{
 "schema_version": "0.2",
 "name": "[[373,8,15]] reduced single-layer planar bivariate-bicycle code (L=14)",
 "code_type": "CSS",
 "n": 373,
 "k": 8,
 "checks": {
  "X": [
   [
    0,
    187,
    188
   ],
   [
    1,
    188,
    189
   ],
   [
    2,
    189,
    190
   ],
   [
    3,
    190,
    191
   ],
   [
    4,
    191,
    192
   ],
   [
    5,
    192,
    193
   ],
   [
    6,
    193,
    194
   ],
   [
    7,
    194,
    195
   ],
   [
    8,
    195,
    196
   ],
   [
    9,
    196,
    197
   ],
   [
    10,
    197,
    198
   ],
   [
    0,
    12,
    200,
    201
   ],
   [
    1,
    13,
    201,
    202
   ],
   [
    2,
    14,
    202,
    203
   ],
   [
    3,
    15,
    203,
    204
   ],
   [
    4,
    16,
    204,
    205
   ],
   [
    5,
    17,
    205,
    206
   ],
   [
    6,
    18,
    206,
    207
   ],
   [
    7,
    19,
    207,
    208
   ],
   [
    8,
    20,
    208,
    209
   ],
   [
    9,
    21,
    209,
    210
   ],
   [
    10,
    22,
    210,
    211
   ],
   [
    11,
    23,
    211,
    212
   ],
   [
    2,
    12,
    25,
    186,
    214,
    215
   ],
   [
    3,
    13,
    26,
    187,
    215,
    216
   ],
   [
    4,
    14,
    27,
    188,
    216,
    217
   ],
   [
    5,
    15,
    28,
    189,
    217,
    218
   ],
   [
    6,
    16,
    29,
    190,
    218,
    219
   ],
   [
    7,
    17,
    30,
    191,
    219,
    220
   ],
   [
    8,
    18,
    31,
    192,
    220,
    221
   ],
   [
    9,
    19,
    32,
    193,
    221,
    222
   ],
   [
    10,
    20,
    33,
    194,
    222,
    223
   ],
   [
    11,
    21,
    34,
    195,
    223,
    224
   ],
   [
    22,
    35,
    196,
    224,
    225
   ],
   [
    14,
    25,
    39,
    199,
    227,
    228
   ],
   [
    15,
    26,
    40,
    200,
    228,
    229
   ],
   [
    16,
    27,
    41,
    201,
    229,
    230
   ],
   [
    17,
    28,
    42,
    202,
    230,
    231
   ],
   [
    18,
    29,
    43,
    203,
    231,
    232
   ],
   [
    19,
    30,
    44,
    204,
    232,
    233
   ],
   [
    20,
    31,
    45,
    205,
    233,
    234
   ],
   [
    21,
    32,
    46,
    206,
    234,
    235
   ],
   [
    22,
    33,
    47,
    207,
    235,
    236
   ],
   [
    23,
    34,
    48,
    208,
    236,
    237
   ],
   [
    24,
    35,
    49,
    209,
    237,
    238
   ],
   [
    36,
    50,
    210,
    238,
    239
   ],
   [
    27,
    39,
    53,
    213,
    241,
    242
   ],
   [
    28,
    40,
    54,
    214,
    242,
    243
   ],
   [
    29,
    41,
    55,
    215,
    243,
    244
   ],
   [
    30,
    42,
    56,
    216,
    244,
    245
   ],
   [
    31,
    43,
    57,
    217,
    245,
    246
   ],
   [
    32,
    44,
    58,
    218,
    246,
    247
   ],
   [
    33,
    45,
    59,
    219,
    247,
    248
   ],
   [
    34,
    46,
    60,
    220,
    248,
    249
   ],
   [
    35,
    47,
    61,
    221,
    249,
    250
   ],
   [
    36,
    48,
    62,
    222,
    250,
    251
   ],
   [
    37,
    49,
    63,
    223,
    251,
    252
   ],
   [
    38,
    50,
    64,
    224,
    252,
    253
   ],
   [
    41,
    53,
    67,
    226,
    255,
    256
   ],
   [
    42,
    54,
    68,
    227,
    256,
    257
   ],
   [
    43,
    55,
    69,
    228,
    257,
    258
   ],
   [
    44,
    56,
    70,
    229,
    258,
    259
   ],
   [
    45,
    57,
    71,
    230,
    259,
    260
   ],
   [
    46,
    58,
    72,
    231,
    260,
    261
   ],
   [
    47,
    59,
    73,
    232,
    261,
    262
   ],
   [
    48,
    60,
    74,
    233,
    262,
    263
   ],
   [
    49,
    61,
    75,
    234,
    263,
    264
   ],
   [
    50,
    62,
    76,
    235,
    264,
    265
   ],
   [
    51,
    63,
    77,
    236,
    265,
    266
   ],
   [
    52,
    64,
    78,
    237,
    266,
    267
   ],
   [
    55,
    67,
    81,
    240,
    269,
    270
   ],
   [
    56,
    68,
    82,
    241,
    270,
    271
   ],
   [
    57,
    69,
    83,
    242,
    271,
    272
   ],
   [
    58,
    70,
    84,
    243,
    272,
    273
   ],
   [
    59,
    71,
    85,
    244,
    273,
    274
   ],
   [
    60,
    72,
    86,
    245,
    274,
    275
   ],
   [
    61,
    73,
    87,
    246,
    275,
    276
   ],
   [
    62,
    74,
    88,
    247,
    276,
    277
   ],
   [
    63,
    75,
    89,
    248,
    277,
    278
   ],
   [
    64,
    76,
    90,
    249,
    278,
    279
   ],
   [
    65,
    77,
    91,
    250,
    279,
    280
   ],
   [
    66,
    78,
    92,
    251,
    280,
    281
   ],
   [
    69,
    81,
    95,
    254,
    283,
    284
   ],
   [
    70,
    82,
    96,
    255,
    284,
    285
   ],
   [
    71,
    83,
    97,
    256,
    285,
    286
   ],
   [
    72,
    84,
    98,
    257,
    286,
    287
   ],
   [
    73,
    85,
    99,
    258,
    287,
    288
   ],
   [
    74,
    86,
    100,
    259,
    288,
    289
   ],
   [
    75,
    87,
    101,
    260,
    289,
    290
   ],
   [
    76,
    88,
    102,
    261,
    290,
    291
   ],
   [
    77,
    89,
    103,
    262,
    291,
    292
   ],
   [
    78,
    90,
    104,
    263,
    292,
    293
   ],
   [
    79,
    91,
    105,
    264,
    293,
    294
   ],
   [
    80,
    92,
    106,
    265,
    294,
    295
   ],
   [
    83,
    95,
    109,
    268,
    297,
    298
   ],
   [
    84,
    96,
    110,
    269,
    298,
    299
   ],
   [
    85,
    97,
    111,
    270,
    299,
    300
   ],
   [
    86,
    98,
    112,
    271,
    300,
    301
   ],
   [
    87,
    99,
    113,
    272,
    301,
    302
   ],
   [
    88,
    100,
    114,
    273,
    302,
    303
   ],
   [
    89,
    101,
    115,
    274,
    303,
    304
   ],
   [
    90,
    102,
    116,
    275,
    304,
    305
   ],
   [
    91,
    103,
    117,
    276,
    305,
    306
   ],
   [
    92,
    104,
    118,
    277,
    306,
    307
   ],
   [
    93,
    105,
    119,
    278,
    307,
    308
   ],
   [
    94,
    106,
    120,
    279,
    308,
    309
   ],
   [
    97,
    109,
    123,
    282,
    311,
    312
   ],
   [
    98,
    110,
    124,
    283,
    312,
    313
   ],
   [
    99,
    111,
    125,
    284,
    313,
    314
   ],
   [
    100,
    112,
    126,
    285,
    314,
    315
   ],
   [
    101,
    113,
    127,
    286,
    315,
    316
   ],
   [
    102,
    114,
    128,
    287,
    316,
    317
   ],
   [
    103,
    115,
    129,
    288,
    317,
    318
   ],
   [
    104,
    116,
    130,
    289,
    318,
    319
   ],
   [
    105,
    117,
    131,
    290,
    319,
    320
   ],
   [
    106,
    118,
    132,
    291,
    320,
    321
   ],
   [
    107,
    119,
    133,
    292,
    321,
    322
   ],
   [
    108,
    120,
    134,
    293,
    322,
    323
   ],
   [
    111,
    123,
    137,
    296,
    325,
    326
   ],
   [
    112,
    124,
    138,
    297,
    326,
    327
   ],
   [
    113,
    125,
    139,
    298,
    327,
    328
   ],
   [
    114,
    126,
    140,
    299,
    328,
    329
   ],
   [
    115,
    127,
    141,
    300,
    329,
    330
   ],
   [
    116,
    128,
    142,
    301,
    330,
    331
   ],
   [
    117,
    129,
    143,
    302,
    331,
    332
   ],
   [
    118,
    130,
    144,
    303,
    332,
    333
   ],
   [
    119,
    131,
    145,
    304,
    333,
    334
   ],
   [
    120,
    132,
    146,
    305,
    334,
    335
   ],
   [
    121,
    133,
    147,
    306,
    335,
    336
   ],
   [
    122,
    134,
    148,
    307,
    336,
    337
   ],
   [
    125,
    137,
    150,
    310,
    339,
    340
   ],
   [
    126,
    138,
    151,
    311,
    340,
    341
   ],
   [
    127,
    139,
    152,
    312,
    341,
    342
   ],
   [
    128,
    140,
    153,
    313,
    342,
    343
   ],
   [
    129,
    141,
    154,
    314,
    343,
    344
   ],
   [
    130,
    142,
    155,
    315,
    344,
    345
   ],
   [
    131,
    143,
    156,
    316,
    345,
    346
   ],
   [
    132,
    144,
    157,
    317,
    346,
    347
   ],
   [
    133,
    145,
    158,
    318,
    347,
    348
   ],
   [
    134,
    146,
    159,
    319,
    348,
    349
   ],
   [
    135,
    147,
    160,
    320,
    349,
    350
   ],
   [
    136,
    148,
    161,
    321,
    350,
    351
   ],
   [
    139,
    150,
    164,
    324,
    352,
    353
   ],
   [
    140,
    151,
    165,
    325,
    353,
    354
   ],
   [
    141,
    152,
    166,
    326,
    354,
    355
   ],
   [
    142,
    153,
    167,
    327,
    355,
    356
   ],
   [
    143,
    154,
    168,
    328,
    356,
    357
   ],
   [
    144,
    155,
    169,
    329,
    357,
    358
   ],
   [
    145,
    156,
    170,
    330,
    358,
    359
   ],
   [
    146,
    157,
    171,
    331,
    359,
    360
   ],
   [
    147,
    158,
    172,
    332,
    360,
    361
   ],
   [
    148,
    159,
    173,
    333,
    361,
    362
   ],
   [
    149,
    160,
    174,
    334,
    362,
    363
   ],
   [
    152,
    164,
    177,
    338
   ],
   [
    153,
    165,
    178,
    339,
    364
   ],
   [
    154,
    166,
    340,
    364,
    365
   ],
   [
    155,
    167,
    341,
    365,
    366
   ],
   [
    156,
    168,
    342,
    366,
    367
   ],
   [
    157,
    169,
    179,
    343,
    367,
    368
   ],
   [
    158,
    170,
    180,
    344,
    368,
    369
   ],
   [
    159,
    171,
    181,
    345,
    369,
    370
   ],
   [
    160,
    172,
    182,
    346,
    370,
    371
   ],
   [
    161,
    173,
    183,
    347,
    371
   ],
   [
    162,
    174,
    184,
    348,
    372
   ],
   [
    163,
    175,
    185,
    349,
    372
   ],
   [
    167,
    178,
    352
   ],
   [
    168,
    353
   ],
   [
    169,
    354
   ],
   [
    170,
    355
   ],
   [
    171,
    179,
    356
   ],
   [
    172,
    180,
    357
   ],
   [
    173,
    181,
    358
   ],
   [
    174,
    182,
    359
   ],
   [
    175,
    183,
    360
   ],
   [
    176,
    184,
    361
   ],
   [
    179,
    364
   ],
   [
    180,
    365
   ],
   [
    181,
    366
   ],
   [
    182,
    367
   ],
   [
    183,
    368
   ],
   [
    184,
    369
   ],
   [
    185,
    370
   ]
  ],
  "Z": [
   [
    25,
    186,
    199
   ],
   [
    0,
    26,
    187,
    200
   ],
   [
    0,
    1,
    27,
    188,
    201,
    213
   ],
   [
    1,
    2,
    28,
    189,
    202,
    214
   ],
   [
    2,
    3,
    29,
    190,
    203,
    215
   ],
   [
    3,
    4,
    30,
    191,
    204,
    216
   ],
   [
    4,
    5,
    31,
    192,
    205,
    217
   ],
   [
    5,
    6,
    32,
    193,
    206,
    218
   ],
   [
    6,
    7,
    33,
    194,
    207,
    219
   ],
   [
    7,
    8,
    34,
    195,
    208,
    220
   ],
   [
    8,
    9,
    35,
    196,
    209,
    221
   ],
   [
    9,
    10,
    36,
    197,
    210,
    222
   ],
   [
    10,
    11,
    37,
    198,
    211,
    223
   ],
   [
    11,
    38,
    212,
    224,
    225
   ],
   [
    39,
    199,
    213
   ],
   [
    12,
    40,
    200,
    214
   ],
   [
    12,
    13,
    41,
    201,
    215,
    226
   ],
   [
    13,
    14,
    42,
    202,
    216,
    227
   ],
   [
    14,
    15,
    43,
    203,
    217,
    228
   ],
   [
    15,
    16,
    44,
    204,
    218,
    229
   ],
   [
    16,
    17,
    45,
    205,
    219,
    230
   ],
   [
    17,
    18,
    46,
    206,
    220,
    231
   ],
   [
    18,
    19,
    47,
    207,
    221,
    232
   ],
   [
    19,
    20,
    48,
    208,
    222,
    233
   ],
   [
    20,
    21,
    49,
    209,
    223,
    234
   ],
   [
    21,
    22,
    50,
    210,
    224,
    235
   ],
   [
    22,
    23,
    51,
    211,
    225,
    236
   ],
   [
    23,
    24,
    52,
    212,
    237
   ],
   [
    24,
    238,
    239
   ],
   [
    53,
    213,
    226
   ],
   [
    25,
    54,
    214,
    227
   ],
   [
    25,
    26,
    55,
    215,
    228,
    240
   ],
   [
    26,
    27,
    56,
    216,
    229,
    241
   ],
   [
    27,
    28,
    57,
    217,
    230,
    242
   ],
   [
    28,
    29,
    58,
    218,
    231,
    243
   ],
   [
    29,
    30,
    59,
    219,
    232,
    244
   ],
   [
    30,
    31,
    60,
    220,
    233,
    245
   ],
   [
    31,
    32,
    61,
    221,
    234,
    246
   ],
   [
    32,
    33,
    62,
    222,
    235,
    247
   ],
   [
    33,
    34,
    63,
    223,
    236,
    248
   ],
   [
    34,
    35,
    64,
    224,
    237,
    249
   ],
   [
    35,
    36,
    65,
    225,
    238,
    250
   ],
   [
    36,
    37,
    66,
    239,
    251
   ],
   [
    37,
    38,
    252
   ],
   [
    38,
    253
   ],
   [
    67,
    226,
    240
   ],
   [
    39,
    68,
    227,
    241
   ],
   [
    39,
    40,
    69,
    228,
    242,
    254
   ],
   [
    40,
    41,
    70,
    229,
    243,
    255
   ],
   [
    41,
    42,
    71,
    230,
    244,
    256
   ],
   [
    42,
    43,
    72,
    231,
    245,
    257
   ],
   [
    43,
    44,
    73,
    232,
    246,
    258
   ],
   [
    44,
    45,
    74,
    233,
    247,
    259
   ],
   [
    45,
    46,
    75,
    234,
    248,
    260
   ],
   [
    46,
    47,
    76,
    235,
    249,
    261
   ],
   [
    47,
    48,
    77,
    236,
    250,
    262
   ],
   [
    48,
    49,
    78,
    237,
    251,
    263
   ],
   [
    49,
    50,
    79,
    238,
    252,
    264
   ],
   [
    50,
    51,
    80,
    239,
    253,
    265
   ],
   [
    51,
    52,
    266
   ],
   [
    52,
    267
   ],
   [
    81,
    240,
    254
   ],
   [
    53,
    82,
    241,
    255
   ],
   [
    53,
    54,
    83,
    242,
    256,
    268
   ],
   [
    54,
    55,
    84,
    243,
    257,
    269
   ],
   [
    55,
    56,
    85,
    244,
    258,
    270
   ],
   [
    56,
    57,
    86,
    245,
    259,
    271
   ],
   [
    57,
    58,
    87,
    246,
    260,
    272
   ],
   [
    58,
    59,
    88,
    247,
    261,
    273
   ],
   [
    59,
    60,
    89,
    248,
    262,
    274
   ],
   [
    60,
    61,
    90,
    249,
    263,
    275
   ],
   [
    61,
    62,
    91,
    250,
    264,
    276
   ],
   [
    62,
    63,
    92,
    251,
    265,
    277
   ],
   [
    63,
    64,
    93,
    252,
    266,
    278
   ],
   [
    64,
    65,
    94,
    253,
    267,
    279
   ],
   [
    65,
    66,
    280
   ],
   [
    66,
    281
   ],
   [
    95,
    254,
    268
   ],
   [
    67,
    96,
    255,
    269
   ],
   [
    67,
    68,
    97,
    256,
    270,
    282
   ],
   [
    68,
    69,
    98,
    257,
    271,
    283
   ],
   [
    69,
    70,
    99,
    258,
    272,
    284
   ],
   [
    70,
    71,
    100,
    259,
    273,
    285
   ],
   [
    71,
    72,
    101,
    260,
    274,
    286
   ],
   [
    72,
    73,
    102,
    261,
    275,
    287
   ],
   [
    73,
    74,
    103,
    262,
    276,
    288
   ],
   [
    74,
    75,
    104,
    263,
    277,
    289
   ],
   [
    75,
    76,
    105,
    264,
    278,
    290
   ],
   [
    76,
    77,
    106,
    265,
    279,
    291
   ],
   [
    77,
    78,
    107,
    266,
    280,
    292
   ],
   [
    78,
    79,
    108,
    267,
    281,
    293
   ],
   [
    79,
    80,
    294
   ],
   [
    80,
    295
   ],
   [
    109,
    268,
    282
   ],
   [
    81,
    110,
    269,
    283
   ],
   [
    81,
    82,
    111,
    270,
    284,
    296
   ],
   [
    82,
    83,
    112,
    271,
    285,
    297
   ],
   [
    83,
    84,
    113,
    272,
    286,
    298
   ],
   [
    84,
    85,
    114,
    273,
    287,
    299
   ],
   [
    85,
    86,
    115,
    274,
    288,
    300
   ],
   [
    86,
    87,
    116,
    275,
    289,
    301
   ],
   [
    87,
    88,
    117,
    276,
    290,
    302
   ],
   [
    88,
    89,
    118,
    277,
    291,
    303
   ],
   [
    89,
    90,
    119,
    278,
    292,
    304
   ],
   [
    90,
    91,
    120,
    279,
    293,
    305
   ],
   [
    91,
    92,
    121,
    280,
    294,
    306
   ],
   [
    92,
    93,
    122,
    281,
    295,
    307
   ],
   [
    93,
    94,
    308
   ],
   [
    94,
    309
   ],
   [
    123,
    282,
    296
   ],
   [
    95,
    124,
    283,
    297
   ],
   [
    95,
    96,
    125,
    284,
    298,
    310
   ],
   [
    96,
    97,
    126,
    285,
    299,
    311
   ],
   [
    97,
    98,
    127,
    286,
    300,
    312
   ],
   [
    98,
    99,
    128,
    287,
    301,
    313
   ],
   [
    99,
    100,
    129,
    288,
    302,
    314
   ],
   [
    100,
    101,
    130,
    289,
    303,
    315
   ],
   [
    101,
    102,
    131,
    290,
    304,
    316
   ],
   [
    102,
    103,
    132,
    291,
    305,
    317
   ],
   [
    103,
    104,
    133,
    292,
    306,
    318
   ],
   [
    104,
    105,
    134,
    293,
    307,
    319
   ],
   [
    105,
    106,
    135,
    294,
    308,
    320
   ],
   [
    106,
    107,
    136,
    295,
    309,
    321
   ],
   [
    107,
    108,
    322
   ],
   [
    108,
    323
   ],
   [
    137,
    296,
    310
   ],
   [
    109,
    138,
    297,
    311
   ],
   [
    109,
    110,
    139,
    298,
    312,
    324
   ],
   [
    110,
    111,
    140,
    299,
    313,
    325
   ],
   [
    111,
    112,
    141,
    300,
    314,
    326
   ],
   [
    112,
    113,
    142,
    301,
    315,
    327
   ],
   [
    113,
    114,
    143,
    302,
    316,
    328
   ],
   [
    114,
    115,
    144,
    303,
    317,
    329
   ],
   [
    115,
    116,
    145,
    304,
    318,
    330
   ],
   [
    116,
    117,
    146,
    305,
    319,
    331
   ],
   [
    117,
    118,
    147,
    306,
    320,
    332
   ],
   [
    118,
    119,
    148,
    307,
    321,
    333
   ],
   [
    119,
    120,
    149,
    308,
    322,
    334
   ],
   [
    120,
    121,
    309,
    323,
    335
   ],
   [
    121,
    122,
    336
   ],
   [
    122,
    337
   ],
   [
    150,
    310,
    324
   ],
   [
    123,
    151,
    311,
    325
   ],
   [
    123,
    124,
    152,
    312,
    326,
    338
   ],
   [
    124,
    125,
    153,
    313,
    327,
    339
   ],
   [
    125,
    126,
    154,
    314,
    328,
    340
   ],
   [
    126,
    127,
    155,
    315,
    329,
    341
   ],
   [
    127,
    128,
    156,
    316,
    330,
    342
   ],
   [
    128,
    129,
    157,
    317,
    331,
    343
   ],
   [
    129,
    130,
    158,
    318,
    332,
    344
   ],
   [
    130,
    131,
    159,
    319,
    333,
    345
   ],
   [
    131,
    132,
    160,
    320,
    334,
    346
   ],
   [
    132,
    133,
    161,
    321,
    335,
    347
   ],
   [
    133,
    134,
    162,
    322,
    336,
    348
   ],
   [
    134,
    135,
    163,
    323,
    337,
    349
   ],
   [
    135,
    136,
    350
   ],
   [
    136,
    351
   ],
   [
    164,
    324,
    338
   ],
   [
    137,
    165,
    325,
    339
   ],
   [
    137,
    138,
    166,
    326,
    340
   ],
   [
    138,
    139,
    167,
    327,
    341,
    352
   ],
   [
    139,
    140,
    168,
    328,
    342,
    353
   ],
   [
    140,
    141,
    169,
    329,
    343,
    354
   ],
   [
    141,
    142,
    170,
    330,
    344,
    355
   ],
   [
    142,
    143,
    171,
    331,
    345,
    356
   ],
   [
    143,
    144,
    172,
    332,
    346,
    357
   ],
   [
    144,
    145,
    173,
    333,
    347,
    358
   ],
   [
    145,
    146,
    174,
    334,
    348,
    359
   ],
   [
    146,
    147,
    175,
    335,
    349,
    360
   ],
   [
    147,
    148,
    176,
    336,
    350,
    361
   ],
   [
    148,
    149,
    337,
    351,
    362
   ],
   [
    149,
    363
   ],
   [
    177,
    338
   ],
   [
    150,
    178,
    339,
    352
   ],
   [
    153,
    154,
    179,
    343,
    356,
    364
   ],
   [
    154,
    155,
    180,
    344,
    357,
    365
   ],
   [
    155,
    156,
    181,
    345,
    358,
    366
   ],
   [
    156,
    157,
    182,
    346,
    359,
    367
   ],
   [
    157,
    158,
    183,
    347,
    360,
    368
   ],
   [
    158,
    159,
    184,
    348,
    361,
    369
   ],
   [
    159,
    160,
    185,
    349,
    362,
    370
   ],
   [
    160,
    161,
    350,
    363,
    371
   ],
   [
    162,
    163,
    372
   ]
  ]
 },
 "distance": {
  "d": 15,
  "X": {
   "value": 15,
   "confidence": "upper_bound",
   "witness": [
    25,
    54,
    55,
    95,
    124,
    125,
    137,
    152,
    165,
    186,
    268,
    270,
    282,
    296,
    340
   ],
   "witness_provenance": {
    "found_by": [
     "@dorakingx"
    ],
    "date": "2026-09-09",
    "found_at_samples": 20000,
    "survived_samples": 5000000,
    "tool": "gf2_fast RIS ladder (verify/gf2_fast.cpp), both sides searched jointly",
    "seeds": [
     92001,
     92138,
     92275,
     92412
    ]
   }
  },
  "Z": {
   "value": 15,
   "confidence": "upper_bound",
   "witness": [
    110,
    112,
    124,
    130,
    144,
    299,
    300,
    315,
    316,
    317,
    318,
    329,
    346,
    347,
    371
   ],
   "witness_provenance": {
    "found_by": [
     "@dorakingx"
    ],
    "date": "2026-09-09",
    "found_at_samples": 4000,
    "survived_samples": 5000000,
    "tool": "gf2_fast RIS in the packaging search; the ladder searched both sides jointly",
    "seeds": [
     7,
     92001,
     92138,
     92275,
     92412
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "@dorakingx"
  ],
  "construction": "Open-boundary planar bivariate-bicycle code (Liang, Eberhardt, Chen, arXiv:2504.08887, Sec. II and Table V) with f = x + x^2 + y^2 and g = 1 + x^2 y + x^2 y^2 on a 14 x 14 grid (research/local2d/planar.py build_open_directional(14, 14), n = 2*14^2 = 392, k = 8), then reduced to n = 373 by 19 qubit removals of three kinds. (14) Restricted r=1 lattice grafting (Sec. III E): a qubit lying in exactly one stabilizer of some type is removed together with that stabilizer; accepted only if k stayed 8 and a bit-packed RIS search found nothing lighter than 15, screened at 20000 trials with a FIXED seed and then confirmed at a deeper rung, a qubit failing the confirm rung being blacklisted. Those in-loop rungs are a filter, not the evidence -- on other members of this family they let a unit of distance through -- so the claim below rests on the separate fresh-seed ladder. Its upper bound for this code equals the unreduced L = 14 code's own ladder bound, which is consistent with the reduction having lost nothing at this size but does not prove it: both are upper bounds and no lower bound exists for either. (3) Weight-1 stabilizer cleanup, which runs no distance search at all because it needs none (Sec. III D step 4, research/local2d/boundary_engine.py _cleanup): a qubit carrying a weight-1 stabilizer cannot appear in any opposite-type check, so multiplying that row into the same-type rows containing it and deleting the qubit preserves k and the distance exactly; the elimination cascades until no weight-1 or zero-degree qubit is left. (2) Capped merge-graft, a new step, searched at r <= 3: when a qubit lies in exactly r stabilizers of one type, pick a pivot row R_p and replace every other R_i by R_p + R_i. Those are row operations on the stabilizer generators and so change no code, only the generating set, and they leave that qubit in R_p alone, where the r=1 graft above applies; every choice of pivot is tried, since each gives a different resulting code. Each merged row is taken only if it still has weight at most 6 and its support still has maximum pairwise distance at most 4 in the layout below -- exactly the quantity the verifier measures as the interaction radius -- so the weight class and the 2D-local single-layer class are preserved by construction; the resulting graft is then accepted under the same k check and the same screen and confirm rungs, and the whole layout radius is recomputed after every accepted move. The first two moves cannot enlarge a check support -- grafting deletes, and the cleanup XOR removes exactly the one fixed qubit from a row -- while the third genuinely can: the merged row may be heavier and wider than either of the two it replaces. The caps bound that growth rather than forbidding it, and the whole layout is re-measured after every accepted move, which is why the code below still has max check weight 6 and radius exactly 4. SINGLE-LAYER integer layout: a surviving qubit whose index in the unreduced code is q = c*196 + i*14 + j (block c in {0,1}, site (i,j)) sits at (i + j, j - i + c), the unit square lattice rotated 45 degrees with the two blocks on its two sublattices; one qubit per site, minimum spacing exactly 1, maximum check diameter exactly 4. The reduction is a randomised search, so the surviving qubit set is recorded by the coordinates in this file rather than re-derived.",
  "references": [
   "arXiv:2504.08887",
   "arXiv:2308.07915"
  ],
  "date": "2026-09-09",
  "notes": "Checked, not equivalent to any board entry: the gate reports no exact duplicate and no WL-equivalent entry. No board entry has n = 373. It dominates [[392,8,15]] on (n, k, d, w), which therefore leaves the frontier of every cell the two share. Board entries at the unreduced size n = 392 with k = 8: [[392,8,15]]. The construction and both published reduction moves are from arXiv:2504.08887 (Sec. II, Sec. III D step 4 and Sec. III E; this repository's own research/local2d modules cite Table V of that paper for the family's ungrafted distances and Tables II-IV for its qubit-removal layouts such as [[188,8,9]], which come out of the cleanup rather than the graft), but this parameter set, the capped r=2 merge-graft step and this single-layer layout are not, so novelty is left unknown and literature novelty is unverified.",
  "model": "Claude Opus 5 (Claude Code)",
  "origin": "submission",
  "novelty": "unknown"
 },
 "family": "bivariate-bicycle",
 "locality": {
  "coordinates": [
   [
    0.0,
    0.0
   ],
   [
    1.0,
    1.0
   ],
   [
    2.0,
    2.0
   ],
   [
    3.0,
    3.0
   ],
   [
    4.0,
    4.0
   ],
   [
    5.0,
    5.0
   ],
   [
    6.0,
    6.0
   ],
   [
    7.0,
    7.0
   ],
   [
    8.0,
    8.0
   ],
   [
    9.0,
    9.0
   ],
   [
    10.0,
    10.0
   ],
   [
    11.0,
    11.0
   ],
   [
    1.0,
    -1.0
   ],
   [
    2.0,
    0.0
   ],
   [
    3.0,
    1.0
   ],
   [
    4.0,
    2.0
   ],
   [
    5.0,
    3.0
   ],
   [
    6.0,
    4.0
   ],
   [
    7.0,
    5.0
   ],
   [
    8.0,
    6.0
   ],
   [
    9.0,
    7.0
   ],
   [
    10.0,
    8.0
   ],
   [
    11.0,
    9.0
   ],
   [
    12.0,
    10.0
   ],
   [
    13.0,
    11.0
   ],
   [
    2.0,
    -2.0
   ],
   [
    3.0,
    -1.0
   ],
   [
    4.0,
    0.0
   ],
   [
    5.0,
    1.0
   ],
   [
    6.0,
    2.0
   ],
   [
    7.0,
    3.0
   ],
   [
    8.0,
    4.0
   ],
   [
    9.0,
    5.0
   ],
   [
    10.0,
    6.0
   ],
   [
    11.0,
    7.0
   ],
   [
    12.0,
    8.0
   ],
   [
    13.0,
    9.0
   ],
   [
    14.0,
    10.0
   ],
   [
    15.0,
    11.0
   ],
   [
    3.0,
    -3.0
   ],
   [
    4.0,
    -2.0
   ],
   [
    5.0,
    -1.0
   ],
   [
    6.0,
    0.0
   ],
   [
    7.0,
    1.0
   ],
   [
    8.0,
    2.0
   ],
   [
    9.0,
    3.0
   ],
   [
    10.0,
    4.0
   ],
   [
    11.0,
    5.0
   ],
   [
    12.0,
    6.0
   ],
   [
    13.0,
    7.0
   ],
   [
    14.0,
    8.0
   ],
   [
    15.0,
    9.0
   ],
   [
    16.0,
    10.0
   ],
   [
    4.0,
    -4.0
   ],
   [
    5.0,
    -3.0
   ],
   [
    6.0,
    -2.0
   ],
   [
    7.0,
    -1.0
   ],
   [
    8.0,
    0.0
   ],
   [
    9.0,
    1.0
   ],
   [
    10.0,
    2.0
   ],
   [
    11.0,
    3.0
   ],
   [
    12.0,
    4.0
   ],
   [
    13.0,
    5.0
   ],
   [
    14.0,
    6.0
   ],
   [
    15.0,
    7.0
   ],
   [
    16.0,
    8.0
   ],
   [
    17.0,
    9.0
   ],
   [
    5.0,
    -5.0
   ],
   [
    6.0,
    -4.0
   ],
   [
    7.0,
    -3.0
   ],
   [
    8.0,
    -2.0
   ],
   [
    9.0,
    -1.0
   ],
   [
    10.0,
    0.0
   ],
   [
    11.0,
    1.0
   ],
   [
    12.0,
    2.0
   ],
   [
    13.0,
    3.0
   ],
   [
    14.0,
    4.0
   ],
   [
    15.0,
    5.0
   ],
   [
    16.0,
    6.0
   ],
   [
    17.0,
    7.0
   ],
   [
    18.0,
    8.0
   ],
   [
    6.0,
    -6.0
   ],
   [
    7.0,
    -5.0
   ],
   [
    8.0,
    -4.0
   ],
   [
    9.0,
    -3.0
   ],
   [
    10.0,
    -2.0
   ],
   [
    11.0,
    -1.0
   ],
   [
    12.0,
    0.0
   ],
   [
    13.0,
    1.0
   ],
   [
    14.0,
    2.0
   ],
   [
    15.0,
    3.0
   ],
   [
    16.0,
    4.0
   ],
   [
    17.0,
    5.0
   ],
   [
    18.0,
    6.0
   ],
   [
    19.0,
    7.0
   ],
   [
    7.0,
    -7.0
   ],
   [
    8.0,
    -6.0
   ],
   [
    9.0,
    -5.0
   ],
   [
    10.0,
    -4.0
   ],
   [
    11.0,
    -3.0
   ],
   [
    12.0,
    -2.0
   ],
   [
    13.0,
    -1.0
   ],
   [
    14.0,
    0.0
   ],
   [
    15.0,
    1.0
   ],
   [
    16.0,
    2.0
   ],
   [
    17.0,
    3.0
   ],
   [
    18.0,
    4.0
   ],
   [
    19.0,
    5.0
   ],
   [
    20.0,
    6.0
   ],
   [
    8.0,
    -8.0
   ],
   [
    9.0,
    -7.0
   ],
   [
    10.0,
    -6.0
   ],
   [
    11.0,
    -5.0
   ],
   [
    12.0,
    -4.0
   ],
   [
    13.0,
    -3.0
   ],
   [
    14.0,
    -2.0
   ],
   [
    15.0,
    -1.0
   ],
   [
    16.0,
    0.0
   ],
   [
    17.0,
    1.0
   ],
   [
    18.0,
    2.0
   ],
   [
    19.0,
    3.0
   ],
   [
    20.0,
    4.0
   ],
   [
    21.0,
    5.0
   ],
   [
    9.0,
    -9.0
   ],
   [
    10.0,
    -8.0
   ],
   [
    11.0,
    -7.0
   ],
   [
    12.0,
    -6.0
   ],
   [
    13.0,
    -5.0
   ],
   [
    14.0,
    -4.0
   ],
   [
    15.0,
    -3.0
   ],
   [
    16.0,
    -2.0
   ],
   [
    17.0,
    -1.0
   ],
   [
    18.0,
    0.0
   ],
   [
    19.0,
    1.0
   ],
   [
    20.0,
    2.0
   ],
   [
    21.0,
    3.0
   ],
   [
    22.0,
    4.0
   ],
   [
    10.0,
    -10.0
   ],
   [
    11.0,
    -9.0
   ],
   [
    12.0,
    -8.0
   ],
   [
    13.0,
    -7.0
   ],
   [
    14.0,
    -6.0
   ],
   [
    15.0,
    -5.0
   ],
   [
    16.0,
    -4.0
   ],
   [
    17.0,
    -3.0
   ],
   [
    18.0,
    -2.0
   ],
   [
    19.0,
    -1.0
   ],
   [
    20.0,
    0.0
   ],
   [
    21.0,
    1.0
   ],
   [
    22.0,
    2.0
   ],
   [
    11.0,
    -11.0
   ],
   [
    12.0,
    -10.0
   ],
   [
    13.0,
    -9.0
   ],
   [
    14.0,
    -8.0
   ],
   [
    15.0,
    -7.0
   ],
   [
    16.0,
    -6.0
   ],
   [
    17.0,
    -5.0
   ],
   [
    18.0,
    -4.0
   ],
   [
    19.0,
    -3.0
   ],
   [
    20.0,
    -2.0
   ],
   [
    21.0,
    -1.0
   ],
   [
    22.0,
    0.0
   ],
   [
    23.0,
    1.0
   ],
   [
    24.0,
    2.0
   ],
   [
    12.0,
    -12.0
   ],
   [
    13.0,
    -11.0
   ],
   [
    14.0,
    -10.0
   ],
   [
    15.0,
    -9.0
   ],
   [
    16.0,
    -8.0
   ],
   [
    17.0,
    -7.0
   ],
   [
    18.0,
    -6.0
   ],
   [
    19.0,
    -5.0
   ],
   [
    20.0,
    -4.0
   ],
   [
    21.0,
    -3.0
   ],
   [
    22.0,
    -2.0
   ],
   [
    23.0,
    -1.0
   ],
   [
    24.0,
    0.0
   ],
   [
    13.0,
    -13.0
   ],
   [
    14.0,
    -12.0
   ],
   [
    18.0,
    -8.0
   ],
   [
    19.0,
    -7.0
   ],
   [
    20.0,
    -6.0
   ],
   [
    21.0,
    -5.0
   ],
   [
    22.0,
    -4.0
   ],
   [
    23.0,
    -3.0
   ],
   [
    24.0,
    -2.0
   ],
   [
    0.0,
    1.0
   ],
   [
    1.0,
    2.0
   ],
   [
    2.0,
    3.0
   ],
   [
    3.0,
    4.0
   ],
   [
    4.0,
    5.0
   ],
   [
    5.0,
    6.0
   ],
   [
    6.0,
    7.0
   ],
   [
    7.0,
    8.0
   ],
   [
    8.0,
    9.0
   ],
   [
    9.0,
    10.0
   ],
   [
    10.0,
    11.0
   ],
   [
    11.0,
    12.0
   ],
   [
    12.0,
    13.0
   ],
   [
    1.0,
    0.0
   ],
   [
    2.0,
    1.0
   ],
   [
    3.0,
    2.0
   ],
   [
    4.0,
    3.0
   ],
   [
    5.0,
    4.0
   ],
   [
    6.0,
    5.0
   ],
   [
    7.0,
    6.0
   ],
   [
    8.0,
    7.0
   ],
   [
    9.0,
    8.0
   ],
   [
    10.0,
    9.0
   ],
   [
    11.0,
    10.0
   ],
   [
    12.0,
    11.0
   ],
   [
    13.0,
    12.0
   ],
   [
    14.0,
    13.0
   ],
   [
    2.0,
    -1.0
   ],
   [
    3.0,
    0.0
   ],
   [
    4.0,
    1.0
   ],
   [
    5.0,
    2.0
   ],
   [
    6.0,
    3.0
   ],
   [
    7.0,
    4.0
   ],
   [
    8.0,
    5.0
   ],
   [
    9.0,
    6.0
   ],
   [
    10.0,
    7.0
   ],
   [
    11.0,
    8.0
   ],
   [
    12.0,
    9.0
   ],
   [
    13.0,
    10.0
   ],
   [
    14.0,
    11.0
   ],
   [
    3.0,
    -2.0
   ],
   [
    4.0,
    -1.0
   ],
   [
    5.0,
    0.0
   ],
   [
    6.0,
    1.0
   ],
   [
    7.0,
    2.0
   ],
   [
    8.0,
    3.0
   ],
   [
    9.0,
    4.0
   ],
   [
    10.0,
    5.0
   ],
   [
    11.0,
    6.0
   ],
   [
    12.0,
    7.0
   ],
   [
    13.0,
    8.0
   ],
   [
    14.0,
    9.0
   ],
   [
    15.0,
    10.0
   ],
   [
    16.0,
    11.0
   ],
   [
    4.0,
    -3.0
   ],
   [
    5.0,
    -2.0
   ],
   [
    6.0,
    -1.0
   ],
   [
    7.0,
    0.0
   ],
   [
    8.0,
    1.0
   ],
   [
    9.0,
    2.0
   ],
   [
    10.0,
    3.0
   ],
   [
    11.0,
    4.0
   ],
   [
    12.0,
    5.0
   ],
   [
    13.0,
    6.0
   ],
   [
    14.0,
    7.0
   ],
   [
    15.0,
    8.0
   ],
   [
    16.0,
    9.0
   ],
   [
    17.0,
    10.0
   ],
   [
    5.0,
    -4.0
   ],
   [
    6.0,
    -3.0
   ],
   [
    7.0,
    -2.0
   ],
   [
    8.0,
    -1.0
   ],
   [
    9.0,
    0.0
   ],
   [
    10.0,
    1.0
   ],
   [
    11.0,
    2.0
   ],
   [
    12.0,
    3.0
   ],
   [
    13.0,
    4.0
   ],
   [
    14.0,
    5.0
   ],
   [
    15.0,
    6.0
   ],
   [
    16.0,
    7.0
   ],
   [
    17.0,
    8.0
   ],
   [
    18.0,
    9.0
   ],
   [
    6.0,
    -5.0
   ],
   [
    7.0,
    -4.0
   ],
   [
    8.0,
    -3.0
   ],
   [
    9.0,
    -2.0
   ],
   [
    10.0,
    -1.0
   ],
   [
    11.0,
    0.0
   ],
   [
    12.0,
    1.0
   ],
   [
    13.0,
    2.0
   ],
   [
    14.0,
    3.0
   ],
   [
    15.0,
    4.0
   ],
   [
    16.0,
    5.0
   ],
   [
    17.0,
    6.0
   ],
   [
    18.0,
    7.0
   ],
   [
    19.0,
    8.0
   ],
   [
    7.0,
    -6.0
   ],
   [
    8.0,
    -5.0
   ],
   [
    9.0,
    -4.0
   ],
   [
    10.0,
    -3.0
   ],
   [
    11.0,
    -2.0
   ],
   [
    12.0,
    -1.0
   ],
   [
    13.0,
    0.0
   ],
   [
    14.0,
    1.0
   ],
   [
    15.0,
    2.0
   ],
   [
    16.0,
    3.0
   ],
   [
    17.0,
    4.0
   ],
   [
    18.0,
    5.0
   ],
   [
    19.0,
    6.0
   ],
   [
    20.0,
    7.0
   ],
   [
    8.0,
    -7.0
   ],
   [
    9.0,
    -6.0
   ],
   [
    10.0,
    -5.0
   ],
   [
    11.0,
    -4.0
   ],
   [
    12.0,
    -3.0
   ],
   [
    13.0,
    -2.0
   ],
   [
    14.0,
    -1.0
   ],
   [
    15.0,
    0.0
   ],
   [
    16.0,
    1.0
   ],
   [
    17.0,
    2.0
   ],
   [
    18.0,
    3.0
   ],
   [
    19.0,
    4.0
   ],
   [
    20.0,
    5.0
   ],
   [
    21.0,
    6.0
   ],
   [
    9.0,
    -8.0
   ],
   [
    10.0,
    -7.0
   ],
   [
    11.0,
    -6.0
   ],
   [
    12.0,
    -5.0
   ],
   [
    13.0,
    -4.0
   ],
   [
    14.0,
    -3.0
   ],
   [
    15.0,
    -2.0
   ],
   [
    16.0,
    -1.0
   ],
   [
    17.0,
    0.0
   ],
   [
    18.0,
    1.0
   ],
   [
    19.0,
    2.0
   ],
   [
    20.0,
    3.0
   ],
   [
    21.0,
    4.0
   ],
   [
    22.0,
    5.0
   ],
   [
    10.0,
    -9.0
   ],
   [
    11.0,
    -8.0
   ],
   [
    12.0,
    -7.0
   ],
   [
    13.0,
    -6.0
   ],
   [
    14.0,
    -5.0
   ],
   [
    15.0,
    -4.0
   ],
   [
    16.0,
    -3.0
   ],
   [
    17.0,
    -2.0
   ],
   [
    18.0,
    -1.0
   ],
   [
    19.0,
    0.0
   ],
   [
    20.0,
    1.0
   ],
   [
    21.0,
    2.0
   ],
   [
    22.0,
    3.0
   ],
   [
    23.0,
    4.0
   ],
   [
    11.0,
    -10.0
   ],
   [
    12.0,
    -9.0
   ],
   [
    13.0,
    -8.0
   ],
   [
    14.0,
    -7.0
   ],
   [
    15.0,
    -6.0
   ],
   [
    16.0,
    -5.0
   ],
   [
    17.0,
    -4.0
   ],
   [
    18.0,
    -3.0
   ],
   [
    19.0,
    -2.0
   ],
   [
    20.0,
    -1.0
   ],
   [
    21.0,
    0.0
   ],
   [
    22.0,
    1.0
   ],
   [
    23.0,
    2.0
   ],
   [
    24.0,
    3.0
   ],
   [
    13.0,
    -10.0
   ],
   [
    14.0,
    -9.0
   ],
   [
    15.0,
    -8.0
   ],
   [
    16.0,
    -7.0
   ],
   [
    17.0,
    -6.0
   ],
   [
    18.0,
    -5.0
   ],
   [
    19.0,
    -4.0
   ],
   [
    20.0,
    -3.0
   ],
   [
    21.0,
    -2.0
   ],
   [
    22.0,
    -1.0
   ],
   [
    23.0,
    0.0
   ],
   [
    24.0,
    1.0
   ],
   [
    16.0,
    -9.0
   ],
   [
    17.0,
    -8.0
   ],
   [
    18.0,
    -7.0
   ],
   [
    19.0,
    -6.0
   ],
   [
    20.0,
    -5.0
   ],
   [
    21.0,
    -4.0
   ],
   [
    22.0,
    -3.0
   ],
   [
    23.0,
    -2.0
   ],
   [
    25.0,
    0.0
   ]
  ],
  "interaction_radius": 4.0,
  "layers": 1
 }
}