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 "distance": {
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  "X": {
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    "date": "2026-09-23",
    "found_at_samples": 1,
    "tool": "norm-lift quotient bound, m' = 63, quotient weight 15",
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   }
  },
  "Z": {
   "value": 45,
   "confidence": "upper_bound",
   "witness": [
    1,
    2,
    11,
    17,
    21,
    33,
    43,
    56,
    58,
    61,
    62,
    64,
    65,
    74,
    80,
    84,
    96,
    106,
    119,
    121,
    124,
    125,
    127,
    128,
    137,
    143,
    147,
    159,
    169,
    182,
    184,
    187,
    188,
    207,
    213,
    234,
    235,
    270,
    276,
    297,
    298,
    333,
    339,
    360,
    361
   ],
   "witness_provenance": {
    "found_by": [
     "@vprusso"
    ],
    "date": "2026-09-23",
    "found_at_samples": 1,
    "tool": "norm-lift quotient bound, m' = 63, quotient weight 15",
    "survived_samples": 300000000
   }
  }
 },
 "provenance": {
  "authors": [
   "@vprusso"
  ],
  "construction": "Cyclic generalized-bicycle code on the ring x^189 - 1 with a(x) = x^49 + x^59 + x^72 + x^111 + x^121 + x^173, b(x) = x^7 + x^18 + x^30 + x^57 + x^60 + x^77 + x^123 + x^150 + x^154 + x^166 + x^172 + x^174 + x^177 + x^179; 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"
}