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    108,
    109,
    124,
    167,
    172
   ],
   [
    5,
    75,
    84,
    109,
    125,
    168,
    173,
    180
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   [
    73,
    76,
    85,
    126,
    169,
    174,
    180,
    181
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   [
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    74,
    77,
    127,
    170,
    175,
    181,
    182
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   [
    6,
    78,
    86,
    132,
    158,
    176,
    178,
    180
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   [
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    79,
    87,
    133,
    159,
    177,
    179,
    181
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   [
    8,
    80,
    88,
    98,
    104,
    178,
    182,
    194
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   [
    12,
    78,
    81,
    105,
    128,
    154,
    179,
    183
   ],
   [
    9,
    82,
    89,
    115,
    116,
    135,
    176,
    180
   ],
   [
    10,
    83,
    90,
    116,
    117,
    136,
    177,
    181
   ],
   [
    11,
    84,
    91,
    117,
    137,
    178,
    182,
    187
   ],
   [
    16,
    82,
    85,
    138,
    179,
    183,
    187,
    188
   ],
   [
    13,
    86,
    92,
    145,
    170,
    184,
    186,
    187
   ],
   [
    14,
    87,
    93,
    100,
    110,
    146,
    185,
    188
   ],
   [
    15,
    20,
    88,
    101,
    111,
    140,
    186,
    189
   ],
   [
    17,
    89,
    94,
    125,
    126,
    149,
    184,
    187
   ],
   [
    18,
    90,
    95,
    126,
    127,
    150,
    185,
    188
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   [
    19,
    25,
    91,
    127,
    151,
    186,
    189,
    192
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   [
    22,
    92,
    96,
    104,
    118,
    159,
    190,
    192
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   [
    23,
    30,
    93,
    98,
    105,
    119,
    191,
    193
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   [
    27,
    94,
    97,
    137,
    138,
    162,
    190,
    192
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   [
    28,
    36,
    95,
    138,
    139,
    163,
    191,
    193
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   [
    33,
    42,
    96,
    100,
    111,
    129,
    194,
    195
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   [
    39,
    49,
    97,
    151,
    152,
    173,
    194,
    195
   ]
  ]
 },
 "distance": {
  "d": 20,
  "X": {
   "value": 20,
   "confidence": "upper_bound",
   "witness": [
    10,
    12,
    44,
    47,
    48,
    52,
    65,
    76,
    79,
    85,
    100,
    102,
    110,
    114,
    129,
    141,
    169,
    175,
    181,
    183
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1011
    ]
   }
  },
  "Z": {
   "value": 20,
   "confidence": "upper_bound",
   "witness": [
    58,
    59,
    64,
    79,
    83,
    103,
    109,
    111,
    115,
    125,
    136,
    150,
    154,
    157,
    169,
    174,
    184,
    188,
    190,
    195
   ],
   "witness_provenance": {
    "found_by": [
     "@mathysrennela"
    ],
    "date": "2026-10-12",
    "found_at_samples": 2000,
    "survived_samples": 2000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
     1012
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "Lee, Gideon"
  ],
  "construction": "Two-block group-algebra code C(a,b) over C7 x D14 = SmallGroup(98, 3) (order 98), elements numbered as in GAP Elements(SmallGroup(order,id)) with element 0 the identity. n = 2|G| = 196; H_X = [L(a)|R(b)], H_Z = [R(b)^T|L(a)^T]; a = {0, 1, 13, 32, 57}, b = {0, 3, 59} as element indices. Check weight 8. 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"
}