{
 "schema_version": "0.2",
 "name": "[[54,21,3]]",
 "code_type": "CSS",
 "n": 54,
 "k": 21,
 "checks": {
  "X": [
   [
    3,
    7,
    16,
    33,
    36,
    42
   ],
   [
    10,
    13,
    21,
    42,
    50,
    51
   ],
   [
    0,
    3,
    15,
    39,
    45,
    46
   ],
   [
    21,
    31,
    35,
    39,
    40,
    44
   ],
   [
    12,
    17,
    22,
    25,
    27,
    32
   ],
   [
    1,
    5,
    8,
    14,
    18,
    29
   ],
   [
    1,
    2,
    10,
    19,
    26,
    27
   ],
   [
    6,
    24,
    31,
    34,
    36,
    41
   ],
   [
    0,
    4,
    14,
    17,
    34,
    37
   ],
   [
    5,
    11,
    12,
    13,
    48,
    53
   ],
   [
    8,
    9,
    25,
    43,
    49,
    51
   ],
   [
    7,
    11,
    19,
    28,
    44,
    49
   ],
   [
    6,
    23,
    28,
    38,
    46,
    50
   ],
   [
    9,
    20,
    26,
    37,
    52,
    53
   ],
   [
    4,
    16,
    30,
    35,
    38,
    47
   ],
   [
    15,
    18,
    20,
    30,
    32,
    41
   ]
  ],
  "Z": [
   [
    1,
    2,
    16,
    18,
    30,
    33
   ],
   [
    3,
    10,
    15,
    20,
    26,
    42
   ],
   [
    0,
    1,
    14,
    19,
    39,
    44
   ],
   [
    11,
    12,
    22,
    24,
    31,
    44
   ],
   [
    5,
    11,
    15,
    18,
    28,
    46
   ],
   [
    16,
    22,
    25,
    42,
    47,
    51
   ],
   [
    2,
    26,
    31,
    34,
    37,
    40
   ],
   [
    5,
    29,
    35,
    40,
    47,
    48
   ],
   [
    4,
    10,
    17,
    21,
    27,
    35
   ],
   [
    4,
    8,
    14,
    23,
    38,
    43
   ],
   [
    6,
    20,
    23,
    41,
    48,
    53
   ],
   [
    13,
    21,
    39,
    45,
    52,
    53
   ],
   [
    9,
    24,
    33,
    36,
    43,
    52
   ],
   [
    3,
    7,
    8,
    29,
    45,
    49
   ],
   [
    6,
    17,
    25,
    28,
    34,
    49
   ],
   [
    0,
    9,
    37,
    46,
    50,
    51
   ],
   [
    12,
    13,
    30,
    32,
    38,
    50
   ]
  ]
 },
 "distance": {
  "d": 3,
  "X": {
   "value": 4,
   "confidence": "upper_bound",
   "witness": [
    12,
    14,
    38,
    44
   ]
  },
  "Z": {
   "value": 3,
   "confidence": "upper_bound",
   "witness": [
    16,
    33,
    47
   ]
  }
 },
 "provenance": {
  "authors": [
   "@vprusso"
  ],
  "model": "Claude Opus 5",
  "novelty": "known_parameters",
  "origin": "submission",
  "date": "2026-09-21",
  "construction": "Check deletion from the board entry [[54,20,4]] (codes/54-20-4.json): row 2 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",
 "locality": {
  "coordinates": [
   [
    2.0,
    1.0
   ],
   [
    1.0,
    3.0
   ],
   [
    0.0,
    3.0
   ],
   [
    0.0,
    2.0
   ],
   [
    5.0,
    1.0
   ],
   [
    5.0,
    3.0
   ],
   [
    5.0,
    2.0
   ],
   [
    0.0,
    1.0
   ],
   [
    2.0,
    0.0
   ],
   [
    1.0,
    2.0
   ],
   [
    3.0,
    0.0
   ],
   [
    3.0,
    1.0
   ],
   [
    6.0,
    3.0
   ],
   [
    4.0,
    2.0
   ],
   [
    3.0,
    3.0
   ],
   [
    3.0,
    0.0
   ],
   [
    4.0,
    3.0
   ],
   [
    5.0,
    1.0
   ],
   [
    3.0,
    3.0
   ],
   [
    0.0,
    1.0
   ],
   [
    3.0,
    2.0
   ],
   [
    2.0,
    2.0
   ],
   [
    6.0,
    1.0
   ],
   [
    6.0,
    1.0
   ],
   [
    2.0,
    3.0
   ],
   [
    5.0,
    0.0
   ],
   [
    0.0,
    2.0
   ],
   [
    3.0,
    1.0
   ],
   [
    4.0,
    2.0
   ],
   [
    2.0,
    0.0
   ],
   [
    4.0,
    3.0
   ],
   [
    2.0,
    3.0
   ],
   [
    6.0,
    2.0
   ],
   [
    0.0,
    3.0
   ],
   [
    1.0,
    1.0
   ],
   [
    4.0,
    0.0
   ],
   [
    1.0,
    3.0
   ],
   [
    1.0,
    2.0
   ],
   [
    6.0,
    0.0
   ],
   [
    1.0,
    0.0
   ],
   [
    2.0,
    1.0
   ],
   [
    5.0,
    2.0
   ],
   [
    4.0,
    1.0
   ],
   [
    2.0,
    2.0
   ],
   [
    4.0,
    0.0
   ],
   [
    1.0,
    0.0
   ],
   [
    4.0,
    1.0
   ],
   [
    6.0,
    0.0
   ],
   [
    6.0,
    2.0
   ],
   [
    1.0,
    1.0
   ],
   [
    5.0,
    3.0
   ],
   [
    5.0,
    0.0
   ],
   [
    0.0,
    0.0
   ],
   [
    3.0,
    2.0
   ]
  ],
  "layers": 2,
  "interaction_radius": 4.4722,
  "contributed_by": {
   "by": [
    "@dorakingx"
   ],
   "date": "2026-10-02",
   "method": "Simulated annealing over site assignments on an integer grid with the repo's own research/local2d/fold_layout.search_layout (max-diameter objective, several bounding boxes and seeds); single layer at radius 4 tried first, then two layers at 7. Radius and per-site occupancy re-measured with the verifier's rule."
  }
 }
}
