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 },
 "distance": {
  "d": 16,
  "X": {
   "value": 16,
   "confidence": "upper_bound",
   "witness": [
    9,
    10,
    25,
    30,
    35,
    36,
    44,
    47,
    59,
    86,
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   ]
  },
  "Z": {
   "value": 16,
   "confidence": "upper_bound",
   "witness": [
    1,
    25,
    30,
    35,
    37,
    44,
    46,
    54,
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    154,
    161,
    179
   ]
  }
 },
 "provenance": {
  "authors": [
   "@EthanFeld"
  ],
  "origin": "submission",
  "novelty": "unknown",
  "construction": "generic 1x2 group-algebra chain product over semidirect(15,4,13); A=[[6, 8, 9, 21, 24], [0, 3, 9, 38, 50]]; B=[[10, 21, 24, 52, 54], [0, 24, 43, 49, 56]]",
  "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"
}