{
 "schema_version": "0.3",
 "name": "[[168,28,10]]",
 "code_type": "CSS",
 "n": 168,
 "k": 28,
 "checks": {
  "X": [
   [
    0,
    16,
    27,
    28,
    84,
    85,
    132,
    137
   ],
   [
    1,
    14,
    17,
    29,
    85,
    86,
    133,
    138
   ],
   [
    2,
    15,
    18,
    30,
    86,
    87,
    134,
    139
   ],
   [
    3,
    16,
    19,
    31,
    87,
    88,
    126,
    135
   ],
   [
    4,
    17,
    20,
    32,
    88,
    89,
    127,
    136
   ],
   [
    5,
    18,
    21,
    33,
    89,
    90,
    128,
    137
   ],
   [
    6,
    19,
    22,
    34,
    90,
    91,
    129,
    138
   ],
   [
    7,
    20,
    23,
    35,
    91,
    92,
    130,
    139
   ],
   [
    8,
    21,
    24,
    36,
    92,
    93,
    126,
    131
   ],
   [
    9,
    22,
    25,
    37,
    93,
    94,
    127,
    132
   ],
   [
    10,
    23,
    26,
    38,
    94,
    95,
    128,
    133
   ],
   [
    11,
    24,
    27,
    39,
    95,
    96,
    129,
    134
   ],
   [
    12,
    14,
    25,
    40,
    96,
    97,
    130,
    135
   ],
   [
    13,
    15,
    26,
    41,
    84,
    97,
    131,
    136
   ],
   [
    14,
    30,
    41,
    42,
    98,
    99,
    146,
    151
   ],
   [
    15,
    28,
    31,
    43,
    99,
    100,
    147,
    152
   ],
   [
    16,
    29,
    32,
    44,
    100,
    101,
    148,
    153
   ],
   [
    17,
    30,
    33,
    45,
    101,
    102,
    140,
    149
   ],
   [
    18,
    31,
    34,
    46,
    102,
    103,
    141,
    150
   ],
   [
    19,
    32,
    35,
    47,
    103,
    104,
    142,
    151
   ],
   [
    20,
    33,
    36,
    48,
    104,
    105,
    143,
    152
   ],
   [
    21,
    34,
    37,
    49,
    105,
    106,
    144,
    153
   ],
   [
    22,
    35,
    38,
    50,
    106,
    107,
    140,
    145
   ],
   [
    23,
    36,
    39,
    51,
    107,
    108,
    141,
    146
   ],
   [
    24,
    37,
    40,
    52,
    108,
    109,
    142,
    147
   ],
   [
    25,
    38,
    41,
    53,
    109,
    110,
    143,
    148
   ],
   [
    26,
    28,
    39,
    54,
    110,
    111,
    144,
    149
   ],
   [
    27,
    29,
    40,
    55,
    98,
    111,
    145,
    150
   ],
   [
    28,
    44,
    55,
    56,
    112,
    113,
    160,
    165
   ],
   [
    29,
    42,
    45,
    57,
    113,
    114,
    161,
    166
   ],
   [
    30,
    43,
    46,
    58,
    114,
    115,
    162,
    167
   ],
   [
    31,
    44,
    47,
    59,
    115,
    116,
    154,
    163
   ],
   [
    32,
    45,
    48,
    60,
    116,
    117,
    155,
    164
   ],
   [
    33,
    46,
    49,
    61,
    117,
    118,
    156,
    165
   ],
   [
    34,
    47,
    50,
    62,
    118,
    119,
    157,
    166
   ],
   [
    35,
    48,
    51,
    63,
    119,
    120,
    158,
    167
   ],
   [
    36,
    49,
    52,
    64,
    120,
    121,
    154,
    159
   ],
   [
    37,
    50,
    53,
    65,
    121,
    122,
    155,
    160
   ],
   [
    38,
    51,
    54,
    66,
    122,
    123,
    156,
    161
   ],
   [
    39,
    52,
    55,
    67,
    123,
    124,
    157,
    162
   ],
   [
    40,
    42,
    53,
    68,
    124,
    125,
    158,
    163
   ],
   [
    41,
    43,
    54,
    69,
    112,
    125,
    159,
    164
   ],
   [
    42,
    58,
    69,
    70,
    90,
    95,
    126,
    127
   ],
   [
    43,
    56,
    59,
    71,
    91,
    96,
    127,
    128
   ],
   [
    44,
    57,
    60,
    72,
    92,
    97,
    128,
    129
   ],
   [
    45,
    58,
    61,
    73,
    84,
    93,
    129,
    130
   ],
   [
    46,
    59,
    62,
    74,
    85,
    94,
    130,
    131
   ],
   [
    47,
    60,
    63,
    75,
    86,
    95,
    131,
    132
   ],
   [
    48,
    61,
    64,
    76,
    87,
    96,
    132,
    133
   ],
   [
    49,
    62,
    65,
    77,
    88,
    97,
    133,
    134
   ],
   [
    50,
    63,
    66,
    78,
    84,
    89,
    134,
    135
   ],
   [
    51,
    64,
    67,
    79,
    85,
    90,
    135,
    136
   ],
   [
    52,
    65,
    68,
    80,
    86,
    91,
    136,
    137
   ],
   [
    53,
    66,
    69,
    81,
    87,
    92,
    137,
    138
   ],
   [
    54,
    56,
    67,
    82,
    88,
    93,
    138,
    139
   ],
   [
    55,
    57,
    68,
    83,
    89,
    94,
    126,
    139
   ],
   [
    0,
    56,
    72,
    83,
    104,
    109,
    140,
    141
   ],
   [
    1,
    57,
    70,
    73,
    105,
    110,
    141,
    142
   ],
   [
    2,
    58,
    71,
    74,
    106,
    111,
    142,
    143
   ],
   [
    3,
    59,
    72,
    75,
    98,
    107,
    143,
    144
   ],
   [
    4,
    60,
    73,
    76,
    99,
    108,
    144,
    145
   ],
   [
    5,
    61,
    74,
    77,
    100,
    109,
    145,
    146
   ],
   [
    6,
    62,
    75,
    78,
    101,
    110,
    146,
    147
   ],
   [
    7,
    63,
    76,
    79,
    102,
    111,
    147,
    148
   ],
   [
    8,
    64,
    77,
    80,
    98,
    103,
    148,
    149
   ],
   [
    9,
    65,
    78,
    81,
    99,
    104,
    149,
    150
   ],
   [
    10,
    66,
    79,
    82,
    100,
    105,
    150,
    151
   ],
   [
    11,
    67,
    80,
    83,
    101,
    106,
    151,
    152
   ],
   [
    12,
    68,
    70,
    81,
    102,
    107,
    152,
    153
   ],
   [
    13,
    69,
    71,
    82,
    103,
    108,
    140,
    153
   ],
   [
    2,
    13,
    14,
    70,
    118,
    123,
    154,
    155
   ],
   [
    0,
    3,
    15,
    71,
    119,
    124,
    155,
    156
   ],
   [
    1,
    4,
    16,
    72,
    120,
    125,
    156,
    157
   ],
   [
    2,
    5,
    17,
    73,
    112,
    121,
    157,
    158
   ],
   [
    3,
    6,
    18,
    74,
    113,
    122,
    158,
    159
   ],
   [
    4,
    7,
    19,
    75,
    114,
    123,
    159,
    160
   ],
   [
    5,
    8,
    20,
    76,
    115,
    124,
    160,
    161
   ],
   [
    6,
    9,
    21,
    77,
    116,
    125,
    161,
    162
   ],
   [
    7,
    10,
    22,
    78,
    112,
    117,
    162,
    163
   ],
   [
    8,
    11,
    23,
    79,
    113,
    118,
    163,
    164
   ],
   [
    9,
    12,
    24,
    80,
    114,
    119,
    164,
    165
   ],
   [
    10,
    13,
    25,
    81,
    115,
    120,
    165,
    166
   ],
   [
    0,
    11,
    26,
    82,
    116,
    121,
    166,
    167
   ],
   [
    1,
    12,
    27,
    83,
    117,
    122,
    154,
    167
   ]
  ],
  "Z": [
   [
    0,
    13,
    45,
    50,
    84,
    140,
    155,
    166
   ],
   [
    0,
    1,
    46,
    51,
    85,
    141,
    156,
    167
   ],
   [
    1,
    2,
    47,
    52,
    86,
    142,
    154,
    157
   ],
   [
    2,
    3,
    48,
    53,
    87,
    143,
    155,
    158
   ],
   [
    3,
    4,
    49,
    54,
    88,
    144,
    156,
    159
   ],
   [
    4,
    5,
    50,
    55,
    89,
    145,
    157,
    160
   ],
   [
    5,
    6,
    42,
    51,
    90,
    146,
    158,
    161
   ],
   [
    6,
    7,
    43,
    52,
    91,
    147,
    159,
    162
   ],
   [
    7,
    8,
    44,
    53,
    92,
    148,
    160,
    163
   ],
   [
    8,
    9,
    45,
    54,
    93,
    149,
    161,
    164
   ],
   [
    9,
    10,
    46,
    55,
    94,
    150,
    162,
    165
   ],
   [
    10,
    11,
    42,
    47,
    95,
    151,
    163,
    166
   ],
   [
    11,
    12,
    43,
    48,
    96,
    152,
    164,
    167
   ],
   [
    12,
    13,
    44,
    49,
    97,
    153,
    154,
    165
   ],
   [
    14,
    27,
    59,
    64,
    85,
    96,
    98,
    154
   ],
   [
    14,
    15,
    60,
    65,
    86,
    97,
    99,
    155
   ],
   [
    15,
    16,
    61,
    66,
    84,
    87,
    100,
    156
   ],
   [
    16,
    17,
    62,
    67,
    85,
    88,
    101,
    157
   ],
   [
    17,
    18,
    63,
    68,
    86,
    89,
    102,
    158
   ],
   [
    18,
    19,
    64,
    69,
    87,
    90,
    103,
    159
   ],
   [
    19,
    20,
    56,
    65,
    88,
    91,
    104,
    160
   ],
   [
    20,
    21,
    57,
    66,
    89,
    92,
    105,
    161
   ],
   [
    21,
    22,
    58,
    67,
    90,
    93,
    106,
    162
   ],
   [
    22,
    23,
    59,
    68,
    91,
    94,
    107,
    163
   ],
   [
    23,
    24,
    60,
    69,
    92,
    95,
    108,
    164
   ],
   [
    24,
    25,
    56,
    61,
    93,
    96,
    109,
    165
   ],
   [
    25,
    26,
    57,
    62,
    94,
    97,
    110,
    166
   ],
   [
    26,
    27,
    58,
    63,
    84,
    95,
    111,
    167
   ],
   [
    28,
    41,
    73,
    78,
    84,
    99,
    110,
    112
   ],
   [
    28,
    29,
    74,
    79,
    85,
    100,
    111,
    113
   ],
   [
    29,
    30,
    75,
    80,
    86,
    98,
    101,
    114
   ],
   [
    30,
    31,
    76,
    81,
    87,
    99,
    102,
    115
   ],
   [
    31,
    32,
    77,
    82,
    88,
    100,
    103,
    116
   ],
   [
    32,
    33,
    78,
    83,
    89,
    101,
    104,
    117
   ],
   [
    33,
    34,
    70,
    79,
    90,
    102,
    105,
    118
   ],
   [
    34,
    35,
    71,
    80,
    91,
    103,
    106,
    119
   ],
   [
    35,
    36,
    72,
    81,
    92,
    104,
    107,
    120
   ],
   [
    36,
    37,
    73,
    82,
    93,
    105,
    108,
    121
   ],
   [
    37,
    38,
    74,
    83,
    94,
    106,
    109,
    122
   ],
   [
    38,
    39,
    70,
    75,
    95,
    107,
    110,
    123
   ],
   [
    39,
    40,
    71,
    76,
    96,
    108,
    111,
    124
   ],
   [
    40,
    41,
    72,
    77,
    97,
    98,
    109,
    125
   ],
   [
    3,
    8,
    42,
    55,
    98,
    113,
    124,
    126
   ],
   [
    4,
    9,
    42,
    43,
    99,
    114,
    125,
    127
   ],
   [
    5,
    10,
    43,
    44,
    100,
    112,
    115,
    128
   ],
   [
    6,
    11,
    44,
    45,
    101,
    113,
    116,
    129
   ],
   [
    7,
    12,
    45,
    46,
    102,
    114,
    117,
    130
   ],
   [
    8,
    13,
    46,
    47,
    103,
    115,
    118,
    131
   ],
   [
    0,
    9,
    47,
    48,
    104,
    116,
    119,
    132
   ],
   [
    1,
    10,
    48,
    49,
    105,
    117,
    120,
    133
   ],
   [
    2,
    11,
    49,
    50,
    106,
    118,
    121,
    134
   ],
   [
    3,
    12,
    50,
    51,
    107,
    119,
    122,
    135
   ],
   [
    4,
    13,
    51,
    52,
    108,
    120,
    123,
    136
   ],
   [
    0,
    5,
    52,
    53,
    109,
    121,
    124,
    137
   ],
   [
    1,
    6,
    53,
    54,
    110,
    122,
    125,
    138
   ],
   [
    2,
    7,
    54,
    55,
    111,
    112,
    123,
    139
   ],
   [
    17,
    22,
    56,
    69,
    112,
    127,
    138,
    140
   ],
   [
    18,
    23,
    56,
    57,
    113,
    128,
    139,
    141
   ],
   [
    19,
    24,
    57,
    58,
    114,
    126,
    129,
    142
   ],
   [
    20,
    25,
    58,
    59,
    115,
    127,
    130,
    143
   ],
   [
    21,
    26,
    59,
    60,
    116,
    128,
    131,
    144
   ],
   [
    22,
    27,
    60,
    61,
    117,
    129,
    132,
    145
   ],
   [
    14,
    23,
    61,
    62,
    118,
    130,
    133,
    146
   ],
   [
    15,
    24,
    62,
    63,
    119,
    131,
    134,
    147
   ],
   [
    16,
    25,
    63,
    64,
    120,
    132,
    135,
    148
   ],
   [
    17,
    26,
    64,
    65,
    121,
    133,
    136,
    149
   ],
   [
    18,
    27,
    65,
    66,
    122,
    134,
    137,
    150
   ],
   [
    14,
    19,
    66,
    67,
    123,
    135,
    138,
    151
   ],
   [
    15,
    20,
    67,
    68,
    124,
    136,
    139,
    152
   ],
   [
    16,
    21,
    68,
    69,
    125,
    126,
    137,
    153
   ],
   [
    31,
    36,
    70,
    83,
    126,
    141,
    152,
    154
   ],
   [
    32,
    37,
    70,
    71,
    127,
    142,
    153,
    155
   ],
   [
    33,
    38,
    71,
    72,
    128,
    140,
    143,
    156
   ],
   [
    34,
    39,
    72,
    73,
    129,
    141,
    144,
    157
   ],
   [
    35,
    40,
    73,
    74,
    130,
    142,
    145,
    158
   ],
   [
    36,
    41,
    74,
    75,
    131,
    143,
    146,
    159
   ],
   [
    28,
    37,
    75,
    76,
    132,
    144,
    147,
    160
   ],
   [
    29,
    38,
    76,
    77,
    133,
    145,
    148,
    161
   ],
   [
    30,
    39,
    77,
    78,
    134,
    146,
    149,
    162
   ],
   [
    31,
    40,
    78,
    79,
    135,
    147,
    150,
    163
   ],
   [
    32,
    41,
    79,
    80,
    136,
    148,
    151,
    164
   ],
   [
    28,
    33,
    80,
    81,
    137,
    149,
    152,
    165
   ],
   [
    29,
    34,
    81,
    82,
    138,
    150,
    153,
    166
   ],
   [
    30,
    35,
    82,
    83,
    139,
    140,
    151,
    167
   ]
  ]
 },
 "distance": {
  "d": 10,
  "X": {
   "value": 10,
   "confidence": "upper_bound",
   "witness": [
    18,
    22,
    24,
    57,
    61,
    62,
    66,
    67,
    68,
    69
   ]
  },
  "Z": {
   "value": 10,
   "confidence": "upper_bound",
   "witness": [
    99,
    101,
    103,
    109,
    140,
    145,
    147,
    148,
    150,
    151
   ]
  }
 },
 "provenance": {
  "authors": [
   "@FarLab"
  ],
  "construction": "bivariate bicycle on Z_6 x Z_14: A = x^0y^0 + x^1y^13 + x^1y^2 + x^2y^0, B = x^0y^0 + x^3y^6 + x^0y^1 + x^3y^11",
  "origin": "submission",
  "date": "2026-10-17",
  "model": "Claude Fable 5.1",
  "search_budget": {
   "candidates_screened": 20444,
   "ris_trials_per_side": 4000000,
   "cpu_hours": 7.0,
   "tool": "research/kit/search.py + gf2_fast on Brev n2d-highcpu-64"
  }
 },
 "family": "bivariate-bicycle",
 "circuit": {
  "d_circ": {
   "Z": {
    "value": 10,
    "confidence": "upper_bound",
    "witness": [
     93288,
     93289,
     93292,
     93293,
     93295,
     93296,
     93300,
     93306,
     93308,
     93313
    ]
   },
   "X": {
    "value": 10,
    "confidence": "upper_bound",
    "witness": [
     93170,
     93174,
     93194,
     93199,
     93203,
     93213,
     93218,
     93225,
     93256,
     93268
    ]
   }
  },
  "rounds": 10,
  "stim_version": "1.16.0",
  "notes": "Generic sequential two-block extraction: one ancilla per check, X checks then Z checks each round with joint reset and measurement layers; CX layers are a proper edge coloring of each Tanner graph (10 X + 10 Z CX layers per round, coloring candidate 0); generated by qldpc submit (research/circuit_autogen.py, seed 0), the first of up to 6 candidates whose RIS screen at 2 rounds found nothing below d; witnesses from RIS on ker(H_dem) at twice the gate's trial budget, validated in GF(2)"
 }
}
