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  ]
 },
 "distance": {
  "d": 20,
  "X": {
   "value": 20,
   "confidence": "upper_bound",
   "witness": [
    10,
    57,
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    60,
    61,
    73,
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   ]
  },
  "Z": {
   "value": 20,
   "confidence": "upper_bound",
   "witness": [
    1,
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    238,
    239,
    243,
    249
   ]
  }
 },
 "provenance": {
  "authors": [
   "Lee, Gideon"
  ],
  "construction": "Two-block group-algebra code C(a,b) of arXiv:2610.13880 (Tables 2 and 11) over the non-abelian group C7 x D18 (GAP SmallGroup(126,3), order 126): 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 = e0 + e3 + e5 + e66, b = e0 + e23 + e27 with elements numbered as GAP's Elements(SmallGroup(126,3)), e0 the identity. Table 2 of the paper writes the same code as a = 1 + r + x s + x^3 r^7 s, b = 1 + r^4 + x r^2 over C7 x D18 = <x> x <r, s | r^9 = s^2 = 1, s r s^-1 = r^-1> with x of order 7. Taken from record e79d1e333e70af13 of the paper's database (github.com/gideonlsx/bicycle-race @ aed705a, data/codes.jsonl, CC BY 4.0), whose data/groups.jsonl gives the generators' right-multiplication permutations in that numbering; qubits 0..125 are the left block and 126..251 the right block. 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 = 20 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: checked: GAP rebuild, QDistRnd and QDistEvol find nothing below d). 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/252-16-20.md.",
  "novelty": "known_parameters",
  "references": [
   "arXiv:2610.13880"
  ]
 },
 "family": "generalized-bicycle"
}