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 },
 "distance": {
  "d": 15,
  "X": {
   "value": 15,
   "confidence": "upper_bound",
   "witness": [
    7,
    12,
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    81,
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   ]
  },
  "Z": {
   "value": 16,
   "confidence": "upper_bound",
   "witness": [
    1,
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   ]
  }
 },
 "provenance": {
  "authors": [
   "@FarLab"
  ],
  "construction": "2BGA on the symmetric group S5 (order 120): H_X=[L(a)|R(b)], H_Z=[R(b)^T|L(a)^T] with supports a=[1,34,61,111], b=[30,66,69,71] (indices into the deterministic BFS element order of research/kit/group_algebra.sym(5); identity is index 0). Found by a random support sweep over exotic groups.",
  "references": [
   "arXiv:2306.16400 (2BGA family; exhaustive W<=8 tables stop at n<=200)",
   "arXiv:2606.17268 (coset-code searches to n=306: no n=240, all k even)"
  ],
  "date": "2026-07-08",
  "notes": "Odd k=13 -- impossible for abelian two-block codes, so the BB/GB literature is excluded by parity. Claimed d is the lightest logical found by deep self-refutation: RIS flat at 15 across 1M/4M/16M trials/side x 2 seeds (gf2_fast, ~66M side-trials total), weight-15 X witness re-validated by the pinned python stack, BP+OSD (1M trials) found nothing lighter. Upper bound only. Novelty check 2026-07-08 against both references found no [[240,13,*]] and no odd-k code in any published 2BGA/coset enumeration.",
  "model": "Claude Fable 5",
  "novelty": "new_parameters"
 },
 "family": "generalized-bicycle"
}