    12,
    28,
    37,
    109,
    128,
    138
   ],
   [
    13,
    29,
    38,
    110,
    129,
    139
   ],
   [
    14,
    30,
    39,
    111,
    130,
    140
   ],
   [
    15,
    31,
    40,
    112,
    131,
    141
   ],
   [
    16,
    32,
    41,
    113,
    132,
    142
   ],
   [
    17,
    33,
    42,
    114,
    133,
    143
   ],
   [
    20,
    36,
    45,
    117,
    136,
    146
   ],
   [
    21,
    37,
    46,
    118,
    137,
    147
   ],
   [
    22,
    38,
    47,
    119,
    138,
    148
   ],
   [
    23,
    39,
    48,
    120,
    139,
    149
   ],
   [
    24,
    40,
    49,
    121,
    140,
    150
   ],
   [
    25,
    41,
    50,
    122,
    141,
    151
   ],
   [
    26,
    42,
    51,
    123,
    142,
    152
   ],
   [
    29,
    45,
    54,
    126,
    145,
    155
   ],
   [
    30,
    46,
    55,
    127,
    146,
    156
   ],
   [
    31,
    47,
    56,
    128,
    147,
    157
   ],
   [
    32,
    48,
    57,
    129,
    148,
    158
   ],
   [
    33,
    49,
    58,
    130,
    149,
    159
   ],
   [
    34,
    50,
    59,
    131,
    150,
    160
   ],
   [
    35,
    51,
    60,
    132,
    151,
    161
   ],
   [
    38,
    54,
    63,
    135,
    154,
    164
   ],
   [
    39,
    55,
    64,
    136,
    155,
    165
   ],
   [
    40,
    56,
    65,
    137,
    156,
    166
   ],
   [
    41,
    57,
    66,
    138,
    157,
    167
   ],
   [
    42,
    58,
    67,
    139,
    158,
    168
   ],
   [
    43,
    59,
    68,
    140,
    159,
    169
   ],
   [
    44,
    60,
    69,
    141,
    160,
    170
   ],
   [
    47,
    63,
    72,
    144,
    163,
    173
   ],
   [
    48,
    64,
    73,
    145,
    164,
    174
   ],
   [
    49,
    65,
    74,
    146,
    165,
    175
   ],
   [
    50,
    66,
    75,
    147,
    166,
    176
   ],
   [
    51,
    67,
    76,
    148,
    167,
    177
   ],
   [
    52,
    68,
    77,
    149,
    168,
    178
   ],
   [
    53,
    69,
    78,
    150,
    169,
    179
   ],
   [
    56,
    72,
    81,
    153,
    172,
    182
   ],
   [
    57,
    73,
    82,
    154,
    173,
    183
   ],
   [
    58,
    74,
    83,
    155,
    174,
    184
   ],
   [
    59,
    75,
    84,
    156,
    175,
    185
   ],
   [
    60,
    76,
    85,
    157,
    176,
    186
   ],
   [
    61,
    77,
    86,
    158,
    177,
    187
   ],
   [
    62,
    78,
    87,
    159,
    178,
    188
   ],
   [
    65,
    81,
    90,
    162,
    181,
    191
   ],
   [
    66,
    82,
    91,
    163,
    182,
    192
   ],
   [
    67,
    83,
    92,
    164,
    183,
    193
   ],
   [
    68,
    84,
    93,
    165,
    184,
    194
   ],
   [
    69,
    85,
    94,
    166,
    185,
    195
   ],
   [
    70,
    86,
    95,
    167,
    186,
    196
   ],
   [
    71,
    87,
    96,
    168,
    187,
    197
   ],
   [
    0,
    101
   ],
   [
    1,
    102
   ],
   [
    2,
    103
   ],
   [
    3,
    104
   ],
   [
    4,
    105
   ],
   [
    5,
    106
   ],
   [
    6,
    107
   ],
   [
    92,
    189
   ],
   [
    93,
    190
   ],
   [
    94,
    191
   ],
   [
    95,
    192
   ],
   [
    96,
    193
   ],
   [
    97,
    194
   ],
   [
    98,
    195
   ],
   [
    83,
    180
   ],
   [
    84,
    181
   ],
   [
    85,
    182
   ],
   [
    86,
    183
   ],
   [
    87,
    184
   ],
   [
    88,
    185
   ],
   [
    89,
    186
   ],
   [
    9,
    100,
    101,
    110
   ],
   [
    10,
    101,
    102,
    111
   ],
   [
    11,
    102,
    103,
    112
   ],
   [
    12,
    103,
    104,
    113
   ],
   [
    13,
    104,
    105,
    114
   ],
   [
    14,
    105,
    106,
    115
   ],
   [
    15,
    106,
    107,
    116
   ],
   [
    9,
    18,
    109,
    119
   ],
   [
    10,
    19,
    110,
    120
   ],
   [
    11,
    20,
    111,
    121
   ],
   [
    12,
    21,
    112,
    122
   ],
   [
    13,
    22,
    113,
    123
   ],
   [
    14,
    23,
    114,
    124
   ],
   [
    15,
    24,
    115,
    125
   ],
   [
    76,
    173,
    189,
    192
   ],
   [
    77,
    174,
    190,
    193
   ],
   [
    78,
    175,
    191,
    194
   ],
   [
    79,
    176,
    192,
    195
   ],
   [
    80,
    177,
    193,
    196
   ],
   [
    74,
    90,
    171,
    190
   ],
   [
    75,
    91,
    172,
    191
   ],
   [
    76,
    92,
    173,
    192
   ],
   [
    77,
    93,
    174,
    193
   ],
   [
    78,
    94,
    175,
    194
   ],
   [
    79,
    95,
    176,
    195
   ],
   [
    80,
    96,
    177,
    196
   ]
  ],
  "Z": [
   [
    0,
    10,
    29,
    101,
    110,
    126
   ],
   [
    1,
    11,
    30,
    102,
    111,
    127
   ],
   [
    2,
    12,
    31,
    103,
    112,
    128
   ],
   [
    3,
    13,
    32,
    104,
    113,
    129
   ],
   [
    4,
    14,
    33,
    105,
    114,
    130
   ],
   [
    5,
    15,
    34,
    106,
    115,
    131
   ],
   [
    6,
    16,
    35,
    107,
    116,
    132
   ],
   [
    9,
    19,
    38,
    110,
    119,
    135
   ],
   [
    10,
    20,
    39,
    111,
    120,
    136
   ],
   [
    11,
    21,
    40,
    112,
    121,
    137
   ],
   [
    12,
    22,
    41,
    113,
    122,
    138
   ],
   [
    13,
    23,
    42,
    114,
    123,
    139
   ],
   [
    14,
    24,
    43,
    115,
    124,
    140
   ],
   [
    15,
    25,
    44,
    116,
    125,
    141
   ],
   [
    18,
    28,
    47,
    119,
    128,
    144
   ],
   [
    19,
    29,
    48,
    120,
    129,
    145
   ],
   [
    20,
    30,
    49,
    121,
    130,
    146
   ],
   [
    21,
    31,
    50,
    122,
    131,
    147
   ],
   [
    22,
    32,
    51,
    123,
    132,
    148
   ],
   [
    23,
    33,
    52,
    124,
    133,
    149
   ],
   [
    24,
    34,
    53,
    125,
    134,
    150
   ],
   [
    27,
    37,
    56,
    128,
    137,
    153
   ],
   [
    28,
    38,
    57,
    129,
    138,
    154
   ],
   [
    29,
    39,
    58,
    130,
    139,
    155
   ],
   [
    30,
    40,
    59,
    131,
    140,
    156
   ],
   [
    31,
    41,
    60,
    132,
    141,
    157
   ],
   [
    32,
    42,
    61,
    133,
    142,
    158
   ],
   [
    33,
    43,
    62,
    134,
    143,
    159
   ],
   [
    36,
    46,
    65,
    137,
    146,
    162
   ],
   [
    37,
    47,
    66,
    138,
    147,
    163
   ],
   [
    38,
    48,
    67,
    139,
    148,
    164
   ],
   [
    39,
    49,
    68,
    140,
    149,
    165
   ],
   [
    40,
    50,
    69,
    141,
    150,
    166
   ],
   [
    41,
    51,
    70,
    142,
    151,
    167
   ],
   [
    42,
    52,
    71,
    143,
    152,
    168
   ],
   [
    45,
    55,
    74,
    146,
    155,
    171
   ],
   [
    46,
    56,
    75,
    147,
    156,
    172
   ],
   [
    47,
    57,
    76,
    148,
    157,
    173
   ],
   [
    48,
    58,
    77,
    149,
    158,
    174
   ],
   [
    49,
    59,
    78,
    150,
    159,
    175
   ],
   [
    50,
    60,
    79,
    151,
    160,
    176
   ],
   [
    51,
    61,
    80,
    152,
    161,
    177
   ],
   [
    54,
    64,
    83,
    155,
    164,
    180
   ],
   [
    55,
    65,
    84,
    156,
    165,
    181
   ],
   [
    56,
    66,
    85,
    157,
    166,
    182
   ],
   [
    57,
    67,
    86,
    158,
    167,
    183
   ],
   [
    58,
    68,
    87,
    159,
    168,
    184
   ],
   [
    59,
    69,
    88,
    160,
    169,
    185
   ],
   [
    60,
    70,
    89,
    161,
    170,
    186
   ],
   [
    63,
    73,
    92,
    164,
    173,
    189
   ],
   [
    64,
    74,
    93,
    165,
    174,
    190
   ],
   [
    65,
    75,
    94,
    166,
    175,
    191
   ],
   [
    66,
    76,
    95,
    167,
    176,
    192
   ],
   [
    67,
    77,
    96,
    168,
    177,
    193
   ],
   [
    68,
    78,
    97,
    169,
    178,
    194
   ],
   [
    69,
    79,
    98,
    170,
    179,
    195
   ],
   [
    8,
    134
   ],
   [
    17,
    143
   ],
   [
    26,
    152
   ],
   [
    35,
    161
   ],
   [
    44,
    170
   ],
   [
    53,
    179
   ],
   [
    62,
    188
   ],
   [
    71,
    197
   ],
   [
    27,
    99,
    108
   ],
   [
    36,
    108,
    117
   ],
   [
    45,
    117,
    126
   ],
   [
    54,
    126,
    135
   ],
   [
    63,
    135,
    144
   ],
   [
    72,
    144,
    153
   ],
   [
    81,
    153,
    162
   ],
   [
    90,
    162,
    171
   ],
   [
    7,
    133,
    143
   ],
   [
    16,
    142,
    152
   ],
   [
    25,
    151,
    161
   ],
   [
    34,
    160,
    170
   ],
   [
    43,
    169,
    179
   ],
   [
    52,
    178,
    188
   ],
   [
    61,
    187,
    197
   ],
   [
    7,
    17,
    133
   ],
   [
    16,
    26,
    142
   ],
   [
    25,
    35,
    151
   ],
   [
    34,
    44,
    160
   ],
   [
    43,
    53,
    169
   ],
   [
    52,
    62,
    178
   ],
   [
    61,
    71,
    187
   ],
   [
    70,
    80,
    196
   ],
   [
    9,
    28,
    100,
    109
   ],
   [
    18,
    37,
    109,
    118
   ],
   [
    27,
    46,
    118,
    127
   ],
   [
    36,
    55,
    127,
    136
   ],
   [
    45,
    64,
    136,
    145
   ],
   [
    54,
    73,
    145,
    154
   ],
   [
    63,
    82,
    154,
    163
   ],
   [
    72,
    91,
    163,
    172
   ]
  ]
 },
 "distance": {
  "d": 7,
  "X": {
   "value": 7,
   "confidence": "exact",
   "witness": [
    23,
    33,
    87,
    114,
    159,
    175,
    191
   ]
  },
  "Z": {
   "value": 7,
   "confidence": "exact",
   "witness": [
    61,
    70,
    73,
    86,
    135,
    164,
    183
   ]
  }
 },
 "provenance": {
  "authors": [
   "@FarLab",
   "@vprusso"
  ],
  "origin": "submission",
  "construction": "f = 1 + x + x^-2 y^2, g = 1 + xy + x^-2 y^-1; annulus-type boundary engine, (11,9) lattice.",
  "model": "Claude Opus 4.8",
  "references": [
   "arXiv:2504.08887"
  ],
  "date": "2026-06-16",
  "notes": "Distance certified exact by cutoff MILP."
 },
 "family": "bivariate-bicycle",
 "locality": {
  "coordinates": [
   [
    0,
    0
   ],
   [
    0,
    1
   ],
   [
    0,
    2
   ],
   [
    0,
    3
   ],
   [
    0,
    4
   ],
   [
    0,
    5
   ],
   [
    0,
    6
   ],
   [
    0,
    7
   ],
   [
    0,
    8
   ],
   [
    1,
    0
   ],
   [
    1,
    1
   ],
   [
    1,
    2
   ],
   [
    1,
    3
   ],
   [
    1,
    4
   ],
   [
    1,
    5
   ],
   [
    1,
    6
   ],
   [
    1,
    7
   ],
   [
    1,
    8
   ],
   [
    2,
    0
   ],
   [
    2,
    1
   ],
   [
    2,
    2
   ],
   [
    2,
    3
   ],
   [
    2,
    4
   ],
   [
    2,
    5
   ],
   [
    2,
    6
   ],
   [
    2,
    7
   ],
   [
    2,
    8
   ],
   [
    3,
    0
   ],
   [
    3,
    1
   ],
   [
    3,
    2
   ],
   [
    3,
    3
   ],
   [
    3,
    4
   ],
   [
    3,
    5
   ],
   [
    3,
    6
   ],
   [
    3,
    7
   ],
   [
    3,
    8
   ],
   [
    4,
    0
   ],
   [
    4,
    1
   ],
   [
    4,
    2
   ],
   [
    4,
    3
   ],
   [
    4,
    4
   ],
   [
    4,
    5
   ],
   [
    4,
    6
   ],
   [
    4,
    7
   ],
   [
    4,
    8
   ],
   [
    5,
    0
   ],
   [
    5,
    1
   ],
   [
    5,
    2
   ],
   [
    5,
    3
   ],
   [
    5,
    4
   ],
   [
    5,
    5
   ],
   [
    5,
    6
   ],
   [
    5,
    7
   ],
   [
    5,
    8
   ],
   [
    6,
    0
   ],
   [
    6,
    1
   ],
   [
    6,
    2
   ],
   [
    6,
    3
   ],
   [
    6,
    4
   ],
   [
    6,
    5
   ],
   [
    6,
    6
   ],
   [
    6,
    7
   ],
   [
    6,
    8
   ],
   [
    7,
    0
   ],
   [
    7,
    1
   ],
   [
    7,
    2
   ],
   [
    7,
    3
   ],
   [
    7,
    4
   ],
   [
    7,
    5
   ],
   [
    7,
    6
   ],
   [
    7,
    7
   ],
   [
    7,
    8
   ],
   [
    8,
    0
   ],
   [
    8,
    1
   ],
   [
    8,
    2
   ],
   [
    8,
    3
   ],
   [
    8,
    4
   ],
   [
    8,
    5
   ],
   [
    8,
    6
   ],
   [
    8,
    7
   ],
   [
    8,
    8
   ],
   [
    9,
    0
   ],
   [
    9,
    1
   ],
   [
    9,
    2
   ],
   [
    9,
    3
   ],
   [
    9,
    4
   ],
   [
    9,
    5
   ],
   [
    9,
    6
   ],
   [
    9,
    7
   ],
   [
    9,
    8
   ],
   [
    10,
    0
   ],
   [
    10,
    1
   ],
   [
    10,
    2
   ],
   [
    10,
    3
   ],
   [
    10,
    4
   ],
   [
    10,
    5
   ],
   [
    10,
    6
   ],
   [
    10,
    7
   ],
   [
    10,
    8
   ],
   [
    0,
    0
   ],
   [
    0,
    1
   ],
   [
    0,
    2
   ],
   [
    0,
    3
   ],
   [
    0,
    4
   ],
   [
    0,
    5
   ],
   [
    0,
    6
   ],
   [
    0,
    7
   ],
   [
    0,
    8
   ],
   [
    1,
    0
   ],
   [
    1,
    1
   ],
   [
    1,
    2
   ],
   [
    1,
    3
   ],
   [
    1,
    4
   ],
   [
    1,
    5
   ],
   [
    1,
    6
   ],
   [
    1,
    7
   ],
   [
    1,
    8
   ],
   [
    2,
    0
   ],
   [
    2,
    1
   ],
   [
    2,
    2
   ],
   [
    2,
    3
   ],
   [
    2,
    4
   ],
   [
    2,
    5
   ],
   [
    2,
    6
   ],
   [
    2,
    7
   ],
   [
    2,
    8
   ],
   [
    3,
    0
   ],
   [
    3,
    1
   ],
   [
    3,
    2
   ],
   [
    3,
    3
   ],
   [
    3,
    4
   ],
   [
    3,
    5
   ],
   [
    3,
    6
   ],
   [
    3,
    7
   ],
   [
    3,
    8
   ],
   [
    4,
    0
   ],
   [
    4,
    1
   ],
   [
    4,
    2
   ],
   [
    4,
    3
   ],
   [
    4,
    4
   ],
   [
    4,
    5
   ],
   [
    4,
    6
   ],
   [
    4,
    7
   ],
   [
    4,
    8
   ],
   [
    5,
    0
   ],
   [
    5,
    1
   ],
   [
    5,
    2
   ],
   [
    5,
    3
   ],
   [
    5,
    4
   ],
   [
    5,
    5
   ],
   [
    5,
    6
   ],
   [
    5,
    7
   ],
   [
    5,
    8
   ],
   [
    6,
    0
   ],
   [
    6,
    1
   ],
   [
    6,
    2
   ],
   [
    6,
    3
   ],
   [
    6,
    4
   ],
   [
    6,
    5
   ],
   [
    6,
    6
   ],
   [
    6,
    7
   ],
   [
    6,
    8
   ],
   [
    7,
    0
   ],
   [
    7,
    1
   ],
   [
    7,
    2
   ],
   [
    7,
    3
   ],
   [
    7,
    4
   ],
   [
    7,
    5
   ],
   [
    7,
    6
   ],
   [
    7,
    7
   ],
   [
    7,
    8
   ],
   [
    8,
    0
   ],
   [
    8,
    1
   ],
   [
    8,
    2
   ],
   [
    8,
    3
   ],
   [
    8,
    4
   ],
   [
    8,
    5
   ],
   [
    8,
    6
   ],
   [
    8,
    7
   ],
   [
    8,
    8
   ],
   [
    9,
    0
   ],
   [
    9,
    1
   ],
   [
    9,
    2
   ],
   [
    9,
    3
   ],
   [
    9,
    4
   ],
   [
    9,
    5
   ],
   [
    9,
    6
   ],
   [
    9,
    7
   ],
   [
    9,
    8
   ],
   [
    10,
    0
   ],
   [
    10,
    1
   ],
   [
    10,
    2
   ],
   [
    10,
    3
   ],
   [
    10,
    4
   ],
   [
    10,
    5
   ],
   [
    10,
    6
   ],
   [
    10,
    7
   ],
   [
    10,
    8
   ]
  ],
  "layers": 2,
  "interaction_radius": 4.47213595499958
 }
}