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 },
 "distance": {
  "d": 26,
  "X": {
   "value": 26,
   "confidence": "upper_bound",
   "witness": [
    2,
    7,
    17,
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   ],
   "witness_provenance": {
    "found_by": [
     "@ethanfeld"
    ],
    "date": "2026-09-09",
    "found_at_samples": 1,
    "tool": "Issue #942 witness report; search budget not reported"
   }
  },
  "Z": {
   "value": 26,
   "confidence": "upper_bound",
   "witness": [
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   ],
   "witness_provenance": {
    "found_by": [
     "@ethanfeld"
    ],
    "date": "2026-09-09",
    "found_at_samples": 1,
    "tool": "Issue #942 witness report; search budget not reported"
   }
  }
 },
 "provenance": {
  "authors": [
   "@seunomonije"
  ],
  "model": "Claude Fable 5",
  "construction": "Generalized bicycle (two-block) code on the cyclic group Z_195: H_X = [A|B], H_Z = [B^T|A^T] with A, B circulants; a(x) support {54,68,74,124,148,153} (weight 6), b(x) support {41,53,74,89,101,148,153} (weight 7), max check weight 13. Both a and b are sparse multiples of a common divisor of x^195-1 with k = 2*deg gcd(a,b,x^195-1) = 68 at n = 390. Found in the same divisor-trick sweep as the [[390,82,27]] entry, selected for minimal check weight at high kd^2/n. Distance evidence: rising RIS ladder 20k-2M trials, then 8M-trial refutation passes (seeds 777/999/424242) and pair-depth passes (depths 16/24, 3M trials) all bottoming at d<=28; the 12M-trial witness search returned the embedded weight-28 Z logical, and the GB transpose symmetry (block swap + index reversal) maps it to the embedded weight-28 X logical, machine-verified against ker/rowspace.",
  "references": [
   "arXiv:1904.02703",
   "arXiv:2203.17216"
  ],
  "date": "2026-07-15",
  "notes": "Search and verification by Claude Fable 5. Sibling of the [[390,82,27]] entry: lower check weight (13 vs 16) and higher distance at lower k; Pareto-incomparable, kd^2/n = 136.7. Distance corrected from d<=28 to d<=26 using the verified weight-26 X and Z witnesses reported in issue #942. The issue's verification checks place both witnesses in the appropriate opposite-check kernels and outside the stabilizer row spaces; the search budget is not reported. @ethanfeld supplied the correction."
 },
 "family": "generalized-bicycle"
}