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   ]
  ]
 },
 "distance": {
  "d": 35,
  "X": {
   "value": 35,
   "confidence": "upper_bound",
   "witness": [
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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": [
     4102
    ]
   }
  },
  "Z": {
   "value": 35,
   "confidence": "upper_bound",
   "witness": [
    4,
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  }
 },
 "provenance": {
  "authors": [
   "@mathysrennela"
  ],
  "construction": "Bivariate bicycle on Z_12 x Z_12; A has 14 terms and B has 13 terms; exact supports are in the submitted JSON.",
  "origin": "submission",
  "date": "2026-08-18",
  "model": "GPT-5.6 Luna"
 },
 "family": "bivariate-bicycle"
}