{
 "schema_version": "0.4",
 "name": "[[93,6,14]] cyclic mirror",
 "code_type": "stabilizer",
 "n": 93,
 "k": 6,
 "checks": {
  "S": [
   {
    "X": [
     0,
     8,
     25,
     36
    ],
    "Z": [
     0,
     20,
     54,
     92
    ]
   },
   {
    "X": [
     1,
     9,
     26,
     37
    ],
    "Z": [
     19,
     53,
     91,
     92
    ]
   },
   {
    "X": [
     2,
     10,
     27,
     38
    ],
    "Z": [
     18,
     52,
     90,
     91
    ]
   },
   {
    "X": [
     3,
     11,
     28,
     39
    ],
    "Z": [
     17,
     51,
     89,
     90
    ]
   },
   {
    "X": [
     4,
     12,
     29,
     40
    ],
    "Z": [
     16,
     50,
     88,
     89
    ]
   },
   {
    "X": [
     5,
     13,
     30,
     41
    ],
    "Z": [
     15,
     49,
     87,
     88
    ]
   },
   {
    "X": [
     6,
     14,
     31,
     42
    ],
    "Z": [
     14,
     48,
     86,
     87
    ]
   },
   {
    "X": [
     7,
     15,
     32,
     43
    ],
    "Z": [
     13,
     47,
     85,
     86
    ]
   },
   {
    "X": [
     8,
     16,
     33,
     44
    ],
    "Z": [
     12,
     46,
     84,
     85
    ]
   },
   {
    "X": [
     9,
     17,
     34,
     45
    ],
    "Z": [
     11,
     45,
     83,
     84
    ]
   },
   {
    "X": [
     10,
     18,
     35,
     46
    ],
    "Z": [
     10,
     44,
     82,
     83
    ]
   },
   {
    "X": [
     11,
     19,
     36,
     47
    ],
    "Z": [
     9,
     43,
     81,
     82
    ]
   },
   {
    "X": [
     12,
     20,
     37,
     48
    ],
    "Z": [
     8,
     42,
     80,
     81
    ]
   },
   {
    "X": [
     13,
     21,
     38,
     49
    ],
    "Z": [
     7,
     41,
     79,
     80
    ]
   },
   {
    "X": [
     14,
     22,
     39,
     50
    ],
    "Z": [
     6,
     40,
     78,
     79
    ]
   },
   {
    "X": [
     15,
     23,
     40,
     51
    ],
    "Z": [
     5,
     39,
     77,
     78
    ]
   },
   {
    "X": [
     16,
     24,
     41,
     52
    ],
    "Z": [
     4,
     38,
     76,
     77
    ]
   },
   {
    "X": [
     17,
     25,
     42,
     53
    ],
    "Z": [
     3,
     37,
     75,
     76
    ]
   },
   {
    "X": [
     18,
     26,
     43,
     54
    ],
    "Z": [
     2,
     36,
     74,
     75
    ]
   },
   {
    "X": [
     19,
     27,
     44,
     55
    ],
    "Z": [
     1,
     35,
     73,
     74
    ]
   },
   {
    "X": [
     20,
     28,
     45,
     56
    ],
    "Z": [
     0,
     34,
     72,
     73
    ]
   },
   {
    "X": [
     21,
     29,
     46,
     57
    ],
    "Z": [
     33,
     71,
     72,
     92
    ]
   },
   {
    "X": [
     22,
     30,
     47,
     58
    ],
    "Z": [
     32,
     70,
     71,
     91
    ]
   },
   {
    "X": [
     23,
     31,
     48,
     59
    ],
    "Z": [
     31,
     69,
     70,
     90
    ]
   },
   {
    "X": [
     24,
     32,
     49,
     60
    ],
    "Z": [
     30,
     68,
     69,
     89
    ]
   },
   {
    "X": [
     25,
     33,
     50,
     61
    ],
    "Z": [
     29,
     67,
     68,
     88
    ]
   },
   {
    "X": [
     26,
     34,
     51,
     62
    ],
    "Z": [
     28,
     66,
     67,
     87
    ]
   },
   {
    "X": [
     27,
     35,
     52,
     63
    ],
    "Z": [
     27,
     65,
     66,
     86
    ]
   },
   {
    "X": [
     28,
     36,
     53,
     64
    ],
    "Z": [
     26,
     64,
     65,
     85
    ]
   },
   {
    "X": [
     29,
     37,
     54,
     65
    ],
    "Z": [
     25,
     63,
     64,
     84
    ]
   },
   {
    "X": [
     30,
     38,
     55,
     66
    ],
    "Z": [
     24,
     62,
     63,
     83
    ]
   },
   {
    "X": [
     31,
     39,
     56,
     67
    ],
    "Z": [
     23,
     61,
     62,
     82
    ]
   },
   {
    "X": [
     32,
     40,
     57,
     68
    ],
    "Z": [
     22,
     60,
     61,
     81
    ]
   },
   {
    "X": [
     33,
     41,
     58,
     69
    ],
    "Z": [
     21,
     59,
     60,
     80
    ]
   },
   {
    "X": [
     34,
     42,
     59,
     70
    ],
    "Z": [
     20,
     58,
     59,
     79
    ]
   },
   {
    "X": [
     35,
     43,
     60,
     71
    ],
    "Z": [
     19,
     57,
     58,
     78
    ]
   },
   {
    "X": [
     36,
     44,
     61,
     72
    ],
    "Z": [
     18,
     56,
     57,
     77
    ]
   },
   {
    "X": [
     37,
     45,
     62,
     73
    ],
    "Z": [
     17,
     55,
     56,
     76
    ]
   },
   {
    "X": [
     38,
     46,
     63,
     74
    ],
    "Z": [
     16,
     54,
     55,
     75
    ]
   },
   {
    "X": [
     39,
     47,
     64,
     75
    ],
    "Z": [
     15,
     53,
     54,
     74
    ]
   },
   {
    "X": [
     40,
     48,
     65,
     76
    ],
    "Z": [
     14,
     52,
     53,
     73
    ]
   },
   {
    "X": [
     41,
     49,
     66,
     77
    ],
    "Z": [
     13,
     51,
     52,
     72
    ]
   },
   {
    "X": [
     42,
     50,
     67,
     78
    ],
    "Z": [
     12,
     50,
     51,
     71
    ]
   },
   {
    "X": [
     43,
     51,
     68,
     79
    ],
    "Z": [
     11,
     49,
     50,
     70
    ]
   },
   {
    "X": [
     44,
     52,
     69,
     80
    ],
    "Z": [
     10,
     48,
     49,
     69
    ]
   },
   {
    "X": [
     45,
     53,
     70,
     81
    ],
    "Z": [
     9,
     47,
     48,
     68
    ]
   },
   {
    "X": [
     46,
     54,
     71,
     82
    ],
    "Z": [
     8,
     46,
     47,
     67
    ]
   },
   {
    "X": [
     47,
     55,
     72,
     83
    ],
    "Z": [
     7,
     45,
     46,
     66
    ]
   },
   {
    "X": [
     48,
     56,
     73,
     84
    ],
    "Z": [
     6,
     44,
     45,
     65
    ]
   },
   {
    "X": [
     49,
     57,
     74,
     85
    ],
    "Z": [
     5,
     43,
     44,
     64
    ]
   },
   {
    "X": [
     50,
     58,
     75,
     86
    ],
    "Z": [
     4,
     42,
     43,
     63
    ]
   },
   {
    "X": [
     51,
     59,
     76,
     87
    ],
    "Z": [
     3,
     41,
     42,
     62
    ]
   },
   {
    "X": [
     52,
     60,
     77,
     88
    ],
    "Z": [
     2,
     40,
     41,
     61
    ]
   },
   {
    "X": [
     53,
     61,
     78,
     89
    ],
    "Z": [
     1,
     39,
     40,
     60
    ]
   },
   {
    "X": [
     54,
     62,
     79,
     90
    ],
    "Z": [
     0,
     38,
     39,
     59
    ]
   },
   {
    "X": [
     55,
     63,
     80,
     91
    ],
    "Z": [
     37,
     38,
     58,
     92
    ]
   },
   {
    "X": [
     56,
     64,
     81,
     92
    ],
    "Z": [
     36,
     37,
     57,
     91
    ]
   },
   {
    "X": [
     0,
     57,
     65,
     82
    ],
    "Z": [
     35,
     36,
     56,
     90
    ]
   },
   {
    "X": [
     1,
     58,
     66,
     83
    ],
    "Z": [
     34,
     35,
     55,
     89
    ]
   },
   {
    "X": [
     2,
     59,
     67,
     84
    ],
    "Z": [
     33,
     34,
     54,
     88
    ]
   },
   {
    "X": [
     3,
     60,
     68,
     85
    ],
    "Z": [
     32,
     33,
     53,
     87
    ]
   },
   {
    "X": [
     4,
     61,
     69,
     86
    ],
    "Z": [
     31,
     32,
     52,
     86
    ]
   },
   {
    "X": [
     5,
     62,
     70,
     87
    ],
    "Z": [
     30,
     31,
     51,
     85
    ]
   },
   {
    "X": [
     6,
     63,
     71,
     88
    ],
    "Z": [
     29,
     30,
     50,
     84
    ]
   },
   {
    "X": [
     7,
     64,
     72,
     89
    ],
    "Z": [
     28,
     29,
     49,
     83
    ]
   },
   {
    "X": [
     8,
     65,
     73,
     90
    ],
    "Z": [
     27,
     28,
     48,
     82
    ]
   },
   {
    "X": [
     9,
     66,
     74,
     91
    ],
    "Z": [
     26,
     27,
     47,
     81
    ]
   },
   {
    "X": [
     10,
     67,
     75,
     92
    ],
    "Z": [
     25,
     26,
     46,
     80
    ]
   },
   {
    "X": [
     0,
     11,
     68,
     76
    ],
    "Z": [
     24,
     25,
     45,
     79
    ]
   },
   {
    "X": [
     1,
     12,
     69,
     77
    ],
    "Z": [
     23,
     24,
     44,
     78
    ]
   },
   {
    "X": [
     2,
     13,
     70,
     78
    ],
    "Z": [
     22,
     23,
     43,
     77
    ]
   },
   {
    "X": [
     3,
     14,
     71,
     79
    ],
    "Z": [
     21,
     22,
     42,
     76
    ]
   },
   {
    "X": [
     4,
     15,
     72,
     80
    ],
    "Z": [
     20,
     21,
     41,
     75
    ]
   },
   {
    "X": [
     5,
     16,
     73,
     81
    ],
    "Z": [
     19,
     20,
     40,
     74
    ]
   },
   {
    "X": [
     6,
     17,
     74,
     82
    ],
    "Z": [
     18,
     19,
     39,
     73
    ]
   },
   {
    "X": [
     7,
     18,
     75,
     83
    ],
    "Z": [
     17,
     18,
     38,
     72
    ]
   },
   {
    "X": [
     8,
     19,
     76,
     84
    ],
    "Z": [
     16,
     17,
     37,
     71
    ]
   },
   {
    "X": [
     9,
     20,
     77,
     85
    ],
    "Z": [
     15,
     16,
     36,
     70
    ]
   },
   {
    "X": [
     10,
     21,
     78,
     86
    ],
    "Z": [
     14,
     15,
     35,
     69
    ]
   },
   {
    "X": [
     11,
     22,
     79,
     87
    ],
    "Z": [
     13,
     14,
     34,
     68
    ]
   },
   {
    "X": [
     12,
     23,
     80,
     88
    ],
    "Z": [
     12,
     13,
     33,
     67
    ]
   },
   {
    "X": [
     13,
     24,
     81,
     89
    ],
    "Z": [
     11,
     12,
     32,
     66
    ]
   },
   {
    "X": [
     14,
     25,
     82,
     90
    ],
    "Z": [
     10,
     11,
     31,
     65
    ]
   },
   {
    "X": [
     15,
     26,
     83,
     91
    ],
    "Z": [
     9,
     10,
     30,
     64
    ]
   },
   {
    "X": [
     16,
     27,
     84,
     92
    ],
    "Z": [
     8,
     9,
     29,
     63
    ]
   },
   {
    "X": [
     0,
     17,
     28,
     85
    ],
    "Z": [
     7,
     8,
     28,
     62
    ]
   },
   {
    "X": [
     1,
     18,
     29,
     86
    ],
    "Z": [
     6,
     7,
     27,
     61
    ]
   },
   {
    "X": [
     2,
     19,
     30,
     87
    ],
    "Z": [
     5,
     6,
     26,
     60
    ]
   },
   {
    "X": [
     3,
     20,
     31,
     88
    ],
    "Z": [
     4,
     5,
     25,
     59
    ]
   },
   {
    "X": [
     4,
     21,
     32,
     89
    ],
    "Z": [
     3,
     4,
     24,
     58
    ]
   },
   {
    "X": [
     5,
     22,
     33,
     90
    ],
    "Z": [
     2,
     3,
     23,
     57
    ]
   },
   {
    "X": [
     6,
     23,
     34,
     91
    ],
    "Z": [
     1,
     2,
     22,
     56
    ]
   },
   {
    "X": [
     7,
     24,
     35,
     92
    ],
    "Z": [
     0,
     1,
     21,
     55
    ]
   }
  ]
 },
 "distance": {
  "d": 14,
  "P": {
   "value": 14,
   "confidence": "upper_bound",
   "witness": {
    "X": [
     4,
     5,
     12,
     33,
     57,
     60,
     61,
     64
    ],
    "Z": [
     4,
     7,
     15,
     24,
     29,
     33,
     60,
     61,
     64,
     67,
     75
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "@mrvee-qC-bee"
  ],
  "construction": "Cyclic mirror on Z_93: row i has X on i+[0, 8, 25, 36] and Z on -i-[0, 1, 39, 73], modulo 93. Common-factor constrained sparse-polynomial instance search.",
  "origin": "submission",
  "date": "2026-10-01",
  "model": "GPT-6 Astra",
  "notes": "Exploratory instance; upper bound only. Novelty unverified.",
  "references": [
   "arXiv:2603.05496v1"
  ],
  "novelty": "unknown"
 },
 "family": "other"
}