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 },
 "distance": {
  "d": 40,
  "X": {
   "value": 40,
   "confidence": "upper_bound",
   "witness": [
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   "witness_provenance": {
    "found_by": [
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    "date": "2026-09-24",
    "found_at_samples": 1,
    "survived_samples": 1,
    "tool": "norm-word lift of a Z_57 quotient logical (exact algebra)",
    "seeds": [
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    ]
   }
  },
  "Z": {
   "value": 40,
   "confidence": "upper_bound",
   "witness": [
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   "witness_provenance": {
    "found_by": [
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    ],
    "date": "2026-09-24",
    "found_at_samples": 1,
    "survived_samples": 1,
    "tool": "norm-word lift of a Z_57 quotient logical (exact algebra)",
    "seeds": [
     0
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   }
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 },
 "provenance": {
  "authors": [
   "@vprusso"
  ],
  "construction": "Cyclic generalized-bicycle code on the ring x^285 - 1 with a(x) = x^8 + x^206 + x^208 + x^237, b(x) = x^42 + x^104 + x^149 + x^206; H_X = [circ(a) | circ(b)], H_Z = [circ(b)^T | circ(a)^T].",
  "origin": "submission",
  "novelty": "known_parameters",
  "model": "Claude Opus 5",
  "date": "2026-09-21",
  "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"
}