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    155,
    164
   ],
   [
    38,
    65,
    69,
    72,
    89,
    96,
    138,
    154,
    156
   ],
   [
    15,
    70,
    71,
    73,
    84,
    120,
    129,
    139,
    157
   ],
   [
    40,
    56,
    74,
    80,
    90,
    107,
    115,
    158,
    166
   ],
   [
    5,
    41,
    75,
    82,
    91,
    92,
    116,
    141,
    159
   ],
   [
    43,
    53,
    70,
    76,
    92,
    112,
    122,
    160,
    165
   ],
   [
    0,
    44,
    77,
    81,
    90,
    93,
    113,
    155,
    161
   ],
   [
    8,
    46,
    73,
    78,
    95,
    108,
    125,
    133,
    162
   ],
   [
    47,
    49,
    75,
    79,
    97,
    106,
    116,
    162,
    163
   ],
   [
    1,
    50,
    78,
    80,
    87,
    98,
    107,
    150,
    164
   ],
   [
    13,
    52,
    68,
    81,
    100,
    102,
    119,
    127,
    165
   ],
   [
    3,
    55,
    65,
    82,
    99,
    103,
    124,
    134,
    166
   ],
   [
    6,
    59,
    61,
    83,
    94,
    109,
    118,
    128,
    167
   ]
  ]
 },
 "distance": {
  "d": 18,
  "X": {
   "value": 18,
   "confidence": "upper_bound",
   "witness": [
    0,
    3,
    18,
    22,
    23,
    29,
    37,
    47,
    51,
    54,
    67,
    79,
    113,
    124,
    140,
    144,
    148,
    153
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1015
    ]
   }
  },
  "Z": {
   "value": 18,
   "confidence": "upper_bound",
   "witness": [
    9,
    16,
    32,
    36,
    43,
    45,
    91,
    105,
    109,
    119,
    127,
    133,
    134,
    135,
    138,
    157,
    164,
    165
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1016
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "Lee, Gideon"
  ],
  "construction": "Two-block group-algebra code C(a,b) over C42 x C2 = SmallGroup(84, 15) (order 84), elements numbered as in GAP Elements(SmallGroup(order,id)) with element 0 the identity. n = 2|G| = 168; H_X = [L(a)|R(b)], H_Z = [R(b)^T|L(a)^T]; a = {0, 14, 33, 64, 71}, b = {0, 13, 30, 69} as element indices. Check weight 9. 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"
}