{
 "schema_version": "0.1",
 "name": "[[93,29,7]] two-qubit Clifford and exact stabilizer rebasing, incidence635",
 "code_type": "CSS",
 "n": 93,
 "k": 29,
 "checks": {
  "X": [
   [
    6,
    19,
    48,
    50,
    54,
    65,
    67
   ],
   [
    16,
    29,
    33,
    58,
    60,
    75,
    77
   ],
   [
    1,
    8,
    13,
    36,
    52,
    69,
    82
   ],
   [
    31,
    37,
    59,
    71,
    76,
    79,
    87
   ],
   [
    17,
    24,
    28,
    43,
    45,
    64,
    79,
    91
   ],
   [
    13,
    18,
    21,
    29,
    35,
    42,
    44,
    48
   ],
   [
    7,
    22,
    27,
    30,
    44,
    51,
    53,
    57
   ],
   [
    1,
    9,
    24,
    29,
    46,
    53,
    55,
    59
   ],
   [
    36,
    42,
    58,
    61,
    70,
    75,
    78,
    86
   ],
   [
    0,
    6,
    22,
    25,
    63,
    65,
    69,
    87
   ],
   [
    32,
    38,
    44,
    60,
    72,
    77,
    80,
    88
   ],
   [
    5,
    15,
    23,
    34,
    59,
    76,
    79,
    80
   ],
   [
    0,
    3,
    5,
    31,
    39,
    50,
    62,
    68,
    72
   ],
   [
    2,
    5,
    7,
    33,
    41,
    52,
    64,
    70,
    74
   ],
   [
    4,
    7,
    9,
    35,
    43,
    54,
    66,
    72,
    76
   ],
   [
    5,
    9,
    30,
    31,
    34,
    36,
    62,
    70,
    81
   ],
   [
    10,
    13,
    15,
    41,
    49,
    60,
    72,
    78,
    82
   ],
   [
    12,
    18,
    22,
    44,
    47,
    49,
    63,
    75,
    83
   ],
   [
    12,
    15,
    17,
    31,
    43,
    51,
    74,
    80,
    84
   ],
   [
    3,
    9,
    13,
    35,
    38,
    40,
    66,
    74,
    85
   ],
   [
    14,
    17,
    19,
    33,
    45,
    53,
    76,
    82,
    86
   ],
   [
    0,
    26,
    29,
    34,
    45,
    57,
    63,
    67,
    88
   ],
   [
    16,
    19,
    21,
    35,
    47,
    55,
    78,
    84,
    88
   ],
   [
    22,
    28,
    30,
    46,
    74,
    83,
    86,
    87,
    89
   ],
   [
    8,
    14,
    20,
    25,
    52,
    54,
    64,
    85,
    90
   ],
   [
    18,
    21,
    23,
    37,
    49,
    57,
    80,
    86,
    90
   ],
   [
    14,
    16,
    18,
    43,
    51,
    62,
    66,
    68,
    91
   ],
   [
    7,
    9,
    10,
    40,
    44,
    54,
    56,
    70,
    92
   ],
   [
    2,
    4,
    30,
    38,
    49,
    61,
    67,
    71,
    92
   ],
   [
    10,
    16,
    20,
    42,
    45,
    47,
    73,
    81,
    92
   ],
   [
    20,
    23,
    25,
    39,
    51,
    59,
    82,
    88,
    92
   ],
   [
    6,
    8,
    35,
    51,
    56,
    64,
    67,
    83,
    86,
    89
   ],
   [
    0,
    4,
    11,
    12,
    27,
    28,
    34,
    41,
    62,
    68,
    69,
    75
   ],
   [
    4,
    6,
    11,
    27,
    40,
    41,
    56,
    59,
    71,
    73,
    76,
    84
   ]
  ],
  "Z": [
   [
    19,
    21,
    32,
    48,
    58,
    77,
    86,
    89
   ],
   [
    1,
    8,
    21,
    24,
    35,
    66,
    90,
    91
   ],
   [
    1,
    5,
    14,
    37,
    41,
    59,
    62,
    82,
    90
   ],
   [
    10,
    34,
    43,
    62,
    71,
    72,
    79,
    84,
    88,
    92
   ],
   [
    0,
    23,
    25,
    28,
    38,
    50,
    64,
    67,
    74,
    80
   ],
   [
    11,
    16,
    27,
    44,
    47,
    48,
    54,
    66,
    77,
    85
   ],
   [
    12,
    17,
    19,
    28,
    37,
    49,
    61,
    65,
    78,
    87
   ],
   [
    14,
    18,
    42,
    47,
    49,
    61,
    78,
    83,
    86,
    90
   ],
   [
    16,
    20,
    22,
    29,
    35,
    43,
    46,
    51,
    63,
    85,
    91
   ],
   [
    3,
    5,
    12,
    30,
    34,
    49,
    57,
    60,
    62,
    68,
    74,
    77
   ],
   [
    0,
    4,
    6,
    13,
    35,
    50,
    58,
    61,
    63,
    69,
    75,
    78
   ],
   [
    1,
    5,
    7,
    14,
    31,
    36,
    51,
    59,
    64,
    70,
    76,
    79
   ],
   [
    2,
    6,
    8,
    15,
    32,
    37,
    52,
    60,
    65,
    71,
    77,
    80
   ],
   [
    3,
    7,
    9,
    16,
    33,
    38,
    53,
    61,
    66,
    72,
    78,
    81
   ],
   [
    4,
    8,
    10,
    17,
    31,
    34,
    39,
    54,
    67,
    73,
    79,
    82
   ],
   [
    5,
    9,
    11,
    18,
    32,
    35,
    40,
    55,
    68,
    74,
    80,
    83
   ],
   [
    6,
    10,
    12,
    19,
    33,
    36,
    41,
    56,
    69,
    75,
    81,
    84
   ],
   [
    7,
    11,
    13,
    20,
    34,
    37,
    42,
    57,
    70,
    76,
    82,
    85
   ],
   [
    0,
    18,
    22,
    24,
    37,
    45,
    48,
    53,
    62,
    65,
    81,
    87
   ],
   [
    9,
    13,
    15,
    22,
    36,
    39,
    44,
    59,
    72,
    78,
    84,
    87
   ],
   [
    0,
    7,
    25,
    29,
    44,
    52,
    55,
    60,
    63,
    69,
    72,
    88
   ],
   [
    10,
    14,
    16,
    23,
    37,
    40,
    45,
    60,
    73,
    79,
    85,
    88
   ],
   [
    1,
    8,
    26,
    30,
    45,
    53,
    56,
    61,
    64,
    70,
    73,
    89
   ],
   [
    2,
    20,
    24,
    26,
    39,
    47,
    50,
    55,
    64,
    67,
    83,
    89
   ],
   [
    11,
    15,
    17,
    24,
    38,
    41,
    46,
    61,
    74,
    80,
    86,
    89
   ],
   [
    0,
    2,
    9,
    27,
    31,
    46,
    54,
    57,
    65,
    71,
    74,
    90
   ],
   [
    3,
    21,
    25,
    27,
    40,
    48,
    51,
    56,
    65,
    68,
    84,
    90
   ],
   [
    4,
    22,
    26,
    28,
    41,
    49,
    52,
    57,
    66,
    69,
    85,
    91
   ],
   [
    2,
    4,
    11,
    29,
    33,
    48,
    56,
    59,
    67,
    73,
    76,
    92
   ],
   [
    17,
    21,
    23,
    30,
    36,
    44,
    47,
    52,
    64,
    80,
    86,
    92
   ]
  ]
 },
 "distance": {
  "d": 7,
  "X": {
   "value": 7,
   "confidence": "upper_bound",
   "witness": [
    7,
    14,
    30,
    37,
    49,
    52,
    53
   ]
  },
  "Z": {
   "value": 7,
   "confidence": "upper_bound",
   "witness": [
    2,
    8,
    32,
    38,
    40,
    52,
    56
   ]
  }
 },
 "provenance": {
  "authors": [
   "@hirobumii"
  ],
  "construction": "Apply physical CNOT(control79,target43), zero-based, to the source93/29/7 I636 CSS stabilizer group, then use the explicit minimum-incidence basis from its complete source stabilizer pools through weight13. The source has polynomial-minor seed a=37,b=268566560,c=1140850720 over F2[x]/(x^31+1), followed by the recorded Koszul, rank-hyperplane and physical-kernel changes. Its candidate SHA256 is 7253bc420e645a12e92fb230a8f8a9b0cca82534c202b91e23d28b5d93a004b3. Select X source cap13 pool indices [0, 1, 2, 9, 3, 4, 5, 6, 7, 8, 10, 14, 11, 12, 13, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 36, 39] and Z source cap13 pool indices [0, 1, 2, 3, 4, 5, 6, 7, 27, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29]; transform X target43 by control79 and Z control79 by target43. The supplied literal matrices have ranks34/30 and resource vector(93,29,7,12,9,64,635).",
  "references": [
   "https://arxiv.org/abs/quant-ph/0304125",
   "https://arxiv.org/abs/2601.18879"
  ],
  "date": "2026-10-17",
  "notes": "Displayed presentation: maximum check weight 12, maximum qubit degree 9, 64 checks and total incidence 635.",
  "model": "GPT-6 Astra + GPT-6.1 Sol (recorded multi-agent configuration)"
 },
 "family": "other"
}
