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 "distance": {
  "d": 72,
  "X": {
   "value": 72,
   "confidence": "upper_bound",
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    "found_by": [
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    "date": "2026-09-24",
    "found_at_samples": 1,
    "survived_samples": 1,
    "tool": "norm-word lift of a Z_164 quotient logical (exact algebra)",
    "seeds": [
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   "confidence": "upper_bound",
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    "date": "2026-09-24",
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    "tool": "norm-word lift of a Z_164 quotient logical (exact algebra)",
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 "provenance": {
  "authors": [
   "@vprusso"
  ],
  "construction": "Cyclic generalized-bicycle code on the ring x^328 - 1 with a(x) = x^26 + x^118 + x^149 + x^190 + x^317 + x^325, b(x) = x^39 + x^48 + x^124 + x^141 + x^163 + x^184; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T].",
  "origin": "submission",
  "novelty": "known_parameters",
  "model": "Claude Opus 5",
  "date": "2026-09-24",
  "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"
}