{
 "schema_version": "0.3",
 "name": "[[48,18,4]]",
 "code_type": "CSS",
 "n": 48,
 "k": 18,
 "checks": {
  "X": [
   [
    0,
    1,
    11,
    12,
    24,
    31,
    46,
    47
   ],
   [
    0,
    1,
    10,
    13,
    25,
    30,
    46,
    47
   ],
   [
    2,
    3,
    9,
    14,
    26,
    29,
    44,
    45
   ],
   [
    2,
    3,
    8,
    15,
    27,
    28,
    44,
    45
   ],
   [
    4,
    5,
    8,
    15,
    27,
    28,
    42,
    43
   ],
   [
    4,
    5,
    9,
    14,
    26,
    29,
    42,
    43
   ],
   [
    6,
    7,
    10,
    13,
    25,
    30,
    40,
    41
   ],
   [
    6,
    7,
    11,
    12,
    24,
    31,
    40,
    41
   ],
   [
    8,
    9,
    19,
    20,
    30,
    31,
    32,
    39
   ],
   [
    8,
    9,
    18,
    21,
    30,
    31,
    33,
    38
   ],
   [
    10,
    11,
    17,
    22,
    28,
    29,
    34,
    37
   ],
   [
    10,
    11,
    16,
    23,
    28,
    29,
    35,
    36
   ],
   [
    12,
    13,
    16,
    23,
    26,
    27,
    35,
    36
   ],
   [
    12,
    13,
    17,
    22,
    26,
    27,
    34,
    37
   ],
   [
    14,
    15,
    18,
    21,
    24,
    25,
    33,
    38
   ],
   [
    14,
    15,
    19,
    20,
    24,
    25,
    32,
    39
   ],
   [
    3,
    4,
    16,
    17,
    38,
    39,
    40,
    47
   ],
   [
    2,
    5,
    16,
    17,
    38,
    39,
    41,
    46
   ],
   [
    1,
    6,
    18,
    19,
    36,
    37,
    42,
    45
   ],
   [
    0,
    7,
    18,
    19,
    36,
    37,
    43,
    44
   ],
   [
    0,
    7,
    20,
    21,
    34,
    35,
    43,
    44
   ],
   [
    1,
    6,
    20,
    21,
    34,
    35,
    42,
    45
   ],
   [
    2,
    5,
    22,
    23,
    32,
    33,
    41,
    46
   ],
   [
    3,
    4,
    22,
    23,
    32,
    33,
    40,
    47
   ]
  ],
  "Z": [
   [
    0,
    7,
    14,
    15,
    24,
    25,
    43,
    44
   ],
   [
    1,
    6,
    14,
    15,
    24,
    25,
    42,
    45
   ],
   [
    2,
    5,
    12,
    13,
    26,
    27,
    41,
    46
   ],
   [
    3,
    4,
    12,
    13,
    26,
    27,
    40,
    47
   ],
   [
    3,
    4,
    10,
    11,
    28,
    29,
    40,
    47
   ],
   [
    2,
    5,
    10,
    11,
    28,
    29,
    41,
    46
   ],
   [
    1,
    6,
    8,
    9,
    30,
    31,
    42,
    45
   ],
   [
    0,
    7,
    8,
    9,
    30,
    31,
    43,
    44
   ],
   [
    8,
    15,
    22,
    23,
    27,
    28,
    32,
    33
   ],
   [
    9,
    14,
    22,
    23,
    26,
    29,
    32,
    33
   ],
   [
    10,
    13,
    20,
    21,
    25,
    30,
    34,
    35
   ],
   [
    11,
    12,
    20,
    21,
    24,
    31,
    34,
    35
   ],
   [
    11,
    12,
    18,
    19,
    24,
    31,
    36,
    37
   ],
   [
    10,
    13,
    18,
    19,
    25,
    30,
    36,
    37
   ],
   [
    9,
    14,
    16,
    17,
    26,
    29,
    38,
    39
   ],
   [
    8,
    15,
    16,
    17,
    27,
    28,
    38,
    39
   ],
   [
    6,
    7,
    16,
    23,
    35,
    36,
    40,
    41
   ],
   [
    6,
    7,
    17,
    22,
    34,
    37,
    40,
    41
   ],
   [
    4,
    5,
    18,
    21,
    33,
    38,
    42,
    43
   ],
   [
    4,
    5,
    19,
    20,
    32,
    39,
    42,
    43
   ],
   [
    2,
    3,
    19,
    20,
    32,
    39,
    44,
    45
   ],
   [
    2,
    3,
    18,
    21,
    33,
    38,
    44,
    45
   ],
   [
    0,
    1,
    17,
    22,
    34,
    37,
    46,
    47
   ],
   [
    0,
    1,
    16,
    23,
    35,
    36,
    46,
    47
   ]
  ]
 },
 "distance": {
  "d": 4,
  "X": {
   "value": 4,
   "confidence": "upper_bound",
   "witness": [
    14,
    15,
    33,
    38
   ]
  },
  "Z": {
   "value": 4,
   "confidence": "upper_bound",
   "witness": [
    12,
    13,
    40,
    47
   ]
  }
 },
 "provenance": {
  "authors": [
   "@FarLab"
  ],
  "construction": "2BGA (two-block group algebra) code on group ab(3,2,2,2) (|G|=24); H_X=[L(a)|R(b)], H_Z=[R(b)^T|L(a)^T] with a = [0, 1, 19, 20], b = [0, 7, 14, 15] as element indices of the Cayley table (identity = 0; table convention in the note)",
  "origin": "submission",
  "date": "2026-10-17",
  "model": "Claude Opus 5.5",
  "search_budget": {
   "candidates_screened": 9880000,
   "ris_trials_per_side": 30000000,
   "cpu_hours": 3,
   "tool": "research/kit 2BGA sweep + gf2_fast on Brev n2d-highcpu-64"
  }
 },
 "family": "bivariate-bicycle",
 "circuit": {
  "d_circ": {
   "Z": {
    "value": 3,
    "confidence": "upper_bound",
    "witness": [
     4400,
     4402,
     4618
    ]
   },
   "X": {
    "value": 3,
    "confidence": "upper_bound",
    "witness": [
     333,
     351,
     1476
    ]
   }
  },
  "rounds": 4,
  "stim_version": "1.16.0",
  "notes": "Interleaved two-block extraction (Bravyi et al. arXiv:2308.07915 Table 5 style): joint reset and measurement layers, 9 CX layers per round; X-check term slots [1, 6, 7, 2, 5, 4, 8, 3], Z-check term slots [6, 2, 1, 7, 5, 3, 0, 4] over terms A_0..A_3, B_0..B_3; terms recovered from H alone by a commuting permutation decomposition; 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)"
 }
}