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 },
 "distance": {
  "d": 66,
  "X": {
   "value": 66,
   "confidence": "upper_bound",
   "witness": [
    10,
    14,
    28,
    41,
    45,
    59,
    72,
    76,
    90,
    103,
    107,
    121,
    134,
    138,
    152,
    165,
    169,
    183,
    196,
    200,
    214,
    227,
    231,
    245,
    258,
    262,
    276,
    289,
    293,
    307,
    320,
    324,
    338,
    343,
    356,
    358,
    374,
    387,
    389,
    405,
    418,
    420,
    436,
    449,
    451,
    467,
    480,
    482,
    498,
    511,
    513,
    529,
    542,
    544,
    560,
    573,
    575,
    591,
    604,
    606,
    622,
    635,
    637,
    653,
    666,
    668
   ],
   "witness_provenance": {
    "found_by": [
     "@vprusso"
    ],
    "date": "2026-09-21",
    "found_at_samples": 1,
    "survived_samples": 1,
    "tool": "norm-word lift of a Z_31 quotient logical",
    "seeds": [
     0
    ]
   }
  },
  "Z": {
   "value": 66,
   "confidence": "upper_bound",
   "witness": [
    14,
    16,
    29,
    45,
    47,
    60,
    76,
    78,
    91,
    107,
    109,
    122,
    138,
    140,
    153,
    169,
    171,
    184,
    200,
    202,
    215,
    231,
    233,
    246,
    262,
    264,
    277,
    293,
    295,
    308,
    324,
    326,
    339,
    344,
    358,
    362,
    375,
    389,
    393,
    406,
    420,
    424,
    437,
    451,
    455,
    468,
    482,
    486,
    499,
    513,
    517,
    530,
    544,
    548,
    561,
    575,
    579,
    592,
    606,
    610,
    623,
    637,
    641,
    654,
    668,
    672
   ],
   "witness_provenance": {
    "found_by": [
     "@vprusso"
    ],
    "date": "2026-09-21",
    "found_at_samples": 1,
    "survived_samples": 1,
    "tool": "norm-word lift of a Z_31 quotient logical",
    "seeds": [
     0
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "@JiahaoYao"
  ],
  "construction": "Generalized bicycle on Z_341 = Z_11 x Z_31 with HX=[A|B], HZ=[B^T|A^T]; weight-16 supports a=[0, 1, 36, 58, 115, 135, 141, 161, 177, 212, 248, 280, 285, 289, 327, 333] and b=[0, 1, 12, 14, 23, 67, 76, 84, 128, 133, 181, 199, 270, 305, 310, 314]. Both words lie in the published leader's degree-91 cyclic ideal.",
  "references": [
   "https://unitaryfoundation.github.io/qldpc-challenge/codes/682-182-75.html",
   "https://arxiv.org/abs/2203.17216"
  ],
  "date": "2026-08-29",
  "origin": "submission",
  "model": "OpenAI GPT-5 (Codex)",
  "notes": "Distance is a witness-backed upper bound, not exact. Fresh-seed ladder: 4,000 (both sides) -> d<=85; 100,000 (both sides) -> d<=82; 200,000 (X side via GB symmetry) -> d<=82; 2,000,000 -> d<=79; 20,000,000 -> d<=76. The trusted gate reported no exact duplicate and no WL-equivalent board entry as of 2026-08-29. Literature novelty is unverified."
 },
 "family": "generalized-bicycle"
}