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 },
 "distance": {
  "d": 14,
  "X": {
   "value": 14,
   "confidence": "upper_bound",
   "witness": [
    7,
    9,
    12,
    13,
    14,
    16,
    20,
    28,
    48,
    50,
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   ]
  },
  "Z": {
   "value": 14,
   "confidence": "upper_bound",
   "witness": [
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   ]
  }
 },
 "provenance": {
  "authors": [
   "@EthanFeld"
  ],
  "origin": "submission",
  "novelty": "unknown",
  "construction": "generic 1x2 group-algebra chain product over semidirect(5,8,4); A=[[2, 3, 4, 27, 39], [0, 8, 12, 15, 18]]; B=[[8, 14, 23, 26, 39], [0, 4, 8, 14, 18]]",
  "references": [],
  "model": "GPT-5.6 Luna",
  "date": "2026-09-10",
  "notes": "Track-frontier candidate from an unrestricted group-algebra search. Local trusted preflight found no exact or WL-equivalent board match. Distance is a witness-backed upper bound, not an exact certification."
 },
 "family": "lifted-product"
}