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 "distance": {
  "d": 6,
  "X": {
   "value": 6,
   "confidence": "upper_bound",
   "witness": [
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    113,
    133,
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   ]
  },
  "Z": {
   "value": 6,
   "confidence": "upper_bound",
   "witness": [
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  }
 },
 "provenance": {
  "authors": [
   "Lee, Gideon"
  ],
  "construction": "Two-block group-algebra code C(a,b) of arXiv:2610.13880 (Table 2) over the abelian group C45 x C3 (GAP SmallGroup(135,2)): 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^6 y^2 + x^10 + x^25 y^2 + x^27 + x^40 y, b = 1 + x^3 y + x^36 in generators x (order 45) and y (order 3), i.e. the bivariate bicycle code with A = a(x,y), B = b(x,y). The stored matrices use the qubit ordering of the paper's database (record 23f7085fc401fb11, github.com/gideonlsx/bicycle-race @ aed705a, data/codes.jsonl, CC BY 4.0): qubits 0..134 are the left block and 135..269 the right block, group elements numbered as GAP's Elements(SmallGroup(135,2)) with e0 the identity, x = e7, y = e2, so a = e0 + e1 + e12 + e20 + e65 + e74, b = e0 + e3 + e76. 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 = 6 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/270-72-6.md.",
  "novelty": "known_parameters",
  "references": [
   "arXiv:2610.13880"
  ]
 },
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  "layers": 2,
  "interaction_radius": 6.7083,
  "contributed_by": {
   "by": [
    "@MathysRennela"
   ],
   "date": "2026-10-13",
   "method": "Simulated annealing over integer-grid site assignments with the repo's own research/local2d/fold_layout.search_layout, single layer at radius 4 then two layers at 7, plus a divisor scan of the two-block index convention Z_l x Z_m which gives the tighter embedding here; radius and per-site occupancy re-measured with the verifier's own rule."
  }
 }
}