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 "distance": {
  "d": 82,
  "X": {
   "value": 82,
   "confidence": "upper_bound",
   "witness": [
    0,
    2,
    7,
    14,
    17,
    23,
    26,
    28,
    31,
    36,
    43,
    44,
    47,
    48,
    51,
    52,
    55,
    58,
    59,
    61,
    62,
    68,
    69,
    74,
    81,
    82,
    86,
    91,
    93,
    95,
    101,
    110,
    115,
    116,
    120,
    132,
    139,
    141,
    150,
    152,
    154,
    155,
    156,
    161,
    173,
    191,
    201,
    207,
    211,
    212,
    213,
    216,
    217,
    218,
    222,
    225,
    237,
    244,
    246,
    249,
    252,
    253,
    254,
    257,
    258,
    259,
    260,
    262,
    268,
    376,
    450,
    459,
    463,
    495,
    511,
    530,
    611,
    619,
    628,
    629,
    630,
    674
   ],
   "witness_provenance": {
    "found_by": [
     "@vprusso"
    ],
    "date": "2026-09-21",
    "found_at_samples": 300000000,
    "survived_samples": 300000000,
    "tool": "ris_gpu",
    "seeds": [
     2031
    ]
   }
  },
  "Z": {
   "value": 83,
   "confidence": "upper_bound",
   "witness": [
    2,
    10,
    13,
    14,
    20,
    23,
    24,
    26,
    28,
    29,
    31,
    32,
    40,
    41,
    44,
    49,
    50,
    58,
    59,
    60,
    62,
    64,
    65,
    66,
    68,
    73,
    78,
    83,
    91,
    95,
    113,
    114,
    115,
    127,
    132,
    134,
    138,
    142,
    144,
    152,
    153,
    154,
    158,
    163,
    164,
    167,
    174,
    177,
    179,
    183,
    188,
    189,
    195,
    197,
    198,
    199,
    211,
    213,
    215,
    225,
    230,
    232,
    233,
    240,
    252,
    254,
    257,
    258,
    259,
    266,
    269,
    344,
    371,
    379,
    403,
    505,
    529,
    607,
    611,
    645,
    646,
    666,
    680
   ],
   "witness_provenance": {
    "found_by": [
     "@vprusso"
    ],
    "date": "2026-09-24",
    "found_at_samples": 300000000,
    "survived_samples": 300000000,
    "tool": "verify/ris_gpu.py recover mode, pair depth 0 (GPU RIS, CPU re-verified)",
    "seeds": [
     4101
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "@DennisWayo"
  ],
  "construction": "Cyclic generalized-bicycle code over Z_341; divisor ideal degree 71 from x^341+1 over GF(2); a=[0, 1, 2, 22, 27, 29, 71, 91, 154, 162, 165, 197, 222, 236, 258, 289]; b=[79, 81, 82, 87, 109, 118, 121, 140, 141, 183, 185, 203, 207, 262, 267, 299]; H_X=[circ(a)|circ(b)], H_Z=[circ(b)^T|circ(a)^T].",
  "references": [],
  "date": "2026-09-14",
  "model": "OpenAI GPT-5 (Codex)",
  "notes": "Found by a cyclic-ideal generalized-bicycle search over Z_341 and tightened before submission. The initial package was reduced by the trusted circulant-GB structural gate, which found an X logical of weight 88. A deeper CI-style pre-submission refutation pass then found the submitted X logical witness of weight 87. A final local CI-style fire test at the submitted d<=87 claim ran the structural circulant-GB pass (400000 trials), the Python RIS pass (106840 trials), and RIS-fast (8000000 trials, seed 1396805778) without finding a lighter logical. This is an honest witness-backed upper-bound claim, not an exact-distance certificate. Refuted the d_Z<=90 claim with the verified weight-85 Z logical supplied by @ethanfeld on 2026-09-15; search budget not reported."
 },
 "family": "generalized-bicycle"
}