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   ],
   [
    42,
    46,
    82,
    111,
    132,
    160,
    197,
    200,
    215,
    320,
    333,
    347,
    388,
    415,
    441,
    448
   ],
   [
    43,
    47,
    83,
    112,
    133,
    161,
    198,
    201,
    216,
    321,
    334,
    348,
    389,
    416,
    442,
    449
   ],
   [
    44,
    48,
    84,
    113,
    134,
    162,
    199,
    202,
    217,
    322,
    335,
    349,
    390,
    417,
    443,
    450
   ],
   [
    45,
    49,
    85,
    114,
    135,
    163,
    200,
    203,
    218,
    323,
    336,
    350,
    391,
    418,
    444,
    451
   ]
  ]
 },
 "family": "generalized-bicycle",
 "provenance": {
  "authors": [
   "@vprusso"
  ],
  "model": "Claude Opus 5",
  "novelty": "unknown",
  "origin": "submission",
  "date": "2026-10-14",
  "construction": "Cyclic generalized bicycle at m=233, a prime with ord_2(m)=29, so the nontrivial cyclotomic cosets of 2 all have size 29. The divisor g is one such coset's minimal polynomial, of degree 29, which fixes k = 2 deg g = 58 by construction. The pair (a,b) was then drawn from the ideal (g) by information-set decoding over sparse supports, keeping weights 7 and 9; both are odd, so x+1 does not divide the gcd and no weight-m block logical is forced. H_X = [circ(a) | circ(b)] and H_Z = [circ(b)^T | circ(a)^T] on n = 2m = 466 qubits at uniform row weight 16, with a = [14, 21, 47, 74, 115, 129, 142] and b = [14, 29, 32, 69, 97, 118, 147, 183, 187].",
  "notes": "Distance is an upper bound from the lighter of two witnesses, weight 52 on X and 56 on Z, both carried in this file. A 24-seed randomized information-set search at 2,000,000 trials per seed spread 52 to 60 with the minimum found by one seed. A single run of 8,000,000 trials, matching the verifier's own depth, reads 56. A search restricted to logicals supported inside one circulant block, which a general search is blind to, found nothing below 64. Folding onto the x^t-invariant subspaces leaves a lightest surviving logical of weight 176. The design point is deg g / m = 0.124."
 }
}