{
 "schema_version": "0.1",
 "name": "[[136,35,10]]",
 "code_type": "CSS",
 "n": 136,
 "k": 35,
 "checks": {
  "X": [
   [
    2,
    18,
    37,
    50,
    63,
    64,
    83,
    89,
    90,
    103,
    116,
    135
   ],
   [
    3,
    19,
    34,
    38,
    64,
    65,
    84,
    90,
    91,
    104,
    117,
    119
   ],
   [
    4,
    20,
    35,
    39,
    65,
    66,
    68,
    91,
    92,
    105,
    118,
    120
   ],
   [
    5,
    21,
    36,
    40,
    66,
    67,
    69,
    92,
    93,
    102,
    106,
    121
   ],
   [
    6,
    22,
    37,
    41,
    51,
    67,
    70,
    93,
    94,
    103,
    107,
    122
   ],
   [
    7,
    23,
    38,
    42,
    51,
    52,
    71,
    94,
    95,
    104,
    108,
    123
   ],
   [
    8,
    24,
    39,
    43,
    52,
    53,
    72,
    95,
    96,
    105,
    109,
    124
   ],
   [
    9,
    25,
    40,
    44,
    53,
    54,
    73,
    96,
    97,
    106,
    110,
    125
   ],
   [
    10,
    26,
    41,
    45,
    54,
    55,
    74,
    97,
    98,
    107,
    111,
    126
   ],
   [
    11,
    27,
    42,
    46,
    55,
    56,
    75,
    98,
    99,
    108,
    112,
    127
   ],
   [
    12,
    28,
    43,
    47,
    56,
    57,
    76,
    99,
    100,
    109,
    113,
    128
   ],
   [
    13,
    29,
    44,
    48,
    57,
    58,
    77,
    100,
    101,
    110,
    114,
    129
   ],
   [
    14,
    30,
    45,
    49,
    58,
    59,
    78,
    85,
    101,
    111,
    115,
    130
   ],
   [
    15,
    31,
    46,
    50,
    59,
    60,
    79,
    85,
    86,
    112,
    116,
    131
   ],
   [
    16,
    32,
    34,
    47,
    60,
    61,
    80,
    86,
    87,
    113,
    117,
    132
   ],
   [
    0,
    33,
    35,
    48,
    61,
    62,
    81,
    87,
    88,
    114,
    118,
    133
   ],
   [
    1,
    17,
    36,
    49,
    62,
    63,
    82,
    88,
    89,
    102,
    115,
    134
   ],
   [
    13,
    14,
    20,
    36,
    51,
    55,
    68,
    101,
    107,
    108,
    121,
    134
   ],
   [
    14,
    15,
    21,
    37,
    52,
    56,
    69,
    85,
    108,
    109,
    122,
    135
   ],
   [
    15,
    16,
    22,
    38,
    53,
    57,
    70,
    86,
    109,
    110,
    119,
    123
   ],
   [
    0,
    16,
    23,
    39,
    54,
    58,
    71,
    87,
    110,
    111,
    120,
    124
   ],
   [
    0,
    1,
    24,
    40,
    55,
    59,
    72,
    88,
    111,
    112,
    121,
    125
   ],
   [
    1,
    2,
    25,
    41,
    56,
    60,
    73,
    89,
    112,
    113,
    122,
    126
   ],
   [
    2,
    3,
    26,
    42,
    57,
    61,
    74,
    90,
    113,
    114,
    123,
    127
   ],
   [
    3,
    4,
    27,
    43,
    58,
    62,
    75,
    91,
    114,
    115,
    124,
    128
   ],
   [
    4,
    5,
    28,
    44,
    59,
    63,
    76,
    92,
    115,
    116,
    125,
    129
   ],
   [
    5,
    6,
    29,
    45,
    60,
    64,
    77,
    93,
    116,
    117,
    126,
    130
   ],
   [
    6,
    7,
    30,
    46,
    61,
    65,
    78,
    94,
    117,
    118,
    127,
    131
   ],
   [
    7,
    8,
    31,
    47,
    62,
    66,
    79,
    95,
    102,
    118,
    128,
    132
   ],
   [
    8,
    9,
    32,
    48,
    63,
    67,
    80,
    96,
    102,
    103,
    129,
    133
   ],
   [
    9,
    10,
    33,
    49,
    51,
    64,
    81,
    97,
    103,
    104,
    130,
    134
   ],
   [
    10,
    11,
    17,
    50,
    52,
    65,
    82,
    98,
    104,
    105,
    131,
    135
   ],
   [
    11,
    12,
    18,
    34,
    53,
    66,
    83,
    99,
    105,
    106,
    119,
    132
   ],
   [
    3,
    16,
    29,
    30,
    36,
    52,
    69,
    82,
    101,
    117,
    123,
    124
   ],
   [
    0,
    4,
    30,
    31,
    37,
    53,
    70,
    83,
    85,
    118,
    124,
    125
   ],
   [
    1,
    5,
    31,
    32,
    38,
    54,
    71,
    84,
    86,
    102,
    125,
    126
   ],
   [
    2,
    6,
    32,
    33,
    39,
    55,
    68,
    72,
    87,
    103,
    126,
    127
   ],
   [
    3,
    7,
    17,
    33,
    40,
    56,
    69,
    73,
    88,
    104,
    127,
    128
   ],
   [
    4,
    8,
    17,
    18,
    41,
    57,
    70,
    74,
    89,
    105,
    128,
    129
   ],
   [
    5,
    9,
    18,
    19,
    42,
    58,
    71,
    75,
    90,
    106,
    129,
    130
   ],
   [
    6,
    10,
    19,
    20,
    43,
    59,
    72,
    76,
    91,
    107,
    130,
    131
   ],
   [
    7,
    11,
    20,
    21,
    44,
    60,
    73,
    77,
    92,
    108,
    131,
    132
   ],
   [
    8,
    12,
    21,
    22,
    45,
    61,
    74,
    78,
    93,
    109,
    132,
    133
   ],
   [
    9,
    13,
    22,
    23,
    46,
    62,
    75,
    79,
    94,
    110,
    133,
    134
   ],
   [
    10,
    14,
    23,
    24,
    47,
    63,
    76,
    80,
    95,
    111,
    134,
    135
   ],
   [
    11,
    15,
    24,
    25,
    48,
    64,
    77,
    81,
    96,
    112,
    119,
    135
   ],
   [
    12,
    16,
    25,
    26,
    49,
    65,
    78,
    82,
    97,
    113,
    119,
    120
   ],
   [
    0,
    13,
    26,
    27,
    50,
    66,
    79,
    83,
    98,
    114,
    120,
    121
   ],
   [
    1,
    14,
    27,
    28,
    34,
    67,
    80,
    84,
    99,
    115,
    121,
    122
   ],
   [
    2,
    15,
    28,
    29,
    35,
    51,
    68,
    81,
    100,
    116,
    122,
    123
   ]
  ],
  "Z": [
   [
    2,
    18,
    37,
    50,
    63,
    64,
    83,
    89,
    90,
    103,
    116,
    135
   ],
   [
    3,
    19,
    34,
    38,
    64,
    65,
    84,
    90,
    91,
    104,
    117,
    119
   ],
   [
    4,
    20,
    35,
    39,
    65,
    66,
    68,
    91,
    92,
    105,
    118,
    120
   ],
   [
    5,
    21,
    36,
    40,
    66,
    67,
    69,
    92,
    93,
    102,
    106,
    121
   ],
   [
    6,
    22,
    37,
    41,
    51,
    67,
    70,
    93,
    94,
    103,
    107,
    122
   ],
   [
    7,
    23,
    38,
    42,
    51,
    52,
    71,
    94,
    95,
    104,
    108,
    123
   ],
   [
    8,
    24,
    39,
    43,
    52,
    53,
    72,
    95,
    96,
    105,
    109,
    124
   ],
   [
    9,
    25,
    40,
    44,
    53,
    54,
    73,
    96,
    97,
    106,
    110,
    125
   ],
   [
    10,
    26,
    41,
    45,
    54,
    55,
    74,
    97,
    98,
    107,
    111,
    126
   ],
   [
    11,
    27,
    42,
    46,
    55,
    56,
    75,
    98,
    99,
    108,
    112,
    127
   ],
   [
    12,
    28,
    43,
    47,
    56,
    57,
    76,
    99,
    100,
    109,
    113,
    128
   ],
   [
    13,
    29,
    44,
    48,
    57,
    58,
    77,
    100,
    101,
    110,
    114,
    129
   ],
   [
    14,
    30,
    45,
    49,
    58,
    59,
    78,
    85,
    101,
    111,
    115,
    130
   ],
   [
    15,
    31,
    46,
    50,
    59,
    60,
    79,
    85,
    86,
    112,
    116,
    131
   ],
   [
    16,
    32,
    34,
    47,
    60,
    61,
    80,
    86,
    87,
    113,
    117,
    132
   ],
   [
    0,
    33,
    35,
    48,
    61,
    62,
    81,
    87,
    88,
    114,
    118,
    133
   ],
   [
    1,
    17,
    36,
    49,
    62,
    63,
    82,
    88,
    89,
    102,
    115,
    134
   ],
   [
    12,
    13,
    19,
    35,
    54,
    67,
    84,
    100,
    106,
    107,
    120,
    133
   ],
   [
    13,
    14,
    20,
    36,
    51,
    55,
    68,
    101,
    107,
    108,
    121,
    134
   ],
   [
    14,
    15,
    21,
    37,
    52,
    56,
    69,
    85,
    108,
    109,
    122,
    135
   ],
   [
    15,
    16,
    22,
    38,
    53,
    57,
    70,
    86,
    109,
    110,
    119,
    123
   ],
   [
    0,
    16,
    23,
    39,
    54,
    58,
    71,
    87,
    110,
    111,
    120,
    124
   ],
   [
    0,
    1,
    24,
    40,
    55,
    59,
    72,
    88,
    111,
    112,
    121,
    125
   ],
   [
    1,
    2,
    25,
    41,
    56,
    60,
    73,
    89,
    112,
    113,
    122,
    126
   ],
   [
    2,
    3,
    26,
    42,
    57,
    61,
    74,
    90,
    113,
    114,
    123,
    127
   ],
   [
    3,
    4,
    27,
    43,
    58,
    62,
    75,
    91,
    114,
    115,
    124,
    128
   ],
   [
    4,
    5,
    28,
    44,
    59,
    63,
    76,
    92,
    115,
    116,
    125,
    129
   ],
   [
    5,
    6,
    29,
    45,
    60,
    64,
    77,
    93,
    116,
    117,
    126,
    130
   ],
   [
    6,
    7,
    30,
    46,
    61,
    65,
    78,
    94,
    117,
    118,
    127,
    131
   ],
   [
    7,
    8,
    31,
    47,
    62,
    66,
    79,
    95,
    102,
    118,
    128,
    132
   ],
   [
    8,
    9,
    32,
    48,
    63,
    67,
    80,
    96,
    102,
    103,
    129,
    133
   ],
   [
    9,
    10,
    33,
    49,
    51,
    64,
    81,
    97,
    103,
    104,
    130,
    134
   ],
   [
    10,
    11,
    17,
    50,
    52,
    65,
    82,
    98,
    104,
    105,
    131,
    135
   ],
   [
    11,
    12,
    18,
    34,
    53,
    66,
    83,
    99,
    105,
    106,
    119,
    132
   ],
   [
    3,
    16,
    29,
    30,
    36,
    52,
    69,
    82,
    101,
    117,
    123,
    124
   ],
   [
    0,
    4,
    30,
    31,
    37,
    53,
    70,
    83,
    85,
    118,
    124,
    125
   ],
   [
    1,
    5,
    31,
    32,
    38,
    54,
    71,
    84,
    86,
    102,
    125,
    126
   ],
   [
    2,
    6,
    32,
    33,
    39,
    55,
    68,
    72,
    87,
    103,
    126,
    127
   ],
   [
    3,
    7,
    17,
    33,
    40,
    56,
    69,
    73,
    88,
    104,
    127,
    128
   ],
   [
    4,
    8,
    17,
    18,
    41,
    57,
    70,
    74,
    89,
    105,
    128,
    129
   ],
   [
    5,
    9,
    18,
    19,
    42,
    58,
    71,
    75,
    90,
    106,
    129,
    130
   ],
   [
    6,
    10,
    19,
    20,
    43,
    59,
    72,
    76,
    91,
    107,
    130,
    131
   ],
   [
    7,
    11,
    20,
    21,
    44,
    60,
    73,
    77,
    92,
    108,
    131,
    132
   ],
   [
    8,
    12,
    21,
    22,
    45,
    61,
    74,
    78,
    93,
    109,
    132,
    133
   ],
   [
    9,
    13,
    22,
    23,
    46,
    62,
    75,
    79,
    94,
    110,
    133,
    134
   ],
   [
    10,
    14,
    23,
    24,
    47,
    63,
    76,
    80,
    95,
    111,
    134,
    135
   ],
   [
    11,
    15,
    24,
    25,
    48,
    64,
    77,
    81,
    96,
    112,
    119,
    135
   ],
   [
    12,
    16,
    25,
    26,
    49,
    65,
    78,
    82,
    97,
    113,
    119,
    120
   ],
   [
    0,
    13,
    26,
    27,
    50,
    66,
    79,
    83,
    98,
    114,
    120,
    121
   ],
   [
    1,
    14,
    27,
    28,
    34,
    67,
    80,
    84,
    99,
    115,
    121,
    122
   ],
   [
    2,
    15,
    28,
    29,
    35,
    51,
    68,
    81,
    100,
    116,
    122,
    123
   ]
  ]
 },
 "distance": {
  "d": 10,
  "X": {
   "value": 12,
   "confidence": "upper_bound",
   "witness": [
    3,
    33,
    50,
    77,
    82,
    86,
    93,
    102,
    103,
    114,
    119,
    132
   ]
  },
  "Z": {
   "value": 10,
   "confidence": "upper_bound",
   "witness": [
    13,
    26,
    42,
    48,
    62,
    75,
    95,
    96,
    97,
    134
   ]
  }
 },
 "provenance": {
  "authors": [
   "@vprusso"
  ],
  "model": "Claude Opus 5",
  "novelty": "known_parameters",
  "origin": "submission",
  "date": "2026-09-21",
  "construction": "Check deletion from the board entry [[136,34,12]] (codes/136-34-12.json): row 17 of H_X removed. Dropping one stabiliser generator frees one logical qubit and cannot raise the distance.",
  "notes": "Found by sweeping every single-row deletion of every small board entry and keeping those that land undominated. The parent's remaining checks are unchanged."
 },
 "family": "check-deletion"
}