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    488,
    496,
    560,
    623,
    628,
    629,
    646,
    650,
    659
   ]
  ]
 },
 "distance": {
  "d": 74,
  "X": {
   "value": 76,
   "confidence": "upper_bound",
   "witness": [
    9,
    23,
    36,
    54,
    63,
    92,
    99,
    103,
    109,
    122,
    128,
    144,
    148,
    165,
    197,
    202,
    203,
    207,
    209,
    219,
    227,
    246,
    248,
    254,
    274,
    276,
    283,
    287,
    289,
    292,
    302,
    312,
    316,
    318,
    324,
    329,
    333,
    334,
    340,
    354,
    356,
    360,
    378,
    415,
    416,
    433,
    436,
    448,
    459,
    476,
    497,
    498,
    507,
    508,
    527,
    538,
    539,
    547,
    569,
    581,
    584,
    587,
    595,
    602,
    615,
    621,
    623,
    624,
    626,
    628,
    635,
    638,
    640,
    641,
    666,
    668
   ],
   "witness_provenance": {
    "found_by": [
     "@vprusso"
    ],
    "date": "2026-09-23",
    "found_at_samples": 300000000,
    "tool": "ris_gpu recover, pair depth 8",
    "seeds": [
     1
    ],
    "survived_samples": 300000000
   }
  },
  "Z": {
   "value": 74,
   "confidence": "upper_bound",
   "witness": [
    5,
    12,
    13,
    16,
    21,
    27,
    31,
    32,
    38,
    39,
    49,
    56,
    58,
    65,
    69,
    72,
    73,
    74,
    75,
    76,
    77,
    78,
    79,
    85,
    99,
    102,
    103,
    105,
    106,
    107,
    114,
    119,
    125,
    129,
    133,
    136,
    146,
    148,
    150,
    151,
    152,
    176,
    185,
    186,
    188,
    189,
    196,
    199,
    203,
    214,
    215,
    225,
    228,
    230,
    233,
    236,
    250,
    263,
    277,
    286,
    294,
    300,
    312,
    323,
    355,
    361,
    367,
    385,
    416,
    528,
    593,
    641,
    663,
    673
   ],
   "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": [
     4102
    ]
   }
  }
 },
 "provenance": {
  "authors": [
   "@vprusso"
  ],
  "construction": "Four-factor m337 ideal: g=33893924722822194880126641; A=[14, 23, 27, 44, 45, 50, 113, 177, 185, 212, 222, 247, 251, 271, 305]; B=[34, 56, 66, 73, 92, 108, 115, 174, 176, 180, 200, 209, 214, 314, 330]",
  "references": [],
  "date": "2026-09-23",
  "notes": "Witness-backed upper bound d <= 76, not an exact-distance claim. Both submitted weight-76 logicals were found by GPU RIS recovery with pair depth 8, 300000000 trials per side, seed 1, and independently CPU-validated. Earlier native searches supported a bound of 80, which was refuted first to 78 by CI and then to 76 by the GPU audit. Literature novelty is unverified. Exact construction and correction details are in the accompanying note."
 },
 "family": "generalized-bicycle"
}