{
 "schema_version": "0.2",
 "name": "[[97,25,2]]",
 "code_type": "CSS",
 "n": 97,
 "k": 25,
 "checks": {
  "X": [
   [
    0,
    9,
    45,
    81
   ],
   [
    1,
    10,
    46,
    81,
    82
   ],
   [
    2,
    11,
    47,
    82,
    83
   ],
   [
    3,
    12,
    48,
    83,
    84
   ],
   [
    4,
    13,
    49,
    84
   ],
   [
    5,
    14,
    50,
    81
   ],
   [
    6,
    15,
    51,
    82
   ],
   [
    7,
    16,
    52,
    83
   ],
   [
    8,
    17,
    53,
    84
   ],
   [
    9,
    18,
    54,
    85
   ],
   [
    10,
    19,
    55,
    85,
    86
   ],
   [
    11,
    20,
    56,
    86,
    87
   ],
   [
    12,
    21,
    57,
    87,
    88
   ],
   [
    13,
    22,
    58,
    88
   ],
   [
    14,
    23,
    59,
    85
   ],
   [
    15,
    24,
    60,
    86
   ],
   [
    16,
    25,
    61,
    87
   ],
   [
    17,
    26,
    62,
    88
   ],
   [
    18,
    27,
    63,
    89
   ],
   [
    19,
    28,
    64,
    89,
    90
   ],
   [
    20,
    29,
    65,
    90,
    91
   ],
   [
    21,
    30,
    66,
    91,
    92
   ],
   [
    22,
    31,
    67,
    92
   ],
   [
    23,
    32,
    68,
    89
   ],
   [
    24,
    33,
    69,
    90
   ],
   [
    25,
    34,
    70,
    91
   ],
   [
    26,
    35,
    71,
    92
   ],
   [
    27,
    36,
    72,
    93
   ],
   [
    28,
    37,
    73,
    93,
    94
   ],
   [
    29,
    38,
    74,
    94,
    95
   ],
   [
    30,
    39,
    75,
    95,
    96
   ],
   [
    31,
    40,
    76,
    96
   ],
   [
    32,
    41,
    77,
    93
   ],
   [
    33,
    42,
    78,
    94
   ],
   [
    34,
    43,
    79,
    95
   ],
   [
    35,
    44,
    80,
    96
   ]
  ],
  "Z": [
   [
    0,
    1,
    5,
    81
   ],
   [
    1,
    2,
    6,
    82
   ],
   [
    2,
    3,
    7,
    83
   ],
   [
    3,
    4,
    8,
    84
   ],
   [
    9,
    10,
    14,
    81,
    85
   ],
   [
    10,
    11,
    15,
    82,
    86
   ],
   [
    11,
    12,
    16,
    83,
    87
   ],
   [
    12,
    13,
    17,
    84,
    88
   ],
   [
    18,
    19,
    23,
    85,
    89
   ],
   [
    19,
    20,
    24,
    86,
    90
   ],
   [
    20,
    21,
    25,
    87,
    91
   ],
   [
    21,
    22,
    26,
    88,
    92
   ],
   [
    27,
    28,
    32,
    89,
    93
   ],
   [
    28,
    29,
    33,
    90,
    94
   ],
   [
    29,
    30,
    34,
    91,
    95
   ],
   [
    30,
    31,
    35,
    92,
    96
   ],
   [
    36,
    37,
    41,
    93
   ],
   [
    37,
    38,
    42,
    94
   ],
   [
    38,
    39,
    43,
    95
   ],
   [
    39,
    40,
    44,
    96
   ],
   [
    45,
    46,
    50,
    81
   ],
   [
    46,
    47,
    51,
    82
   ],
   [
    47,
    48,
    52,
    83
   ],
   [
    48,
    49,
    53,
    84
   ],
   [
    54,
    55,
    59,
    85
   ],
   [
    55,
    56,
    60,
    86
   ],
   [
    56,
    57,
    61,
    87
   ],
   [
    57,
    58,
    62,
    88
   ],
   [
    63,
    64,
    68,
    89
   ],
   [
    64,
    65,
    69,
    90
   ],
   [
    65,
    66,
    70,
    91
   ],
   [
    66,
    67,
    71,
    92
   ],
   [
    72,
    73,
    77,
    93
   ],
   [
    73,
    74,
    78,
    94
   ],
   [
    74,
    75,
    79,
    95
   ],
   [
    75,
    76,
    80,
    96
   ]
  ]
 },
 "distance": {
  "d": 2,
  "X": {
   "value": 2,
   "confidence": "upper_bound",
   "witness": [
    54,
    59
   ]
  },
  "Z": {
   "value": 2,
   "confidence": "upper_bound",
   "witness": [
    7,
    52
   ]
  }
 },
 "provenance": {
  "authors": [
   "@MathysRennela"
  ],
  "construction": "contributed via qldpc submit",
  "origin": "submission",
  "date": "2026-10-18",
  "model": "Beam 1.0"
 },
 "family": "hypergraph-product",
 "locality": {
  "coordinates": [
   [
    0.0,
    0.0
   ],
   [
    1.0,
    0.0
   ],
   [
    2.0,
    0.0
   ],
   [
    3.0,
    0.0
   ],
   [
    4.0,
    0.0
   ],
   [
    5.0,
    0.0
   ],
   [
    6.0,
    0.0
   ],
   [
    7.0,
    0.0
   ],
   [
    8.0,
    0.0
   ],
   [
    0.0,
    1.0
   ],
   [
    1.0,
    1.0
   ],
   [
    2.0,
    1.0
   ],
   [
    3.0,
    1.0
   ],
   [
    4.0,
    1.0
   ],
   [
    5.0,
    1.0
   ],
   [
    6.0,
    1.0
   ],
   [
    7.0,
    1.0
   ],
   [
    8.0,
    1.0
   ],
   [
    0.0,
    2.0
   ],
   [
    1.0,
    2.0
   ],
   [
    2.0,
    2.0
   ],
   [
    3.0,
    2.0
   ],
   [
    4.0,
    2.0
   ],
   [
    5.0,
    2.0
   ],
   [
    6.0,
    2.0
   ],
   [
    7.0,
    2.0
   ],
   [
    8.0,
    2.0
   ],
   [
    0.0,
    3.0
   ],
   [
    1.0,
    3.0
   ],
   [
    2.0,
    3.0
   ],
   [
    3.0,
    3.0
   ],
   [
    4.0,
    3.0
   ],
   [
    5.0,
    3.0
   ],
   [
    6.0,
    3.0
   ],
   [
    7.0,
    3.0
   ],
   [
    8.0,
    3.0
   ],
   [
    0.0,
    4.0
   ],
   [
    1.0,
    4.0
   ],
   [
    2.0,
    4.0
   ],
   [
    3.0,
    4.0
   ],
   [
    4.0,
    4.0
   ],
   [
    5.0,
    4.0
   ],
   [
    6.0,
    4.0
   ],
   [
    7.0,
    4.0
   ],
   [
    8.0,
    4.0
   ],
   [
    0.0,
    5.0
   ],
   [
    1.0,
    5.0
   ],
   [
    2.0,
    5.0
   ],
   [
    3.0,
    5.0
   ],
   [
    4.0,
    5.0
   ],
   [
    5.0,
    5.0
   ],
   [
    6.0,
    5.0
   ],
   [
    7.0,
    5.0
   ],
   [
    8.0,
    5.0
   ],
   [
    0.0,
    6.0
   ],
   [
    1.0,
    6.0
   ],
   [
    2.0,
    6.0
   ],
   [
    3.0,
    6.0
   ],
   [
    4.0,
    6.0
   ],
   [
    5.0,
    6.0
   ],
   [
    6.0,
    6.0
   ],
   [
    7.0,
    6.0
   ],
   [
    8.0,
    6.0
   ],
   [
    0.0,
    7.0
   ],
   [
    1.0,
    7.0
   ],
   [
    2.0,
    7.0
   ],
   [
    3.0,
    7.0
   ],
   [
    4.0,
    7.0
   ],
   [
    5.0,
    7.0
   ],
   [
    6.0,
    7.0
   ],
   [
    7.0,
    7.0
   ],
   [
    8.0,
    7.0
   ],
   [
    0.0,
    8.0
   ],
   [
    1.0,
    8.0
   ],
   [
    2.0,
    8.0
   ],
   [
    3.0,
    8.0
   ],
   [
    4.0,
    8.0
   ],
   [
    5.0,
    8.0
   ],
   [
    6.0,
    8.0
   ],
   [
    7.0,
    8.0
   ],
   [
    8.0,
    8.0
   ],
   [
    1.0,
    0.0
   ],
   [
    2.0,
    0.0
   ],
   [
    3.0,
    0.0
   ],
   [
    4.0,
    0.0
   ],
   [
    1.0,
    1.0
   ],
   [
    2.0,
    1.0
   ],
   [
    3.0,
    1.0
   ],
   [
    4.0,
    1.0
   ],
   [
    1.0,
    2.0
   ],
   [
    2.0,
    2.0
   ],
   [
    3.0,
    2.0
   ],
   [
    4.0,
    2.0
   ],
   [
    1.0,
    3.0
   ],
   [
    2.0,
    3.0
   ],
   [
    3.0,
    3.0
   ],
   [
    4.0,
    3.0
   ]
  ],
  "layers": 2
 },
 "circuit": {
  "d_circ": {
   "Z": {
    "value": 2,
    "confidence": "upper_bound",
    "witness": [
     310,
     311
    ]
   },
   "X": {
    "value": 2,
    "confidence": "upper_bound",
    "witness": [
     6,
     11
    ]
   }
  },
  "rounds": 2,
  "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 (5 X + 6 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)"
 }
}