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 "distance": {
  "d": 24,
  "X": {
   "value": 24,
   "confidence": "upper_bound",
   "witness": [
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   "witness_provenance": {
    "found_by": [
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    ],
    "date": "2026-09-27",
    "found_at_samples": 300000000,
    "tool": "verify/ris_gpu.py (build/ris_gpu, NVIDIA A40)",
    "seeds": [
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    ],
    "survived_samples": 300000000
   }
  },
  "Z": {
   "value": 24,
   "confidence": "upper_bound",
   "witness": [
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   "witness_provenance": {
    "found_by": [
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    "date": "2026-09-27",
    "found_at_samples": 300000000,
    "tool": "verify/ris_gpu.py (build/ris_gpu, NVIDIA A40)",
    "seeds": [
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    ],
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   }
  }
 },
 "provenance": {
  "authors": [
   "@vprusso"
  ],
  "model": "Claude Fable 5.1 (Claude Code)",
  "construction": "Cyclic generalized-bicycle code over Z_168 (n = 2m = 336): a(x) = 1 + x^3 + x^135, b(x) = 1 + x^32 + x^146 + x^154; H_X = [circ(a)|circ(b)], H_Z = [circ(b)^T|circ(a)^T], where circ(v) has first row v and row i = v rolled by i (research/cyclic_gb.py build_cyclic_gb(168, a, b) with a, b the 0/1 first rows). k = 2 deg gcd(a, b, x^168 + 1).",
  "date": "2026-09-27"
 }
}
