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  ]
 },
 "distance": {
  "d": 21,
  "X": {
   "value": 21,
   "confidence": "upper_bound",
   "witness": [
    8,
    9,
    20,
    35,
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    204,
    214,
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   ]
  },
  "Z": {
   "value": 21,
   "confidence": "upper_bound",
   "witness": [
    28,
    31,
    59,
    66,
    97,
    127,
    131,
    158,
    162,
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    184,
    204,
    208,
    212,
    214,
    216,
    234,
    236,
    259,
    265,
    267
   ]
  }
 },
 "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(147,5), 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 + e19 + e44 + e127, b = e0 + e27 + e81 with elements numbered as GAP's Elements(SmallGroup(147,5)), e0 the identity. Table 2 of the paper writes the same code as a = 1 + c + u + u v^4 + u^4 c^2 + u^4 v^6, b = 1 + u^2 v^5 + u^3 v 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^2> (lambda = 2). Taken from record 26191f430029def7 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 = 21 exactly (d_X: cluster ladder (numba), exact, from symmetry roots, one type via a checked X/Z exchange when one exists; witnesses checked (equal to Z by a checked X/Z-exchange automorphism); d_Z: cluster ladder (numba), exact, from symmetry roots, one type via a checked X/Z exchange when one exists; witnesses checked; 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/294-24-21.md.",
  "novelty": "known_parameters",
  "references": [
   "arXiv:2610.13880"
  ]
 },
 "family": "generalized-bicycle"
}