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 },
 "family": "generalized-bicycle",
 "provenance": {
  "authors": [
   "@vprusso"
  ],
  "origin": "submission",
  "construction": "Generalized bicycle (2BGA on Z_195), circulant size 195, a(x) support {0,34,47,72,78,85,187,193}, b(x) support {0,93,117,136,145,163,187,188}; H_X=[A|B], H_Z=[B^T|A^T]. Check weight 16.",
  "model": "Claude Fable 5",
  "date": "2026-07-15",
  "references": [
   "arXiv:1904.02703",
   "arXiv:2306.16400"
  ],
  "novelty": "unknown",
  "notes": "Distance upper bound d<=30 from an explicit weight-30 Z logical witness (both sides weight 30; the X witness is the Z witness under the GB transpose symmetry, machine-verified). Refutation evidence: RIS ladders to 8M/side during discovery, then three fresh-seed passes at 80M trials/side (pair-depth 20) all held at 30-31, plus an independent BP+OSD syndrome-decoder pass found nothing lighter than 41; nothing below 30 across ~240M trials and two methods. Upper bound only; exact certification is out of MILP reach at n=390. Literature novelty unverified."
 }
}