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   [
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   ]
  ]
 },
 "distance": {
  "d": 18,
  "X": {
   "value": 18,
   "confidence": "upper_bound",
   "witness": [
    1,
    15,
    31,
    45,
    53,
    64,
    89,
    118,
    133,
    152,
    173,
    182,
    191,
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    238,
    240,
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    252
   ]
  },
  "Z": {
   "value": 18,
   "confidence": "upper_bound",
   "witness": [
    0,
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    58,
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   ],
   "witness_provenance": {
    "found_by": [
     "@vprusso"
    ],
    "date": "2026-09-25",
    "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": [
   "@mathysrennela"
  ],
  "construction": "Cyclic generalized bicycle over Z_127 (n=2m=254): H_X=[circ(a)|circ(b)], H_Z=[circ(b)^T|circ(a)^T]. a and b are sparse multiples of the BCH-designed divisor g(x) of x^m-1 (g_int=62504535161; zero-set run 3, complement run 8), found by Prange search inside the ideal (g). Zero-set design after arXiv:2609.22503 (BCH run-length floors); construction family per arXiv:1904.02703. a=[1, 4, 10, 23, 48, 68, 101, 107, 126]; b=[19, 28, 57, 63, 84, 90, 101, 106, 121].",
  "origin": "submission",
  "date": "2026-09-22",
  "model": "GLM 5.3 Flash (Zed agent)",
  "search_budget": {
   "candidates_screened": 300,
   "ris_trials_per_side": 100000,
   "wall_clock_hours": 3.5,
   "tool": "research/cyclic_defining_set.py + gf2_fast",
   "notes": "One sweep over BCH-designed divisor ideals on Z_127 and Z_337 (29 records staged, 10 on the mutual Pareto frontier); per-code deep confirm at 100k RIS trials/side; wall clock shared across the batch and inflated by concurrent campaigns on this machine."
  },
  "notes": "The search_budget tool string names cyclic_defining_set.py under a research/ path; that script is kept in the authors' own repo and is not a file of this repository."
 },
 "family": "generalized-bicycle"
}