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 "distance": {
  "d": 38,
  "X": {
   "value": 39,
   "confidence": "upper_bound",
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   "witness_provenance": {
    "found_by": [
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    "date": "2026-09-23",
    "found_at_samples": 300000000,
    "tool": "ris_gpu recover, pair depth 8",
    "seeds": [
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    "survived_samples": 300000000
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  "Z": {
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   "confidence": "upper_bound",
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   "witness_provenance": {
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    "date": "2026-09-23",
    "found_at_samples": 300000000,
    "tool": "ris_gpu recover, pair depth 8",
    "seeds": [
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    "survived_samples": 300000000
   }
  }
 },
 "provenance": {
  "authors": [
   "@vprusso"
  ],
  "construction": "Cyclic generalized-bicycle code on the ring x^159 - 1 with a(x) = x^2 + x^17 + x^20 + x^35 + x^77 + x^86 + x^89 + x^99 + x^132 + x^140 + x^143 + x^149 + x^152 + x^158, b(x) = x^37 + x^38 + x^50 + x^86 + x^101 + x^122 + x^125 + x^154; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T].",
  "origin": "submission",
  "novelty": "known_parameters",
  "model": "Claude Opus 5",
  "date": "2026-09-23",
  "notes": "Found by a randomized sweep over sparse polynomial pairs, screened against the live board before any expensive work. Checked for single-block logicals via the ideal generated by (x^m - 1)/gcd(a, x^m - 1) before the distance was believed."
 },
 "family": "generalized-bicycle"
}