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 },
 "distance": {
  "d": 20,
  "X": {
   "value": 20,
   "confidence": "upper_bound",
   "witness": [
    10,
    37,
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   ]
  },
  "Z": {
   "value": 20,
   "confidence": "upper_bound",
   "witness": [
    6,
    7,
    8,
    23,
    50,
    67,
    68,
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    275,
    276,
    289,
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   ]
  }
 },
 "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 C7) : C3 (GAP SmallGroup(147,4), order 147): 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 + e1 + e2 + e11, b = e0 + e8 + e61 with elements numbered as GAP's Elements(SmallGroup(147,4)), e0 the identity. Table 2 of the paper writes the same code as a = 1 + c + v^2 c^2 + u, b = 1 + u v + u^2 v^4 over (C7 x C7) : C3 = <u, v, c | u^7 = v^7 = c^3 = 1, uv = vu, c u c^-1 = u^4, c v c^-1 = v^4> (lambda = 4). Taken from record 1d70ba96465b3ac1 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..146 are the left block and 147..293 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: equal to d_Z by a checked X/Z-exchange automorphism; d_Z: ladder (cluster engine, symmetry roots), from the screen's lower bound 18, no target; 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/294-18-20.md.",
  "novelty": "known_parameters",
  "references": [
   "arXiv:2610.13880"
  ]
 },
 "family": "generalized-bicycle"
}