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  "X": {
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   "confidence": "upper_bound",
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 "provenance": {
  "authors": [
   "Lee, Gideon"
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  "construction": "Two-block group-algebra code C(a,b) of arXiv:2610.13880 (Tables 2 and 11) over the cyclic group C63 (GAP SmallGroup(63,2)): 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^17 + x^21 + x^31 + x^60, b = 1 + x^6 + x^19 + x^28 in a generator x of order 63, 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 0c949633e5d976da, github.com/gideonlsx/bicycle-race @ aed705a, data/codes.jsonl, CC BY 4.0): qubits 0..62 are the left block and 63..125 the right block, group elements numbered as GAP's Elements(SmallGroup(63,2)) with e0 the identity, x = e5, so a = e0 + e3 + e31 + e44 + e47, b = e0 + e1 + e39 + e58. 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 = 14 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 13, no target; verification record: verified: second exact engine (dist-m4ri from symmetry roots), GAP rebuild, QDistRnd, QDistEvol). 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/126-16-14.md.",
  "novelty": "known_parameters",
  "references": [
   "arXiv:2610.13880"
  ]
 },
 "family": "generalized-bicycle"
}