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 },
 "distance": {
  "d": 39,
  "X": {
   "value": 39,
   "confidence": "upper_bound",
   "witness": [
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   "witness_provenance": {
    "found_by": [
     "@vprusso"
    ],
    "date": "2026-09-23",
    "found_at_samples": 300000000,
    "tool": "ris_gpu recover, pair depth 8",
    "seeds": [
     1
    ],
    "survived_samples": 300000000
   }
  },
  "Z": {
   "value": 39,
   "confidence": "upper_bound",
   "witness": [
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   "witness_provenance": {
    "found_by": [
     "@vprusso"
    ],
    "date": "2026-09-23",
    "found_at_samples": 8000000,
    "tool": "gate_changed.py RIS-fast (CI refuter)",
    "seeds": [
     1872761006
    ],
    "survived_samples": 300000000
   }
  }
 },
 "provenance": {
  "authors": [
   "@vprusso"
  ],
  "construction": "Cyclic generalized-bicycle code on the ring x^156 - 1 with a(x) = x^5 + x^26 + x^106 + x^115 + x^118 + x^124 + x^139 + x^153, b(x) = x^3 + x^7 + x^24 + x^39 + x^43 + x^73 + x^87 + x^97 + x^114 + x^121 + x^144 + x^149; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T].",
  "origin": "submission",
  "novelty": "known_parameters",
  "model": "Claude Opus 5",
  "date": "2026-09-22",
  "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"
}