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    510,
    520,
    539,
    548,
    559,
    564,
    567,
    569,
    570,
    579,
    581,
    585,
    586,
    592,
    599,
    623,
    625,
    626,
    630,
    633,
    635,
    640,
    663,
    664,
    665,
    667,
    669,
    673,
    675,
    682
   ],
   "witness_provenance": {
    "found_by": [
     "@MathysRennela"
    ],
    "date": "2026-10-30",
    "found_at_samples": 200000,
    "survived_samples": 200000,
    "tool": "gf2_fast.dem_rand_witness (verify/gf2_fast.cpp)",
    "seeds": [
     0
    ]
   }
  },
  "Z": {
   "value": 81,
   "confidence": "upper_bound",
   "witness": [
    0,
    19,
    31,
    32,
    40,
    47,
    48,
    49,
    52,
    76,
    78,
    91,
    92,
    101,
    108,
    124,
    132,
    144,
    147,
    148,
    174,
    175,
    205,
    211,
    214,
    216,
    218,
    222,
    224,
    247,
    273,
    277,
    283,
    285,
    294,
    298,
    299,
    303,
    304,
    313,
    333,
    334,
    343,
    344,
    347,
    357,
    369,
    372,
    382,
    385,
    391,
    396,
    404,
    407,
    411,
    425,
    475,
    479,
    495,
    507,
    521,
    523,
    526,
    530,
    553,
    555,
    584,
    589,
    593,
    594,
    597,
    605,
    640,
    643,
    653,
    659,
    660,
    662,
    667,
    677,
    678
   ],
   "witness_provenance": {
    "found_by": [
     "@MathysRennela"
    ],
    "date": "2026-10-30",
    "found_at_samples": 2000000,
    "tool": "gf2_fast"
   }
  }
 },
 "provenance": {
  "authors": [
   "@MathysRennela"
  ],
  "construction": "Generalized bicycle on the affine group Aff(F_19) = Z_19 x| Z_18 (2 a primitive root mod 19), order 342; HX=[L(a)|R(b)], HZ=[R(b)^T|L(a)^T] with a=[167,268,58,61], b=[284,292,32,6] over F2, check weight 8. Sampled by research/kit/search.py sample_kasai_affine.",
  "origin": "submission",
  "date": "2026-10-30",
  "model": "Beam 1.0",
  "notes": "Checked against the board by the submission gate on 2026-10-30: no exact fingerprint match and no WL-signature match against any entry, so no equivalence to an existing entry is claimed. Literature novelty unverified: the [[684,4,81]] parameter set has not been compared against published tables."
 },
 "family": "generalized-bicycle"
}