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   ]
  ]
 },
 "distance": {
  "d": 40,
  "X": {
   "value": 40,
   "confidence": "upper_bound",
   "witness": [
    13,
    25,
    44,
    54,
    55,
    62,
    74,
    77,
    80,
    82,
    90,
    93,
    95,
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    113,
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    133,
    158,
    171,
    178,
    193,
    208,
    210,
    211,
    214,
    224,
    231,
    235,
    236,
    244,
    252,
    254,
    256,
    269,
    295,
    311,
    317,
    320,
    329
   ]
  },
  "Z": {
   "value": 40,
   "confidence": "upper_bound",
   "witness": [
    15,
    24,
    27,
    33,
    49,
    75,
    88,
    90,
    92,
    100,
    108,
    109,
    113,
    120,
    130,
    133,
    134,
    136,
    151,
    166,
    173,
    186,
    211,
    219,
    228,
    231,
    241,
    249,
    251,
    254,
    262,
    264,
    267,
    270,
    282,
    289,
    290,
    300,
    319,
    331
   ]
  }
 },
 "provenance": {
  "authors": [
   "@vprusso"
  ],
  "construction": "Cyclic generalized-bicycle code on the ring x^172 - 1 with a(x) = x^5 + x^65 + x^71 + x^79 + x^96 + x^142 + x^162 + x^164, b(x) = x^9 + x^47 + x^55 + x^68 + x^90 + x^139; 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. Distance corrected from 42 to 40: the submitted claim rested on one search seed, and the verifier found a weight-40 Z-logical. The X witness is its reflection under x -> x^-1, which maps a Z-logical of a cyclic generalized-bicycle code to an X-logical of equal weight."
 },
 "family": "generalized-bicycle"
}