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   [
    32,
    63,
    85,
    160,
    168,
    187,
    193
   ],
   [
    2,
    33,
    86,
    115,
    132,
    194,
    209
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   [
    34,
    59,
    87,
    109,
    116,
    170,
    195
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   [
    4,
    38,
    88,
    173,
    196,
    200,
    212
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   [
    70,
    89,
    104,
    141,
    169,
    175,
    197
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   [
    41,
    71,
    90,
    170,
    195,
    198,
    210
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   [
    42,
    91,
    107,
    143,
    171,
    177,
    199
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   [
    43,
    67,
    92,
    110,
    120,
    200,
    212
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   [
    68,
    93,
    102,
    139,
    167,
    179,
    201
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   [
    45,
    76,
    94,
    147,
    174,
    181,
    202
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   [
    6,
    46,
    95,
    111,
    123,
    203,
    213
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   [
    47,
    72,
    96,
    108,
    112,
    183,
    204
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   [
    8,
    51,
    97,
    186,
    191,
    205,
    208
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   [
    55,
    84,
    98,
    183,
    189,
    204,
    206
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   [
    10,
    56,
    99,
    128,
    153,
    207,
    214
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   [
    57,
    80,
    100,
    114,
    129,
    191,
    208
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   [
    12,
    61,
    101,
    115,
    132,
    194,
    209
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   [
    68,
    93,
    102,
    170,
    195,
    198,
    210
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   [
    19,
    69,
    103,
    119,
    140,
    211,
    215
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   [
    70,
    89,
    104,
    110,
    120,
    200,
    212
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   [
    21,
    74,
    105,
    111,
    123,
    203,
    213
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   [
    29,
    82,
    106,
    128,
    153,
    207,
    214
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   [
    42,
    91,
    107,
    119,
    140,
    211,
    215
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  ]
 },
 "distance": {
  "d": 2,
  "X": {
   "value": 2,
   "confidence": "upper_bound",
   "witness": [
    154,
    182
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1054
    ]
   }
  },
  "Z": {
   "value": 2,
   "confidence": "upper_bound",
   "witness": [
    73,
    94
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1055
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "Lee, Gideon"
  ],
  "construction": "Two-block group-algebra code C(a,b) over C36 x C3 = SmallGroup(108, 12) (order 108), elements numbered as in GAP Elements(SmallGroup(order,id)) with element 0 the identity. n = 2|G| = 216; H_X = [L(a)|R(b)], H_Z = [R(b)^T|L(a)^T]; a = {0, 4, 67, 89}, b = {0, 16, 65} as element indices. Check weight 7. Parameters and blocks taken from the public code database of arXiv:2610.13880v1 (Lee, 'Bicycle Race'), github.com/gideonlsx/bicycle-race.",
  "references": [
   "arXiv:2610.13880"
  ],
  "date": "2026-10-12",
  "notes": "Parameters and construction taken from the public database of arXiv:2610.13880v1. Distance is an upper bound certified by the witnesses attached here. Parameters and blocks taken from the public code database of arXiv:2610.13880v1 (Lee, 'Bicycle Race'), github.com/gideonlsx/bicycle-race @ aed705a, CC BY 4.0; rebuilt here with the repo's own group data. Distance is an upper bound certified by the attached witnesses, not the paper's exact distance.",
  "origin": "baseline",
  "novelty": "known_parameters",
  "model": "Mimo-V2.6-Flash"
 },
 "family": "generalized-bicycle"
}