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  "X": {
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   "confidence": "upper_bound",
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 "provenance": {
  "authors": [
   "@vprusso"
  ],
  "construction": "Cyclic generalized-bicycle code on the ring x^165 - 1 with a(x) = x^5 + x^32 + x^71 + x^81 + x^92 + x^101 + x^105 + x^111 + x^123 + x^160, b(x) = x^40 + x^46 + x^55 + x^59 + x^76 + x^93 + x^108 + x^115 + x^122 + x^141; 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"
}