{
 "schema_version": "0.2",
 "name": "gap-77-27-5",
 "code_type": "CSS",
 "n": 77,
 "k": 27,
 "checks": {
  "X": [
   [
    0,
    14,
    17,
    23,
    37,
    39,
    49,
    59,
    62,
    69
   ],
   [
    7,
    8,
    21,
    25,
    31,
    38,
    47,
    57,
    66,
    69
   ],
   [
    5,
    10,
    20,
    26,
    37,
    43,
    51,
    58,
    67,
    69
   ],
   [
    6,
    10,
    16,
    30,
    31,
    41,
    51,
    54,
    62,
    70
   ],
   [
    1,
    15,
    18,
    24,
    36,
    38,
    48,
    58,
    63,
    70
   ],
   [
    4,
    11,
    19,
    25,
    36,
    42,
    50,
    59,
    68,
    70
   ],
   [
    3,
    9,
    21,
    24,
    37,
    42,
    47,
    55,
    62,
    71
   ],
   [
    2,
    8,
    22,
    23,
    36,
    43,
    46,
    54,
    63,
    72
   ],
   [
    4,
    11,
    20,
    24,
    34,
    41,
    48,
    54,
    67,
    72
   ],
   [
    3,
    12,
    17,
    29,
    35,
    42,
    51,
    61,
    63,
    73
   ],
   [
    4,
    10,
    21,
    27,
    34,
    43,
    53,
    55,
    65,
    73
   ],
   [
    5,
    15,
    16,
    30,
    32,
    40,
    53,
    61,
    67,
    73
   ],
   [
    0,
    15,
    16,
    29,
    33,
    38,
    46,
    55,
    64,
    74
   ],
   [
    2,
    14,
    19,
    26,
    35,
    45,
    47,
    58,
    65,
    74
   ],
   [
    5,
    11,
    22,
    28,
    33,
    42,
    52,
    54,
    66,
    74
   ],
   [
    3,
    12,
    18,
    28,
    32,
    41,
    49,
    56,
    62,
    75
   ],
   [
    1,
    14,
    16,
    27,
    36,
    44,
    53,
    59,
    64,
    75
   ],
   [
    7,
    13,
    17,
    28,
    34,
    38,
    51,
    59,
    65,
    75
   ],
   [
    6,
    8,
    19,
    29,
    32,
    45,
    51,
    57,
    67,
    75
   ],
   [
    1,
    13,
    22,
    23,
    37,
    42,
    48,
    61,
    68,
    75
   ],
   [
    2,
    13,
    17,
    27,
    31,
    40,
    48,
    57,
    63,
    76
   ],
   [
    6,
    12,
    18,
    27,
    33,
    39,
    50,
    58,
    66,
    76
   ],
   [
    0,
    12,
    21,
    24,
    36,
    43,
    49,
    60,
    67,
    76
   ],
   [
    7,
    9,
    20,
    30,
    31,
    44,
    50,
    56,
    68,
    76
   ]
  ],
  "Z": [
   [
    7,
    14,
    21,
    26,
    44,
    47,
    60,
    65,
    69
   ],
   [
    5,
    11,
    23,
    31,
    40,
    52,
    54,
    68,
    69
   ],
   [
    7,
    10,
    19,
    29,
    37,
    45,
    51,
    55,
    68,
    69
   ],
   [
    0,
    10,
    18,
    26,
    36,
    43,
    49,
    58,
    64,
    70
   ],
   [
    6,
    15,
    22,
    25,
    35,
    45,
    46,
    61,
    66,
    70
   ],
   [
    6,
    11,
    20,
    30,
    36,
    44,
    50,
    54,
    67,
    70
   ],
   [
    4,
    10,
    16,
    24,
    32,
    41,
    53,
    55,
    67,
    70
   ],
   [
    1,
    9,
    19,
    25,
    31,
    44,
    47,
    57,
    68,
    70
   ],
   [
    3,
    9,
    16,
    23,
    44,
    46,
    61,
    62,
    71
   ],
   [
    2,
    10,
    22,
    24,
    34,
    43,
    48,
    54,
    65,
    71
   ],
   [
    7,
    9,
    18,
    25,
    33,
    38,
    50,
    56,
    66,
    71
   ],
   [
    4,
    9,
    22,
    28,
    35,
    42,
    52,
    56,
    65,
    72
   ],
   [
    6,
    8,
    17,
    26,
    34,
    39,
    51,
    57,
    65,
    72
   ],
   [
    3,
    11,
    21,
    23,
    33,
    42,
    49,
    55,
    66,
    72
   ],
   [
    4,
    13,
    20,
    23,
    36,
    43,
    48,
    59,
    68,
    72
   ],
   [
    3,
    14,
    16,
    25,
    34,
    41,
    47,
    59,
    64,
    73
   ],
   [
    5,
    15,
    21,
    29,
    34,
    38,
    52,
    55,
    67,
    73
   ],
   [
    2,
    11,
    18,
    29,
    31,
    41,
    50,
    57,
    63,
    74
   ],
   [
    5,
    13,
    16,
    29,
    35,
    40,
    51,
    61,
    64,
    74
   ],
   [
    4,
    14,
    22,
    30,
    33,
    39,
    53,
    54,
    68,
    74
   ],
   [
    6,
    14,
    18,
    28,
    37,
    39,
    52,
    58,
    62,
    75
   ],
   [
    1,
    12,
    17,
    23,
    32,
    39,
    49,
    61,
    63,
    75
   ],
   [
    7,
    13,
    19,
    27,
    32,
    40,
    50,
    57,
    65,
    75
   ],
   [
    0,
    13,
    18,
    24,
    31,
    38,
    48,
    60,
    62,
    76
   ],
   [
    2,
    12,
    21,
    30,
    37,
    43,
    47,
    61,
    62,
    76
   ],
   [
    0,
    9,
    27,
    33,
    39,
    52,
    55,
    64,
    76
   ]
  ]
 },
 "distance": {
  "d": 5,
  "X": {
   "value": 6,
   "confidence": "upper_bound",
   "witness": [
    6,
    32,
    57,
    58,
    63,
    70
   ],
   "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": 5,
   "confidence": "upper_bound",
   "witness": [
    17,
    36,
    59,
    60,
    63
   ],
   "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/78-27-5.json",
  "references": [],
  "date": "2026-11-02",
  "notes": "",
  "model": "Beam 1.0"
 }
}
