{
 "schema_version": "0.1",
 "name": "[[80,42,5]] physical image w16 D11 I552",
 "code_type": "CSS",
 "n": 80,
 "k": 42,
 "checks": {
  "X": [
   [
    0,
    7,
    15,
    16,
    22,
    30,
    32,
    34,
    57,
    59,
    67
   ],
   [
    5,
    6,
    21,
    23,
    26,
    34,
    35,
    43,
    50,
    52,
    54,
    56,
    66,
    69,
    77
   ],
   [
    8,
    11,
    15,
    18,
    19,
    24,
    25,
    30,
    40,
    50,
    60,
    73,
    75
   ],
   [
    4,
    13,
    14,
    20,
    24,
    38,
    39,
    50,
    52,
    61,
    63,
    73,
    78
   ],
   [
    12,
    18,
    19,
    20,
    26,
    27,
    28,
    47,
    49,
    68,
    69,
    77,
    79
   ],
   [
    1,
    12,
    13,
    16,
    28,
    34,
    38,
    46,
    55,
    61,
    64,
    67,
    77,
    78
   ],
   [
    3,
    4,
    15,
    18,
    21,
    30,
    36,
    37,
    38,
    46,
    53,
    63,
    65,
    69,
    73
   ],
   [
    0,
    4,
    18,
    21,
    23,
    24,
    25,
    29,
    39,
    41,
    43,
    44,
    51,
    64,
    70,
    75
   ],
   [
    6,
    14,
    18,
    20,
    35,
    36,
    44,
    47,
    49,
    59,
    63,
    65,
    70,
    71,
    72,
    76
   ],
   [
    0,
    8,
    21,
    23,
    25,
    34,
    42,
    45,
    50,
    51,
    55,
    58,
    63,
    66,
    70,
    78
   ],
   [
    3,
    9,
    23,
    26,
    27,
    33,
    36,
    41,
    48,
    50,
    58,
    68,
    71,
    73,
    77,
    78
   ],
   [
    0,
    2,
    11,
    13,
    33,
    36,
    41,
    44,
    50,
    51,
    53,
    64,
    65,
    76,
    78
   ],
   [
    1,
    2,
    6,
    7,
    19,
    22,
    28,
    32,
    40,
    59,
    60,
    69,
    72,
    79
   ],
   [
    5,
    10,
    13,
    14,
    19,
    31,
    37,
    47,
    49,
    52,
    53,
    62,
    64,
    68,
    70
   ],
   [
    5,
    16,
    26,
    27,
    29,
    31,
    32,
    43,
    45,
    56,
    60,
    64,
    69,
    70,
    73
   ],
   [
    6,
    11,
    17,
    19,
    31,
    36,
    37,
    45,
    47,
    48,
    60,
    64,
    67,
    68,
    71,
    75
   ],
   [
    3,
    9,
    11,
    13,
    14,
    17,
    25,
    27,
    36,
    39,
    48,
    56,
    57,
    62,
    74,
    75
   ],
   [
    1,
    7,
    9,
    17,
    25,
    30,
    33,
    39,
    42,
    56,
    65,
    67,
    71,
    72,
    74,
    78
   ],
   [
    2,
    3,
    7,
    12,
    14,
    29,
    31,
    35,
    41,
    42,
    49,
    56,
    57,
    65,
    76,
    78
   ]
  ],
  "Z": [
   [
    4,
    9,
    36,
    44,
    50,
    51,
    58,
    66,
    74,
    75
   ],
   [
    8,
    15,
    21,
    27,
    33,
    35,
    47,
    48,
    58,
    59,
    70,
    72,
    76
   ],
   [
    12,
    17,
    25,
    26,
    36,
    39,
    44,
    46,
    49,
    58,
    60,
    63,
    69,
    70,
    71
   ],
   [
    8,
    9,
    10,
    17,
    19,
    27,
    34,
    38,
    41,
    45,
    51,
    54,
    57,
    60,
    73
   ],
   [
    2,
    5,
    15,
    28,
    30,
    32,
    35,
    37,
    45,
    54,
    55,
    57,
    69,
    74,
    76
   ],
   [
    5,
    13,
    17,
    20,
    22,
    42,
    45,
    48,
    52,
    58,
    59,
    68,
    74,
    78
   ],
   [
    1,
    4,
    5,
    8,
    10,
    29,
    35,
    56,
    57,
    59,
    63,
    65,
    66,
    73,
    78
   ],
   [
    3,
    10,
    18,
    31,
    33,
    40,
    42,
    53,
    55,
    64,
    65,
    74,
    79
   ],
   [
    2,
    6,
    13,
    14,
    16,
    26,
    29,
    30,
    42,
    43,
    50,
    53,
    55,
    58,
    61,
    68
   ],
   [
    4,
    7,
    20,
    25,
    29,
    31,
    32,
    39,
    44,
    52,
    60,
    62,
    69,
    70,
    74,
    76
   ],
   [
    1,
    5,
    6,
    17,
    20,
    37,
    40,
    46,
    47,
    48,
    49,
    50,
    58,
    65,
    69,
    71
   ],
   [
    0,
    2,
    18,
    23,
    27,
    28,
    55,
    56,
    61,
    67,
    68,
    70,
    73
   ],
   [
    2,
    5,
    7,
    8,
    15,
    19,
    25,
    35,
    36,
    47,
    49,
    60,
    62,
    68,
    75
   ],
   [
    7,
    14,
    15,
    18,
    28,
    29,
    38,
    43,
    47,
    48,
    51,
    55,
    65,
    77
   ],
   [
    0,
    11,
    12,
    17,
    18,
    24,
    25,
    32,
    35,
    41,
    51,
    56,
    65,
    72,
    78
   ],
   [
    11,
    13,
    17,
    19,
    23,
    35,
    40,
    50,
    56,
    62,
    64,
    72,
    74,
    79
   ],
   [
    3,
    7,
    9,
    16,
    18,
    24,
    28,
    37,
    38,
    46,
    51,
    61,
    63,
    64
   ],
   [
    2,
    9,
    11,
    15,
    22,
    25,
    30,
    32,
    34,
    41,
    56,
    67,
    72,
    76
   ],
   [
    1,
    6,
    18,
    21,
    24,
    41,
    43,
    51,
    53,
    58,
    68,
    69,
    78,
    79
   ]
  ]
 },
 "distance": {
  "d": 5,
  "X": {
   "value": 5,
   "confidence": "upper_bound",
   "witness": [
    11,
    12,
    13,
    22,
    26
   ]
  },
  "Z": {
   "value": 5,
   "confidence": "upper_bound",
   "witness": [
    2,
    11,
    14,
    19,
    20
   ]
  }
 },
 "provenance": {
  "authors": [
   "@hirobumii"
  ],
  "construction": "Take the explicitly recorded coefficient hyperplane(s) in the accepted80/41/5 parent, then apply the recorded ordered physical CNOT sequence.",
  "references": [],
  "date": "2026-10-18",
  "notes": "Displayed presentation: maximum check weight 16, maximum qubit degree 11, 38 checks and total incidence 552.",
  "model": "GPT-6 Astra + GPT-6.1 Sol (recorded multi-agent configuration)"
 }
}
