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 "distance": {
  "d": 15,
  "X": {
   "value": 15,
   "confidence": "upper_bound",
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   "confidence": "upper_bound",
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 "provenance": {
  "authors": [
   "Lee, Gideon"
  ],
  "construction": "Two-block group-algebra code C(a,b) of arXiv:2610.13880 (Table 11) over the cyclic group C84 (GAP SmallGroup(84,6)): H_X = (L(a) | R(b)), H_Z = (R(b)^T | L(a)^T) with L and R the left and right regular representations, a = 1 + x^57 + x^68 + x^82, b = 1 + x^33 + x^36 in a generator x of order 84, i.e. the generalized bicycle code with A = a(x), B = b(x). The stored matrices use the qubit ordering of the paper's database (record 16fca86b7d866735, github.com/gideonlsx/bicycle-race @ aed705a, data/codes.jsonl, CC BY 4.0): qubits 0..83 are the left block and 84..167 the right block, group elements numbered as GAP's Elements(SmallGroup(84,6)) with e0 the identity, x = e14, so a = e0 + e6 + e66 + e69, b = e0 + e3 + e52. Rebuilt from the database's group data; CSS commutation, k, check weight and both of the paper's witnesses were re-checked on the rebuilt matrices.",
  "origin": "baseline",
  "date": "2026-10-12",
  "model": "Claude Fable 5.1 (Claude Code)",
  "notes": "Literature reconstruction. The paper states d = 15 exactly (d_X: ladder in the screen (frontier mode, exact_on_accept; cluster engine, symmetry roots); d_Z: ladder in the screen (frontier mode, exact_on_accept; cluster engine, symmetry roots); verification record: one engine). Readings here: qldpc submit's RIS (20,000 NumPy trials per side) and its 2,000,000-trial accelerator pass, plus the verifier's refutation search; witnessed upper bound, see notes/168-12-15.md.",
  "novelty": "known_parameters",
  "references": [
   "arXiv:2610.13880"
  ]
 },
 "family": "generalized-bicycle"
}