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   [
    106,
    120,
    214,
    229,
    253
   ],
   [
    14,
    107,
    186,
    254,
    263
   ],
   [
    108,
    121,
    255,
    264,
    287
   ],
   [
    109,
    122,
    256,
    265,
    288
   ],
   [
    110,
    123,
    182,
    257,
    266
   ],
   [
    111,
    124,
    183,
    258,
    267
   ],
   [
    18,
    112,
    177,
    259,
    268
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   [
    113,
    125,
    260,
    269,
    282
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   [
    114,
    126,
    261,
    270,
    283
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   [
    115,
    127,
    173,
    262,
    271
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   [
    21,
    116,
    236,
    243,
    263
   ],
   [
    117,
    128,
    230,
    244,
    264
   ],
   [
    118,
    129,
    231,
    245,
    265
   ],
   [
    119,
    130,
    232,
    246,
    266
   ],
   [
    120,
    131,
    233,
    247,
    267
   ],
   [
    25,
    121,
    203,
    268,
    275
   ],
   [
    122,
    132,
    269,
    276,
    292
   ],
   [
    123,
    133,
    198,
    270,
    277
   ],
   [
    124,
    134,
    199,
    271,
    278
   ],
   [
    30,
    125,
    192,
    272,
    279
   ],
   [
    126,
    135,
    273,
    280,
    289
   ],
   [
    127,
    136,
    187,
    274,
    281
   ],
   [
    34,
    128,
    151,
    259,
    275
   ],
   [
    129,
    137,
    248,
    260,
    276
   ],
   [
    130,
    138,
    249,
    261,
    277
   ],
   [
    131,
    139,
    250,
    262,
    278
   ],
   [
    39,
    132,
    223,
    279,
    284
   ],
   [
    133,
    140,
    217,
    280,
    285
   ],
   [
    134,
    141,
    218,
    281,
    286
   ],
   [
    45,
    135,
    210,
    282,
    287
   ],
   [
    136,
    142,
    204,
    283,
    288
   ],
   [
    50,
    137,
    158,
    272,
    284
   ],
   [
    138,
    143,
    263,
    273,
    285
   ],
   [
    139,
    144,
    264,
    274,
    286
   ],
   [
    56,
    140,
    148,
    287,
    290
   ],
   [
    141,
    145,
    237,
    288,
    291
   ],
   [
    63,
    142,
    147,
    289,
    292
   ],
   [
    69,
    143,
    168,
    282,
    290
   ],
   [
    144,
    146,
    275,
    283,
    291
   ],
   [
    76,
    145,
    153,
    292,
    293
   ],
   [
    89,
    146,
    181,
    289,
    293
   ]
  ]
 },
 "distance": {
  "d": 7,
  "X": {
   "value": 7,
   "confidence": "upper_bound",
   "witness": [
    45,
    62,
    81,
    99,
    114,
    126,
    135
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1053
    ]
   }
  },
  "Z": {
   "value": 7,
   "confidence": "upper_bound",
   "witness": [
    151,
    157,
    166,
    178,
    193,
    211,
    230
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1054
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "Lee, Gideon"
  ],
  "construction": "Two-block group-algebra code C(a,b) over C7 x (C7 : C3) = SmallGroup(147, 3) (order 147), elements numbered as in GAP Elements(SmallGroup(order,id)) with element 0 the identity. n = 2|G| = 294; H_X = [L(a)|R(b)], H_Z = [R(b)^T|L(a)^T]; a = {0, 1, 8}, b = {0, 2} as element indices. Check weight 5. 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": "2bga-nonabelian"
}