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 "distance": {
  "d": 72,
  "X": {
   "value": 72,
   "confidence": "upper_bound",
   "witness": [
    10,
    17,
    19,
    20,
    31,
    38,
    41,
    52,
    59,
    70,
    72,
    79,
    91,
    92,
    101,
    102,
    103,
    105,
    110,
    113,
    132,
    134,
    138,
    148,
    149,
    152,
    153,
    162,
    163,
    164,
    165,
    168,
    171,
    172,
    175,
    185,
    191,
    192,
    196,
    201,
    202,
    222,
    227,
    230,
    233,
    235,
    236,
    246,
    253,
    258,
    260,
    263,
    264,
    266,
    268,
    269,
    272,
    277,
    279,
    284,
    288,
    289,
    293,
    295,
    297,
    304,
    308,
    316,
    319,
    326,
    328,
    339
   ],
   "witness_provenance": {
    "found_by": [
     "@vprusso"
    ],
    "date": "2026-09-21",
    "found_at_samples": 1,
    "survived_samples": 1,
    "tool": "single-block logical from the constituent cyclic code (exact, not sampled)",
    "seeds": [
     0
    ]
   }
  },
  "Z": {
   "value": 72,
   "confidence": "upper_bound",
   "witness": [
    343,
    354,
    356,
    363,
    366,
    374,
    378,
    385,
    387,
    389,
    393,
    394,
    398,
    403,
    405,
    410,
    413,
    414,
    416,
    418,
    419,
    422,
    424,
    429,
    436,
    446,
    447,
    449,
    452,
    455,
    460,
    480,
    481,
    486,
    490,
    491,
    497,
    507,
    510,
    511,
    514,
    517,
    518,
    519,
    520,
    529,
    530,
    533,
    534,
    544,
    548,
    550,
    569,
    572,
    577,
    579,
    580,
    581,
    590,
    591,
    603,
    610,
    612,
    623,
    630,
    641,
    644,
    651,
    662,
    663,
    665,
    672
   ],
   "witness_provenance": {
    "found_by": [
     "@vprusso"
    ],
    "date": "2026-09-21",
    "found_at_samples": 1,
    "survived_samples": 1,
    "tool": "single-block logical from the constituent cyclic code (exact, not sampled)",
    "seeds": [
     0
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "@kessler-frost"
  ],
  "construction": "Cyclic generalized bicycle on Z_341; A=[0, 1, 2, 4, 12, 33, 56, 84, 89, 97, 145, 176, 265, 270, 287, 310]; B=[0, 2, 44, 64, 84, 99, 121, 132, 168, 190, 231, 261, 275, 283, 301, 319].",
  "references": [
   "https://github.com/unitaryfoundation/qldpc-challenge/tree/8933cda94eb6beb803cbaad37d925f8d2a8fadcc"
  ],
  "date": "2026-09-06",
  "notes": "Witness-backed upper bound; literature novelty unverified. {\"engine\": \"upstream gf2_fast.dem_rand_witness\", \"pair_depth\": 24, \"proposal_id\": \"b6d86d076d1b5806\", \"rung\": 4, \"seconds\": 211.35302416599006, \"seed\": 3952028553706826964, \"side\": \"X\", \"source_sha256\": \"d2ad08dffbec95b4650dd30d68275f2db096994420cb377580cffcbb14bf3be1\", \"threads\": 6, \"trials\": 2000000, \"upstream_commit\": \"8933cda94eb6beb803cbaad37d925f8d2a8fadcc\"} Distance corrected from d<=79 to d<=76 using the verified weight-76 X and Z witnesses reported in issue #942. The issue's verification checks place both witnesses in the appropriate opposite-check kernels and outside the stabilizer row spaces; the search budget is not reported.",
  "model": "GPT-6 Astra (openai-codex/gpt-6-astra)"
 },
 "family": "generalized-bicycle"
}