{
 "schema_version": "0.2",
 "name": "[[176,48,8]]",
 "code_type": "CSS",
 "n": 176,
 "k": 48,
 "checks": {
  "X": [
   [
    0,
    4,
    8,
    12,
    16,
    20,
    24,
    28,
    32,
    36,
    168
   ],
   [
    1,
    5,
    9,
    13,
    17,
    21,
    25,
    29,
    33,
    37,
    168
   ],
   [
    2,
    6,
    10,
    14,
    18,
    22,
    26,
    30,
    34,
    38,
    168
   ],
   [
    3,
    7,
    11,
    15,
    19,
    23,
    27,
    31,
    35,
    39,
    168
   ],
   [
    40,
    44,
    48,
    52,
    56,
    60,
    64,
    68,
    72,
    76,
    169
   ],
   [
    41,
    45,
    49,
    53,
    57,
    61,
    65,
    69,
    73,
    77,
    169
   ],
   [
    42,
    46,
    50,
    54,
    58,
    62,
    66,
    70,
    74,
    78,
    169
   ],
   [
    43,
    47,
    51,
    55,
    59,
    63,
    67,
    71,
    75,
    79,
    169
   ],
   [
    80,
    84,
    88,
    92,
    96,
    100,
    104,
    108,
    112,
    116,
    170
   ],
   [
    81,
    85,
    89,
    93,
    97,
    101,
    105,
    109,
    113,
    117,
    170
   ],
   [
    82,
    86,
    90,
    94,
    98,
    102,
    106,
    110,
    114,
    118,
    170
   ],
   [
    83,
    87,
    91,
    95,
    99,
    103,
    107,
    111,
    115,
    119,
    170
   ],
   [
    120,
    124,
    128,
    132,
    136,
    140,
    144,
    148,
    152,
    156,
    171
   ],
   [
    121,
    125,
    129,
    133,
    137,
    141,
    145,
    149,
    153,
    157,
    171
   ],
   [
    122,
    126,
    130,
    134,
    138,
    142,
    146,
    150,
    154,
    158,
    171
   ],
   [
    123,
    127,
    131,
    135,
    139,
    143,
    147,
    151,
    155,
    159,
    171
   ],
   [
    4,
    12,
    20,
    32,
    44,
    52,
    60,
    72,
    84,
    92,
    100,
    112,
    124,
    132,
    140,
    152,
    172
   ],
   [
    5,
    13,
    21,
    33,
    45,
    53,
    61,
    73,
    85,
    93,
    101,
    113,
    125,
    133,
    141,
    153,
    172
   ],
   [
    6,
    14,
    22,
    34,
    46,
    54,
    62,
    74,
    86,
    94,
    102,
    114,
    126,
    134,
    142,
    154,
    172
   ],
   [
    7,
    15,
    23,
    35,
    47,
    55,
    63,
    75,
    87,
    95,
    103,
    115,
    127,
    135,
    143,
    155,
    172
   ],
   [
    8,
    16,
    24,
    32,
    48,
    56,
    64,
    72,
    88,
    96,
    104,
    112,
    128,
    136,
    144,
    152,
    173
   ],
   [
    9,
    17,
    25,
    33,
    49,
    57,
    65,
    73,
    89,
    97,
    105,
    113,
    129,
    137,
    145,
    153,
    173
   ],
   [
    10,
    18,
    26,
    34,
    50,
    58,
    66,
    74,
    90,
    98,
    106,
    114,
    130,
    138,
    146,
    154,
    173
   ],
   [
    11,
    19,
    27,
    35,
    51,
    59,
    67,
    75,
    91,
    99,
    107,
    115,
    131,
    139,
    147,
    155,
    173
   ],
   [
    12,
    16,
    28,
    32,
    52,
    56,
    68,
    72,
    92,
    96,
    108,
    112,
    132,
    136,
    148,
    152,
    174
   ],
   [
    13,
    17,
    29,
    33,
    53,
    57,
    69,
    73,
    93,
    97,
    109,
    113,
    133,
    137,
    149,
    153,
    174
   ],
   [
    14,
    18,
    30,
    34,
    54,
    58,
    70,
    74,
    94,
    98,
    110,
    114,
    134,
    138,
    150,
    154,
    174
   ],
   [
    15,
    19,
    31,
    35,
    55,
    59,
    71,
    75,
    95,
    99,
    111,
    115,
    135,
    139,
    151,
    155,
    174
   ],
   [
    16,
    20,
    24,
    36,
    56,
    60,
    64,
    76,
    96,
    100,
    104,
    116,
    136,
    140,
    144,
    156,
    175
   ],
   [
    17,
    21,
    25,
    37,
    57,
    61,
    65,
    77,
    97,
    101,
    105,
    117,
    137,
    141,
    145,
    157,
    175
   ],
   [
    18,
    22,
    26,
    38,
    58,
    62,
    66,
    78,
    98,
    102,
    106,
    118,
    138,
    142,
    146,
    158,
    175
   ],
   [
    19,
    23,
    27,
    39,
    59,
    63,
    67,
    79,
    99,
    103,
    107,
    119,
    139,
    143,
    147,
    159,
    175
   ],
   [
    0,
    1,
    2,
    3,
    160
   ],
   [
    4,
    5,
    6,
    7,
    160,
    164
   ],
   [
    8,
    9,
    10,
    11,
    160,
    165
   ],
   [
    12,
    13,
    14,
    15,
    160,
    164,
    166
   ],
   [
    16,
    17,
    18,
    19,
    160,
    165,
    166,
    167
   ],
   [
    20,
    21,
    22,
    23,
    160,
    164,
    167
   ],
   [
    24,
    25,
    26,
    27,
    160,
    165,
    167
   ],
   [
    28,
    29,
    30,
    31,
    160,
    166
   ],
   [
    32,
    33,
    34,
    35,
    160,
    164,
    165,
    166
   ],
   [
    36,
    37,
    38,
    39,
    160,
    167
   ],
   [
    40,
    41,
    42,
    43,
    161
   ],
   [
    44,
    45,
    46,
    47,
    161,
    164
   ],
   [
    48,
    49,
    50,
    51,
    161,
    165
   ],
   [
    52,
    53,
    54,
    55,
    161,
    164,
    166
   ],
   [
    56,
    57,
    58,
    59,
    161,
    165,
    166,
    167
   ],
   [
    60,
    61,
    62,
    63,
    161,
    164,
    167
   ],
   [
    64,
    65,
    66,
    67,
    161,
    165,
    167
   ],
   [
    68,
    69,
    70,
    71,
    161,
    166
   ],
   [
    72,
    73,
    74,
    75,
    161,
    164,
    165,
    166
   ],
   [
    76,
    77,
    78,
    79,
    161,
    167
   ],
   [
    80,
    81,
    82,
    83,
    162
   ],
   [
    84,
    85,
    86,
    87,
    162,
    164
   ],
   [
    88,
    89,
    90,
    91,
    162,
    165
   ],
   [
    92,
    93,
    94,
    95,
    162,
    164,
    166
   ],
   [
    96,
    97,
    98,
    99,
    162,
    165,
    166,
    167
   ],
   [
    100,
    101,
    102,
    103,
    162,
    164,
    167
   ],
   [
    104,
    105,
    106,
    107,
    162,
    165,
    167
   ],
   [
    108,
    109,
    110,
    111,
    162,
    166
   ],
   [
    112,
    113,
    114,
    115,
    162,
    164,
    165,
    166
   ],
   [
    116,
    117,
    118,
    119,
    162,
    167
   ],
   [
    120,
    121,
    122,
    123,
    163
   ],
   [
    124,
    125,
    126,
    127,
    163,
    164
   ],
   [
    128,
    129,
    130,
    131,
    163,
    165
   ],
   [
    132,
    133,
    134,
    135,
    163,
    164,
    166
   ],
   [
    136,
    137,
    138,
    139,
    163,
    165,
    166,
    167
   ],
   [
    140,
    141,
    142,
    143,
    163,
    164,
    167
   ],
   [
    144,
    145,
    146,
    147,
    163,
    165,
    167
   ],
   [
    148,
    149,
    150,
    151,
    163,
    166
   ],
   [
    152,
    153,
    154,
    155,
    163,
    164,
    165,
    166
   ],
   [
    156,
    157,
    158,
    159,
    163,
    167
   ]
  ],
  "Z": [
   [
    0,
    4,
    8,
    12,
    16,
    20,
    24,
    28,
    32,
    36,
    160
   ],
   [
    1,
    5,
    9,
    13,
    17,
    21,
    25,
    29,
    33,
    37,
    160
   ],
   [
    2,
    6,
    10,
    14,
    18,
    22,
    26,
    30,
    34,
    38,
    160
   ],
   [
    3,
    7,
    11,
    15,
    19,
    23,
    27,
    31,
    35,
    39,
    160
   ],
   [
    40,
    44,
    48,
    52,
    56,
    60,
    64,
    68,
    72,
    76,
    161
   ],
   [
    41,
    45,
    49,
    53,
    57,
    61,
    65,
    69,
    73,
    77,
    161
   ],
   [
    42,
    46,
    50,
    54,
    58,
    62,
    66,
    70,
    74,
    78,
    161
   ],
   [
    43,
    47,
    51,
    55,
    59,
    63,
    67,
    71,
    75,
    79,
    161
   ],
   [
    80,
    84,
    88,
    92,
    96,
    100,
    104,
    108,
    112,
    116,
    162
   ],
   [
    81,
    85,
    89,
    93,
    97,
    101,
    105,
    109,
    113,
    117,
    162
   ],
   [
    82,
    86,
    90,
    94,
    98,
    102,
    106,
    110,
    114,
    118,
    162
   ],
   [
    83,
    87,
    91,
    95,
    99,
    103,
    107,
    111,
    115,
    119,
    162
   ],
   [
    120,
    124,
    128,
    132,
    136,
    140,
    144,
    148,
    152,
    156,
    163
   ],
   [
    121,
    125,
    129,
    133,
    137,
    141,
    145,
    149,
    153,
    157,
    163
   ],
   [
    122,
    126,
    130,
    134,
    138,
    142,
    146,
    150,
    154,
    158,
    163
   ],
   [
    123,
    127,
    131,
    135,
    139,
    143,
    147,
    151,
    155,
    159,
    163
   ],
   [
    4,
    12,
    20,
    32,
    44,
    52,
    60,
    72,
    84,
    92,
    100,
    112,
    124,
    132,
    140,
    152,
    164
   ],
   [
    5,
    13,
    21,
    33,
    45,
    53,
    61,
    73,
    85,
    93,
    101,
    113,
    125,
    133,
    141,
    153,
    164
   ],
   [
    6,
    14,
    22,
    34,
    46,
    54,
    62,
    74,
    86,
    94,
    102,
    114,
    126,
    134,
    142,
    154,
    164
   ],
   [
    7,
    15,
    23,
    35,
    47,
    55,
    63,
    75,
    87,
    95,
    103,
    115,
    127,
    135,
    143,
    155,
    164
   ],
   [
    8,
    16,
    24,
    32,
    48,
    56,
    64,
    72,
    88,
    96,
    104,
    112,
    128,
    136,
    144,
    152,
    165
   ],
   [
    9,
    17,
    25,
    33,
    49,
    57,
    65,
    73,
    89,
    97,
    105,
    113,
    129,
    137,
    145,
    153,
    165
   ],
   [
    10,
    18,
    26,
    34,
    50,
    58,
    66,
    74,
    90,
    98,
    106,
    114,
    130,
    138,
    146,
    154,
    165
   ],
   [
    11,
    19,
    27,
    35,
    51,
    59,
    67,
    75,
    91,
    99,
    107,
    115,
    131,
    139,
    147,
    155,
    165
   ],
   [
    12,
    16,
    28,
    32,
    52,
    56,
    68,
    72,
    92,
    96,
    108,
    112,
    132,
    136,
    148,
    152,
    166
   ],
   [
    13,
    17,
    29,
    33,
    53,
    57,
    69,
    73,
    93,
    97,
    109,
    113,
    133,
    137,
    149,
    153,
    166
   ],
   [
    14,
    18,
    30,
    34,
    54,
    58,
    70,
    74,
    94,
    98,
    110,
    114,
    134,
    138,
    150,
    154,
    166
   ],
   [
    15,
    19,
    31,
    35,
    55,
    59,
    71,
    75,
    95,
    99,
    111,
    115,
    135,
    139,
    151,
    155,
    166
   ],
   [
    16,
    20,
    24,
    36,
    56,
    60,
    64,
    76,
    96,
    100,
    104,
    116,
    136,
    140,
    144,
    156,
    167
   ],
   [
    17,
    21,
    25,
    37,
    57,
    61,
    65,
    77,
    97,
    101,
    105,
    117,
    137,
    141,
    145,
    157,
    167
   ],
   [
    18,
    22,
    26,
    38,
    58,
    62,
    66,
    78,
    98,
    102,
    106,
    118,
    138,
    142,
    146,
    158,
    167
   ],
   [
    19,
    23,
    27,
    39,
    59,
    63,
    67,
    79,
    99,
    103,
    107,
    119,
    139,
    143,
    147,
    159,
    167
   ],
   [
    0,
    1,
    2,
    3,
    168
   ],
   [
    4,
    5,
    6,
    7,
    168,
    172
   ],
   [
    8,
    9,
    10,
    11,
    168,
    173
   ],
   [
    12,
    13,
    14,
    15,
    168,
    172,
    174
   ],
   [
    16,
    17,
    18,
    19,
    168,
    173,
    174,
    175
   ],
   [
    20,
    21,
    22,
    23,
    168,
    172,
    175
   ],
   [
    24,
    25,
    26,
    27,
    168,
    173,
    175
   ],
   [
    28,
    29,
    30,
    31,
    168,
    174
   ],
   [
    32,
    33,
    34,
    35,
    168,
    172,
    173,
    174
   ],
   [
    36,
    37,
    38,
    39,
    168,
    175
   ],
   [
    40,
    41,
    42,
    43,
    169
   ],
   [
    44,
    45,
    46,
    47,
    169,
    172
   ],
   [
    48,
    49,
    50,
    51,
    169,
    173
   ],
   [
    52,
    53,
    54,
    55,
    169,
    172,
    174
   ],
   [
    56,
    57,
    58,
    59,
    169,
    173,
    174,
    175
   ],
   [
    60,
    61,
    62,
    63,
    169,
    172,
    175
   ],
   [
    64,
    65,
    66,
    67,
    169,
    173,
    175
   ],
   [
    68,
    69,
    70,
    71,
    169,
    174
   ],
   [
    72,
    73,
    74,
    75,
    169,
    172,
    173,
    174
   ],
   [
    76,
    77,
    78,
    79,
    169,
    175
   ],
   [
    80,
    81,
    82,
    83,
    170
   ],
   [
    84,
    85,
    86,
    87,
    170,
    172
   ],
   [
    88,
    89,
    90,
    91,
    170,
    173
   ],
   [
    92,
    93,
    94,
    95,
    170,
    172,
    174
   ],
   [
    96,
    97,
    98,
    99,
    170,
    173,
    174,
    175
   ],
   [
    100,
    101,
    102,
    103,
    170,
    172,
    175
   ],
   [
    104,
    105,
    106,
    107,
    170,
    173,
    175
   ],
   [
    108,
    109,
    110,
    111,
    170,
    174
   ],
   [
    112,
    113,
    114,
    115,
    170,
    172,
    173,
    174
   ],
   [
    116,
    117,
    118,
    119,
    170,
    175
   ],
   [
    120,
    121,
    122,
    123,
    171
   ],
   [
    124,
    125,
    126,
    127,
    171,
    172
   ],
   [
    128,
    129,
    130,
    131,
    171,
    173
   ],
   [
    132,
    133,
    134,
    135,
    171,
    172,
    174
   ],
   [
    136,
    137,
    138,
    139,
    171,
    173,
    174,
    175
   ],
   [
    140,
    141,
    142,
    143,
    171,
    172,
    175
   ],
   [
    144,
    145,
    146,
    147,
    171,
    173,
    175
   ],
   [
    148,
    149,
    150,
    151,
    171,
    174
   ],
   [
    152,
    153,
    154,
    155,
    171,
    172,
    173,
    174
   ],
   [
    156,
    157,
    158,
    159,
    171,
    175
   ]
  ]
 },
 "distance": {
  "d": 8,
  "X": {
   "value": 8,
   "confidence": "upper_bound",
   "witness": [
    45,
    47,
    49,
    51,
    61,
    63,
    65,
    67
   ]
  },
  "Z": {
   "value": 8,
   "confidence": "upper_bound",
   "witness": [
    109,
    111,
    113,
    115,
    125,
    127,
    129,
    131
   ]
  }
 },
 "provenance": {
  "authors": [
   "@MathysRennela"
  ],
  "construction": "One amplification of [[40,24,4]] base by flagged [[4,2,2]] amplifier (arXiv:2609.37231).",
  "origin": "submission",
  "date": "2026-10-18",
  "model": "Beam 1.0"
 },
 "family": "other",
 "circuit": {
  "d_circ": {
   "Z": {
    "value": 4,
    "confidence": "upper_bound",
    "witness": [
     75462,
     75463,
     79665,
     79666
    ]
   },
   "X": {
    "value": 4,
    "confidence": "upper_bound",
    "witness": [
     22431,
     22451,
     27825,
     31297
    ]
   }
  },
  "rounds": 8,
  "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 (18 X + 18 Z CX layers per round, coloring candidate 5); 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)"
 }
}