{
 "schema_version": "0.1",
 "name": "[[85,41,5]]",
 "code_type": "CSS",
 "n": 85,
 "k": 41,
 "checks": {
  "X": [
   [
    0,
    2,
    3,
    9,
    12,
    13,
    18,
    21,
    22,
    27,
    30,
    31,
    32,
    34,
    36,
    38,
    43,
    46,
    48,
    49,
    52,
    54,
    56,
    61
   ],
   [
    1,
    3,
    4,
    10,
    13,
    14,
    19,
    22,
    23,
    28,
    31,
    32,
    33,
    35,
    37,
    39,
    44,
    47,
    49,
    50,
    53,
    55,
    57,
    62
   ],
   [
    2,
    4,
    5,
    11,
    14,
    15,
    20,
    23,
    24,
    29,
    32,
    33,
    34,
    36,
    38,
    40,
    45,
    48,
    50,
    51,
    54,
    56,
    58,
    63
   ],
   [
    3,
    5,
    6,
    12,
    15,
    16,
    21,
    24,
    25,
    30,
    33,
    34,
    35,
    37,
    39,
    41,
    46,
    49,
    51,
    52,
    55,
    57,
    59,
    64
   ],
   [
    4,
    6,
    7,
    13,
    16,
    17,
    22,
    25,
    26,
    31,
    34,
    35,
    36,
    38,
    40,
    42,
    47,
    50,
    52,
    53,
    56,
    58,
    60,
    65
   ],
   [
    5,
    7,
    8,
    14,
    17,
    18,
    23,
    26,
    27,
    32,
    35,
    36,
    37,
    39,
    41,
    43,
    48,
    51,
    53,
    54,
    57,
    59,
    61,
    66
   ],
   [
    6,
    8,
    9,
    15,
    18,
    19,
    24,
    27,
    28,
    33,
    36,
    37,
    38,
    40,
    42,
    44,
    49,
    52,
    54,
    55,
    58,
    60,
    62,
    67
   ],
   [
    10,
    12,
    13,
    19,
    22,
    23,
    28,
    31,
    32,
    37,
    40,
    41,
    42,
    44,
    46,
    48,
    53,
    56,
    58,
    59,
    62,
    64,
    66,
    71
   ],
   [
    11,
    13,
    14,
    20,
    23,
    24,
    29,
    32,
    33,
    38,
    41,
    42,
    43,
    45,
    47,
    49,
    54,
    57,
    59,
    60,
    63,
    65,
    67,
    72
   ],
   [
    12,
    14,
    15,
    21,
    24,
    25,
    30,
    33,
    34,
    39,
    42,
    43,
    44,
    46,
    48,
    50,
    55,
    58,
    60,
    61,
    64,
    66,
    68,
    73
   ],
   [
    13,
    15,
    16,
    22,
    25,
    26,
    31,
    34,
    35,
    40,
    43,
    44,
    45,
    47,
    49,
    51,
    56,
    59,
    61,
    62,
    65,
    67,
    69,
    74
   ],
   [
    14,
    16,
    17,
    23,
    26,
    27,
    32,
    35,
    36,
    41,
    44,
    45,
    46,
    48,
    50,
    52,
    57,
    60,
    62,
    63,
    66,
    68,
    70,
    75
   ],
   [
    15,
    17,
    18,
    24,
    27,
    28,
    33,
    36,
    37,
    42,
    45,
    46,
    47,
    49,
    51,
    53,
    58,
    61,
    63,
    64,
    67,
    69,
    71,
    76
   ],
   [
    16,
    18,
    19,
    25,
    28,
    29,
    34,
    37,
    38,
    43,
    46,
    47,
    48,
    50,
    52,
    54,
    59,
    62,
    64,
    65,
    68,
    70,
    72,
    77
   ],
   [
    17,
    19,
    20,
    26,
    29,
    30,
    35,
    38,
    39,
    44,
    47,
    48,
    49,
    51,
    53,
    55,
    60,
    63,
    65,
    66,
    69,
    71,
    73,
    78
   ],
   [
    18,
    20,
    21,
    27,
    30,
    31,
    36,
    39,
    40,
    45,
    48,
    49,
    50,
    52,
    54,
    56,
    61,
    64,
    66,
    67,
    70,
    72,
    74,
    79
   ],
   [
    19,
    21,
    22,
    28,
    31,
    32,
    37,
    40,
    41,
    46,
    49,
    50,
    51,
    53,
    55,
    57,
    62,
    65,
    67,
    68,
    71,
    73,
    75,
    80
   ],
   [
    20,
    22,
    23,
    29,
    32,
    33,
    38,
    41,
    42,
    47,
    50,
    51,
    52,
    54,
    56,
    58,
    63,
    66,
    68,
    69,
    72,
    74,
    76,
    81
   ],
   [
    21,
    23,
    24,
    30,
    33,
    34,
    39,
    42,
    43,
    48,
    51,
    52,
    53,
    55,
    57,
    59,
    64,
    67,
    69,
    70,
    73,
    75,
    77,
    82
   ],
   [
    22,
    24,
    25,
    31,
    34,
    35,
    40,
    43,
    44,
    49,
    52,
    53,
    54,
    56,
    58,
    60,
    65,
    68,
    70,
    71,
    74,
    76,
    78,
    83
   ],
   [
    23,
    25,
    26,
    32,
    35,
    36,
    41,
    44,
    45,
    50,
    53,
    54,
    55,
    57,
    59,
    61,
    66,
    69,
    71,
    72,
    75,
    77,
    79,
    84
   ]
  ],
  "Z": [
   [
    0,
    2,
    3,
    9,
    12,
    13,
    18,
    21,
    22,
    27,
    30,
    31,
    32,
    34,
    36,
    38,
    43,
    46,
    48,
    49,
    52,
    54,
    56,
    61
   ],
   [
    1,
    3,
    4,
    10,
    13,
    14,
    19,
    22,
    23,
    28,
    31,
    32,
    33,
    35,
    37,
    39,
    44,
    47,
    49,
    50,
    53,
    55,
    57,
    62
   ],
   [
    2,
    4,
    5,
    11,
    14,
    15,
    20,
    23,
    24,
    29,
    32,
    33,
    34,
    36,
    38,
    40,
    45,
    48,
    50,
    51,
    54,
    56,
    58,
    63
   ],
   [
    3,
    5,
    6,
    12,
    15,
    16,
    21,
    24,
    25,
    30,
    33,
    34,
    35,
    37,
    39,
    41,
    46,
    49,
    51,
    52,
    55,
    57,
    59,
    64
   ],
   [
    4,
    6,
    7,
    13,
    16,
    17,
    22,
    25,
    26,
    31,
    34,
    35,
    36,
    38,
    40,
    42,
    47,
    50,
    52,
    53,
    56,
    58,
    60,
    65
   ],
   [
    5,
    7,
    8,
    14,
    17,
    18,
    23,
    26,
    27,
    32,
    35,
    36,
    37,
    39,
    41,
    43,
    48,
    51,
    53,
    54,
    57,
    59,
    61,
    66
   ],
   [
    6,
    8,
    9,
    15,
    18,
    19,
    24,
    27,
    28,
    33,
    36,
    37,
    38,
    40,
    42,
    44,
    49,
    52,
    54,
    55,
    58,
    60,
    62,
    67
   ],
   [
    8,
    10,
    11,
    17,
    20,
    21,
    26,
    29,
    30,
    35,
    38,
    39,
    40,
    42,
    44,
    46,
    51,
    54,
    56,
    57,
    60,
    62,
    64,
    69
   ],
   [
    9,
    11,
    12,
    18,
    21,
    22,
    27,
    30,
    31,
    36,
    39,
    40,
    41,
    43,
    45,
    47,
    52,
    55,
    57,
    58,
    61,
    63,
    65,
    70
   ],
   [
    10,
    12,
    13,
    19,
    22,
    23,
    28,
    31,
    32,
    37,
    40,
    41,
    42,
    44,
    46,
    48,
    53,
    56,
    58,
    59,
    62,
    64,
    66,
    71
   ],
   [
    11,
    13,
    14,
    20,
    23,
    24,
    29,
    32,
    33,
    38,
    41,
    42,
    43,
    45,
    47,
    49,
    54,
    57,
    59,
    60,
    63,
    65,
    67,
    72
   ],
   [
    12,
    14,
    15,
    21,
    24,
    25,
    30,
    33,
    34,
    39,
    42,
    43,
    44,
    46,
    48,
    50,
    55,
    58,
    60,
    61,
    64,
    66,
    68,
    73
   ],
   [
    13,
    15,
    16,
    22,
    25,
    26,
    31,
    34,
    35,
    40,
    43,
    44,
    45,
    47,
    49,
    51,
    56,
    59,
    61,
    62,
    65,
    67,
    69,
    74
   ],
   [
    14,
    16,
    17,
    23,
    26,
    27,
    32,
    35,
    36,
    41,
    44,
    45,
    46,
    48,
    50,
    52,
    57,
    60,
    62,
    63,
    66,
    68,
    70,
    75
   ],
   [
    15,
    17,
    18,
    24,
    27,
    28,
    33,
    36,
    37,
    42,
    45,
    46,
    47,
    49,
    51,
    53,
    58,
    61,
    63,
    64,
    67,
    69,
    71,
    76
   ],
   [
    16,
    18,
    19,
    25,
    28,
    29,
    34,
    37,
    38,
    43,
    46,
    47,
    48,
    50,
    52,
    54,
    59,
    62,
    64,
    65,
    68,
    70,
    72,
    77
   ],
   [
    17,
    19,
    20,
    26,
    29,
    30,
    35,
    38,
    39,
    44,
    47,
    48,
    49,
    51,
    53,
    55,
    60,
    63,
    65,
    66,
    69,
    71,
    73,
    78
   ],
   [
    18,
    20,
    21,
    27,
    30,
    31,
    36,
    39,
    40,
    45,
    48,
    49,
    50,
    52,
    54,
    56,
    61,
    64,
    66,
    67,
    70,
    72,
    74,
    79
   ],
   [
    19,
    21,
    22,
    28,
    31,
    32,
    37,
    40,
    41,
    46,
    49,
    50,
    51,
    53,
    55,
    57,
    62,
    65,
    67,
    68,
    71,
    73,
    75,
    80
   ],
   [
    20,
    22,
    23,
    29,
    32,
    33,
    38,
    41,
    42,
    47,
    50,
    51,
    52,
    54,
    56,
    58,
    63,
    66,
    68,
    69,
    72,
    74,
    76,
    81
   ],
   [
    21,
    23,
    24,
    30,
    33,
    34,
    39,
    42,
    43,
    48,
    51,
    52,
    53,
    55,
    57,
    59,
    64,
    67,
    69,
    70,
    73,
    75,
    77,
    82
   ],
   [
    22,
    24,
    25,
    31,
    34,
    35,
    40,
    43,
    44,
    49,
    52,
    53,
    54,
    56,
    58,
    60,
    65,
    68,
    70,
    71,
    74,
    76,
    78,
    83
   ],
   [
    23,
    25,
    26,
    32,
    35,
    36,
    41,
    44,
    45,
    50,
    53,
    54,
    55,
    57,
    59,
    61,
    66,
    69,
    71,
    72,
    75,
    77,
    79,
    84
   ]
  ]
 },
 "distance": {
  "d": 5,
  "X": {
   "value": 5,
   "confidence": "upper_bound",
   "witness": [
    7,
    15,
    27,
    34,
    70
   ]
  },
  "Z": {
   "value": 5,
   "confidence": "upper_bound",
   "witness": [
    7,
    15,
    27,
    34,
    70
   ]
  }
 },
 "provenance": {
  "authors": [
   "@vprusso"
  ],
  "model": "Claude Opus 5",
  "novelty": "known_parameters",
  "origin": "submission",
  "date": "2026-09-21",
  "construction": "Check deletion from the board entry [[85,40,5]] (codes/85-40-5.json): row 7 of H_Z 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"
}