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    39,
    82,
    88,
    119,
    121,
    134,
    172
   ],
   [
    40,
    54,
    73,
    83,
    93,
    122,
    173,
    179
   ],
   [
    4,
    43,
    57,
    84,
    122,
    125,
    126,
    174
   ],
   [
    5,
    48,
    85,
    89,
    107,
    111,
    113,
    175
   ],
   [
    49,
    62,
    79,
    86,
    108,
    114,
    176,
    178
   ],
   [
    7,
    52,
    65,
    87,
    114,
    117,
    153,
    177
   ],
   [
    10,
    58,
    70,
    88,
    101,
    137,
    140,
    178
   ],
   [
    16,
    66,
    76,
    89,
    124,
    128,
    131,
    179
   ]
  ]
 },
 "distance": {
  "d": 15,
  "X": {
   "value": 15,
   "confidence": "upper_bound",
   "witness": [
    2,
    24,
    25,
    37,
    40,
    61,
    73,
    92,
    115,
    131,
    134,
    160,
    168,
    173,
    179
   ]
  },
  "Z": {
   "value": 15,
   "confidence": "upper_bound",
   "witness": [
    0,
    10,
    12,
    14,
    47,
    54,
    55,
    57,
    90,
    94,
    137,
    142,
    144,
    161,
    178
   ]
  }
 },
 "provenance": {
  "authors": [
   "Lee, Gideon"
  ],
  "construction": "Two-block group-algebra code C(a,b) of arXiv:2610.13880 (Table 11) over the non-abelian group C15 x S3 (GAP SmallGroup(90,6), order 90): 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 + e6 + e45 + e58, b = e0 + e4 + e56 + e88 with elements numbered as GAP's Elements(SmallGroup(90,6)), e0 the identity. Taken from record f6c4062751538dac 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..89 are the left block and 90..179 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 = 15 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/180-20-15.md. The board's dedup flags a Weisfeiler-Leman signature match with [[180,20,14]] (codes/180-20-14.json: a coset two-block code over the metacyclic group C30:C6 of order 180 with qubits indexed by cosets of a C2 subgroup, weight-8 checks, witnessed d <= 14); the exact fingerprint does not match. WL-1 refinement cannot separate regular two-block Tanner graphs with equal block weights, so the match is a signature collision, not an isomorphism. The two codes also differ in distance: this code has exact distance 15 by the paper's search and the submit tool's 2,000,000-trial pass found nothing below 15, while [[180,20,14]] carries an explicit weight-14 logical.",
  "novelty": "known_parameters",
  "references": [
   "arXiv:2610.13880"
  ]
 },
 "family": "generalized-bicycle"
}