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 },
 "distance": {
  "d": 34,
  "X": {
   "value": 34,
   "confidence": "upper_bound",
   "witness": [
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   "witness_provenance": {
    "found_by": [
     "@vprusso"
    ],
    "date": "2026-09-23",
    "found_at_samples": 80000000,
    "survived_samples": 80000000,
    "seeds": [
     5804
    ],
    "tool": "verify/ris_gpu.cu deep kernel, pair depth 8, CPU re-verified (gf2)"
   }
  },
  "Z": {
   "value": 38,
   "confidence": "upper_bound",
   "witness": [
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   ],
   "witness_provenance": {
    "found_by": [
     "@vprusso"
    ],
    "date": "2026-09-23",
    "found_at_samples": 64019768,
    "survived_samples": 64019768,
    "seeds": [
     5803
    ],
    "tool": "verify/ris_gpu.cu deep kernel, pair depth 8, CPU re-verified (gf2)"
   }
  }
 },
 "provenance": {
  "authors": [
   "@mathysrennela"
  ],
  "construction": "Two-block group-algebra code on the metacyclic group Z_43 x| Z_7 (order 301), r=4; a=[101,298,76,82,215], b=[165,152,299].",
  "origin": "submission",
  "date": "2026-09-14",
  "model": "DeepSeek V4 Flash 0731",
  "notes": "Tightened 2026-09-23 by @vprusso: a GPU random-information-set audit (verify/ris_gpu.cu deep kernel: full kernel basis plus pair sums, pair depth 8, recover mode; 80,000,000 X and 64,019,768 Z trials in chunks with fresh seeds 5800 to 5805) exhibits a weight-34 X-type logical, so d <= 34 (X 46 -> 34, Z 40 -> 38). Per chunk: X 72 at 1,000,000 trials (seed 5800); Z 66 at 1,000,000 trials (seed 5801); X 36 at 50,395,839 trials (seed 5802); Z 38 at 50,881,607 trials (seed 5803); X 34 at 28,604,161 trials (seed 5804); Z 50 at 12,138,161 trials (seed 5805). Every GPU operator was re-verified on the CPU with verify/gf2.py. Distance remains a witness-backed upper bound."
 },
 "family": "generalized-bicycle"
}