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    68,
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    194,
    216,
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    143,
    186,
    195,
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    106,
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    152,
    198,
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    190,
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    221
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    200
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    105,
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    201,
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    90,
    124,
    183,
    202,
    219
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    150,
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    120,
    126,
    194,
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   [
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    50,
    93,
    121,
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    193,
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    110,
    128,
    160,
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    47,
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   [
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    24,
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   [
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  ]
 },
 "distance": {
  "d": 21,
  "X": {
   "value": 21,
   "confidence": "upper_bound",
   "witness": [
    3,
    10,
    28,
    48,
    51,
    54,
    64,
    71,
    89,
    95,
    105,
    110,
    135,
    147,
    152,
    156,
    176,
    180,
    197,
    213,
    217
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1028
    ]
   }
  },
  "Z": {
   "value": 21,
   "confidence": "upper_bound",
   "witness": [
    12,
    19,
    32,
    33,
    46,
    51,
    61,
    79,
    101,
    103,
    111,
    122,
    128,
    136,
    146,
    176,
    177,
    197,
    213,
    215,
    218
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1029
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "Lee, Gideon"
  ],
  "construction": "Two-block group-algebra code C(a,b) over C28 x C4 = SmallGroup(112, 19) (order 112), elements numbered as in GAP Elements(SmallGroup(order,id)) with element 0 the identity. n = 2|G| = 224; H_X = [L(a)|R(b)], H_Z = [R(b)^T|L(a)^T]; a = {0, 7, 13, 108}, b = {0, 10, 48} 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"
}