{
 "schema_version": "0.2",
 "name": "gap-111-12-11",
 "code_type": "CSS",
 "n": 111,
 "k": 12,
 "checks": {
  "X": [
   [
    0,
    32,
    45,
    55,
    56,
    82,
    95,
    105
   ],
   [
    2,
    26,
    50,
    57,
    68,
    88,
    89,
    109
   ],
   [
    1,
    3,
    40,
    58,
    59,
    61,
    90,
    103
   ],
   [
    4,
    41,
    52,
    59,
    62,
    73,
    97,
    104
   ],
   [
    5,
    39,
    47,
    60,
    64,
    92,
    93,
    110
   ],
   [
    0,
    6,
    51,
    58,
    61,
    62,
    94,
    106
   ],
   [
    7,
    36,
    49,
    59,
    62,
    77,
    101,
    107
   ],
   [
    5,
    8,
    34,
    63,
    64,
    76,
    96,
    97
   ],
   [
    9,
    35,
    54,
    60,
    64,
    79,
    98,
    103
   ],
   [
    6,
    10,
    47,
    57,
    65,
    66,
    69,
    98
   ],
   [
    7,
    11,
    48,
    55,
    66,
    70,
    81,
    109
   ],
   [
    2,
    12,
    46,
    67,
    68,
    72,
    100,
    101
   ],
   [
    13,
    30,
    53,
    57,
    68,
    83,
    102,
    106
   ],
   [
    3,
    14,
    54,
    60,
    65,
    69,
    70,
    102
   ],
   [
    4,
    15,
    44,
    56,
    66,
    70,
    85,
    110
   ],
   [
    12,
    16,
    42,
    55,
    71,
    72,
    84,
    104
   ],
   [
    13,
    17,
    43,
    57,
    67,
    72,
    87,
    105
   ],
   [
    2,
    14,
    18,
    63,
    73,
    74,
    77,
    105
   ],
   [
    15,
    19,
    53,
    58,
    64,
    74,
    78,
    89
   ],
   [
    8,
    20,
    52,
    56,
    75,
    76,
    80,
    107
   ],
   [
    9,
    21,
    38,
    60,
    63,
    76,
    91,
    108
   ],
   [
    10,
    13,
    22,
    67,
    73,
    77,
    78,
    108
   ],
   [
    11,
    23,
    50,
    61,
    68,
    74,
    78,
    93
   ],
   [
    0,
    20,
    24,
    58,
    79,
    80,
    92,
    109
   ],
   [
    21,
    25,
    49,
    59,
    63,
    75,
    80,
    95
   ],
   [
    8,
    22,
    26,
    59,
    71,
    81,
    82,
    85
   ],
   [
    9,
    23,
    27,
    65,
    72,
    82,
    86,
    97
   ],
   [
    7,
    16,
    28,
    61,
    83,
    84,
    88,
    110
   ],
   [
    17,
    29,
    45,
    62,
    67,
    71,
    84,
    99
   ],
   [
    18,
    21,
    30,
    62,
    75,
    81,
    85,
    86
   ],
   [
    5,
    19,
    31,
    69,
    76,
    82,
    86,
    101
   ],
   [
    3,
    28,
    32,
    64,
    65,
    87,
    88,
    100
   ],
   [
    4,
    29,
    33,
    66,
    71,
    83,
    88,
    103
   ],
   [
    16,
    30,
    34,
    66,
    79,
    89,
    90,
    93
   ],
   [
    17,
    31,
    35,
    55,
    73,
    80,
    90,
    94
   ],
   [
    15,
    24,
    36,
    68,
    69,
    91,
    92,
    96
   ],
   [
    1,
    25,
    37,
    70,
    75,
    79,
    92,
    106
   ],
   [
    26,
    29,
    38,
    70,
    83,
    89,
    93,
    94
   ],
   [
    12,
    27,
    39,
    56,
    77,
    84,
    90,
    94
   ],
   [
    10,
    36,
    40,
    72,
    73,
    95,
    96,
    107
   ],
   [
    11,
    37,
    41,
    57,
    74,
    79,
    91,
    96
   ],
   [
    24,
    38,
    42,
    74,
    87,
    97,
    98,
    101
   ],
   [
    25,
    39,
    43,
    58,
    81,
    88,
    98,
    102
   ],
   [
    23,
    32,
    44,
    76,
    77,
    99,
    100,
    104
   ],
   [
    34,
    37,
    45,
    78,
    91,
    97,
    101,
    102
   ],
   [
    20,
    35,
    46,
    61,
    85,
    92,
    98,
    102
   ],
   [
    18,
    44,
    47,
    80,
    81,
    103,
    104,
    110
   ],
   [
    33,
    46,
    49,
    65,
    89,
    96,
    105,
    108
   ],
   [
    31,
    40,
    50,
    84,
    85,
    106,
    107,
    109
   ]
  ],
  "Z": [
   [
    0,
    1,
    11,
    16,
    35,
    55,
    61,
    79
   ],
   [
    0,
    1,
    15,
    20,
    39,
    56,
    58,
    92
   ],
   [
    2,
    10,
    13,
    17,
    41,
    57,
    67,
    73
   ],
   [
    3,
    6,
    19,
    24,
    43,
    58,
    69,
    87
   ],
   [
    3,
    4,
    7,
    25,
    26,
    59,
    70,
    88
   ],
   [
    5,
    9,
    14,
    21,
    60,
    63,
    86
   ],
   [
    3,
    6,
    23,
    28,
    46,
    61,
    65,
    100
   ],
   [
    4,
    6,
    7,
    29,
    30,
    62,
    66,
    83
   ],
   [
    8,
    18,
    21,
    25,
    48,
    63,
    75,
    81
   ],
   [
    5,
    8,
    9,
    19,
    32,
    64,
    76,
    82
   ],
   [
    10,
    14,
    27,
    32,
    49,
    65,
    77,
    95
   ],
   [
    10,
    11,
    15,
    33,
    34,
    66,
    78,
    96
   ],
   [
    12,
    17,
    22,
    29,
    51,
    67,
    71,
    94
   ],
   [
    2,
    12,
    13,
    23,
    36,
    68,
    72,
    77
   ],
   [
    10,
    14,
    31,
    36,
    52,
    69,
    73,
    107
   ],
   [
    11,
    14,
    15,
    37,
    38,
    70,
    74,
    91
   ],
   [
    16,
    26,
    29,
    33,
    53,
    71,
    83,
    89
   ],
   [
    12,
    16,
    17,
    27,
    40,
    72,
    84,
    90
   ],
   [
    4,
    18,
    22,
    35,
    40,
    73,
    85,
    103
   ],
   [
    18,
    19,
    23,
    41,
    42,
    74,
    86,
    104
   ],
   [
    20,
    25,
    30,
    37,
    54,
    75,
    79,
    102
   ],
   [
    8,
    20,
    21,
    31,
    44,
    76,
    80,
    85
   ],
   [
    7,
    18,
    22,
    39,
    44,
    77,
    81,
    110
   ],
   [
    19,
    22,
    23,
    45,
    78,
    82,
    99
   ],
   [
    9,
    24,
    34,
    37,
    41,
    79,
    91,
    97
   ],
   [
    20,
    24,
    25,
    35,
    47,
    80,
    92,
    98
   ],
   [
    11,
    26,
    30,
    43,
    47,
    57,
    81,
    93
   ],
   [
    0,
    26,
    27,
    31,
    48,
    82,
    94,
    109
   ],
   [
    13,
    28,
    33,
    38,
    83,
    87,
    108
   ],
   [
    16,
    28,
    29,
    39,
    50,
    84,
    88,
    93
   ],
   [
    15,
    26,
    30,
    46,
    50,
    68,
    85,
    89
   ],
   [
    1,
    27,
    30,
    31,
    51,
    86,
    90,
    106
   ],
   [
    17,
    32,
    42,
    48,
    55,
    87,
    99
   ],
   [
    2,
    28,
    32,
    33,
    43,
    88,
    100,
    105
   ],
   [
    2,
    19,
    34,
    38,
    49,
    63,
    89,
    101
   ],
   [
    3,
    34,
    35,
    39,
    53,
    64,
    90,
    102
   ],
   [
    21,
    36,
    41,
    45,
    51,
    62,
    91,
    95
   ],
   [
    5,
    24,
    36,
    37,
    46,
    92,
    96,
    101
   ],
   [
    5,
    23,
    34,
    38,
    52,
    76,
    93,
    97
   ],
   [
    6,
    35,
    38,
    39,
    54,
    60,
    94,
    98
   ],
   [
    0,
    25,
    40,
    51,
    53,
    58,
    95,
    106
   ],
   [
    8,
    36,
    40,
    41,
    49,
    59,
    96,
    107
   ],
   [
    4,
    8,
    27,
    42,
    45,
    56,
    71,
    97
   ],
   [
    9,
    10,
    42,
    43,
    46,
    72,
    98,
    108
   ],
   [
    1,
    29,
    44,
    48,
    54,
    70,
    99,
    103
   ],
   [
    7,
    12,
    31,
    42,
    45,
    55,
    84,
    101
   ],
   [
    13,
    14,
    43,
    45,
    46,
    67,
    102,
    105
   ],
   [
    3,
    9,
    33,
    47,
    54,
    60,
    65,
    103
   ],
   [
    0,
    17,
    18,
    49,
    52,
    62,
    80,
    105
   ],
   [
    6,
    13,
    37,
    50,
    53,
    57,
    78,
    106
   ]
  ]
 },
 "distance": {
  "d": 11,
  "X": {
   "value": 12,
   "confidence": "upper_bound",
   "witness": [
    3,
    18,
    19,
    32,
    48,
    49,
    59,
    64,
    82,
    100,
    103,
    110
   ],
   "witness_provenance": {
    "found_by": [
     "@mathys"
    ],
    "date": "2026-11-02",
    "found_at_samples": 1000,
    "survived_samples": 1000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     0
    ]
   }
  },
  "Z": {
   "value": 11,
   "confidence": "upper_bound",
   "witness": [
    1,
    6,
    16,
    23,
    24,
    34,
    47,
    61,
    92,
    97,
    104
   ],
   "witness_provenance": {
    "found_by": [
     "@mathys"
    ],
    "date": "2026-11-02",
    "found_at_samples": 1000,
    "survived_samples": 1000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "@mathysrennela"
  ],
  "construction": "priced calculus E-PEEL transform of codes/112-12-12.json",
  "references": [],
  "date": "2026-11-02",
  "notes": "",
  "model": "Beam 1.0"
 },
 "locality": {
  "coordinates": [
   [
    3,
    0
   ],
   [
    2,
    4
   ],
   [
    3,
    2
   ],
   [
    7,
    3
   ],
   [
    2,
    0
   ],
   [
    7,
    6
   ],
   [
    5,
    0
   ],
   [
    1,
    2
   ],
   [
    5,
    6
   ],
   [
    6,
    6
   ],
   [
    3,
    5
   ],
   [
    5,
    1
   ],
   [
    0,
    1
   ],
   [
    2,
    2
   ],
   [
    4,
    4
   ],
   [
    7,
    4
   ],
   [
    1,
    0
   ],
   [
    0,
    0
   ],
   [
    0,
    5
   ],
   [
    4,
    6
   ],
   [
    6,
    4
   ],
   [
    3,
    6
   ],
   [
    0,
    4
   ],
   [
    3,
    3
   ],
   [
    6,
    5
   ],
   [
    2,
    5
   ],
   [
    4,
    0
   ],
   [
    0,
    5
   ],
   [
    7,
    0
   ],
   [
    4,
    2
   ],
   [
    2,
    1
   ],
   [
    1,
    4
   ],
   [
    4,
    3
   ],
   [
    7,
    2
   ],
   [
    6,
    1
   ],
   [
    4,
    4
   ],
   [
    2,
    6
   ],
   [
    6,
    5
   ],
   [
    7,
    4
   ],
   [
    2,
    2
   ],
   [
    1,
    3
   ],
   [
    3,
    4
   ],
   [
    2,
    3
   ],
   [
    6,
    2
   ],
   [
    1,
    6
   ],
   [
    0,
    3
   ],
   [
    5,
    2
   ],
   [
    4,
    3
   ],
   [
    0,
    3
   ],
   [
    3,
    3
   ],
   [
    6,
    0
   ],
   [
    0,
    1
   ],
   [
    4,
    1
   ],
   [
    4,
    1
   ],
   [
    5,
    6
   ],
   [
    1,
    1
   ],
   [
    2,
    5
   ],
   [
    6,
    1
   ],
   [
    4,
    0
   ],
   [
    1,
    3
   ],
   [
    7,
    6
   ],
   [
    6,
    0
   ],
   [
    0,
    0
   ],
   [
    3,
    5
   ],
   [
    7,
    3
   ],
   [
    5,
    5
   ],
   [
    5,
    1
   ],
   [
    0,
    4
   ],
   [
    5,
    3
   ],
   [
    6,
    2
   ],
   [
    5,
    3
   ],
   [
    1,
    1
   ],
   [
    1,
    5
   ],
   [
    0,
    2
   ],
   [
    3,
    4
   ],
   [
    2,
    6
   ],
   [
    6,
    6
   ],
   [
    0,
    6
   ],
   [
    4,
    5
   ],
   [
    7,
    2
   ],
   [
    3,
    6
   ],
   [
    1,
    2
   ],
   [
    4,
    6
   ],
   [
    5,
    0
   ],
   [
    1,
    0
   ],
   [
    5,
    4
   ],
   [
    1,
    5
   ],
   [
    3,
    2
   ],
   [
    7,
    1
   ],
   [
    7,
    1
   ],
   [
    2,
    1
   ],
   [
    4,
    2
   ],
   [
    7,
    5
   ],
   [
    7,
    0
   ],
   [
    3,
    1
   ],
   [
    0,
    2
   ],
   [
    6,
    3
   ],
   [
    5,
    2
   ],
   [
    7,
    5
   ],
   [
    0,
    6
   ],
   [
    5,
    4
   ],
   [
    2,
    4
   ],
   [
    6,
    4
   ],
   [
    4,
    5
   ],
   [
    1,
    6
   ],
   [
    2,
    0
   ],
   [
    3,
    0
   ],
   [
    1,
    4
   ],
   [
    5,
    5
   ],
   [
    6,
    3
   ],
   [
    3,
    1
   ]
  ],
  "layers": 2,
  "contributed_by": {
   "by": [
    "@vprusso"
   ],
   "date": "2026-11-04",
   "method": "Inherited from the laid-out parent codes/112-12-12.json: the parent's coordinates with the entry of the removed qubit (parent index 45) dropped, since this peel child keeps the parent's qubit order. Radius, layer count, and class re-measured by the verifier."
  }
 }
}