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    133,
    140,
    155
   ],
   [
    49,
    65,
    75,
    102,
    120,
    130,
    138,
    146,
    156
   ],
   [
    55,
    69,
    76,
    83,
    84,
    114,
    116,
    125,
    157
   ],
   [
    56,
    70,
    77,
    85,
    117,
    126,
    128,
    158,
    159
   ],
   [
    71,
    78,
    80,
    85,
    117,
    126,
    128,
    158,
    159
   ],
   [
    62,
    74,
    79,
    86,
    104,
    113,
    142,
    147,
    160
   ],
   [
    71,
    78,
    80,
    92,
    94,
    135,
    137,
    144,
    161
   ]
  ]
 },
 "distance": {
  "d": 2,
  "X": {
   "value": 2,
   "confidence": "upper_bound",
   "witness": [
    5,
    15
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1045
    ]
   }
  },
  "Z": {
   "value": 2,
   "confidence": "upper_bound",
   "witness": [
    41,
    73
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1046
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "Lee, Gideon"
  ],
  "construction": "Two-block group-algebra code C(a,b) over (C9 x C3) : C3 = SmallGroup(81, 3) (order 81), elements numbered as in GAP Elements(SmallGroup(order,id)) with element 0 the identity. n = 2|G| = 162; H_X = [L(a)|R(b)], H_Z = [R(b)^T|L(a)^T]; a = {0, 2, 8, 9, 20, 38}, b = {0, 2, 9} 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": "2bga-nonabelian"
}