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 },
 "distance": {
  "d": 34,
  "X": {
   "value": 34,
   "confidence": "upper_bound",
   "witness": [
    14,
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    74,
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   ],
   "witness_provenance": {
    "found_by": [
     "@dorakingx"
    ],
    "date": "2026-09-05",
    "found_at_samples": 200000,
    "tool": "gf2_fast RIS (verify/gf2_fast.cpp), both sides searched jointly",
    "seeds": [
     11774,
     1137,
     1793,
     4711,
     8888,
     424242,
     515151
    ],
    "survived_samples": 5000000
   }
  },
  "Z": {
   "value": 34,
   "confidence": "upper_bound",
   "witness": [
    49,
    50,
    57,
    117,
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    121,
    122,
    123,
    125,
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    445,
    450,
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    530,
    543,
    556,
    582,
    588,
    616
   ],
   "witness_provenance": {
    "found_by": [
     "@dorakingx"
    ],
    "date": "2026-09-05",
    "found_at_samples": 200000,
    "tool": "mirror of the other side's witness (L(e)<->R(-e)); sides searched jointly",
    "seeds": [
     11774,
     1137,
     1793,
     4711,
     8888,
     424242,
     515151
    ],
    "survived_samples": 5000000
   }
  }
 },
 "provenance": {
  "authors": [
   "@dorakingx"
  ],
  "construction": "Generalized bicycle (two-block) code on Z_315: H_X=[A|B], H_Z=[B^T|A^T] with A, B the 315x315 circulants of a(x)=1+x+x^8, b(x)=1+x^52+x^229 (circulant row u touches qubits u-e mod 315 for each exponent e; right block index offset 315). k = 2*deg gcd(a, b, x^315-1) = 12. Found by exhaustive designed-divisor enumeration of all weight-6 trinomial pairs on Z_N, N=181..350 (k >= 8; 109,888 listed pairs = 102,092 classes under monomial factors, units and swap), then fresh-seed fast-RIS ladders; the distance is a witness-backed upper bound (deepest null result 5000000 trials).",
  "references": [
   "arXiv:1904.02703",
   "arXiv:2203.17216",
   "arXiv:2306.16400",
   "arXiv:2503.03827"
  ],
  "date": "2026-09-05",
  "notes": "Checked, not equivalent to any board entry: no board entry has n=630 with k=12 (the two n=630 entries, [[630,86,3]] w=4 and [[630,126,20]] w=9, are not weight-6 codes); closed-walk counts of the Tanner graph differ from every weight-6 board entry and the gate reports no exact duplicate (WL cannot separate circulant codes). The Z witness is the image of the X witness under the two-block symmetry L(e)<->R(-e); the RIS runs searched both sides jointly. Literature novelty unverified.",
  "novelty": "unknown",
  "origin": "submission",
  "model": "Claude Fable 5.1 (Claude Code)"
 },
 "family": "generalized-bicycle"
}