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    198,
    219,
    229,
    237,
    242,
    248
   ],
   [
    107,
    114,
    123,
    127,
    135,
    174,
    179,
    184,
    190,
    199,
    215,
    225,
    238,
    241,
    249
   ]
  ]
 },
 "distance": {
  "d": 16,
  "X": {
   "value": 16,
   "confidence": "upper_bound",
   "witness": [
    2,
    15,
    19,
    22,
    23,
    29,
    33,
    55,
    58,
    59,
    68,
    71,
    78,
    90,
    91,
    95
   ]
  },
  "Z": {
   "value": 16,
   "confidence": "upper_bound",
   "witness": [
    52,
    64,
    65,
    81,
    82,
    83,
    93,
    97,
    152,
    157,
    166,
    176,
    179,
    183,
    187,
    188
   ]
  }
 },
 "provenance": {
  "authors": [
   "@EthanFeld"
  ],
  "origin": "submission",
  "novelty": "unknown",
  "construction": "generic 1x2 group-algebra chain product over product(cyclic(5),dihedral(10)); A=[[0, 12, 13, 18, 22], [0, 5, 21, 31, 44]]; B=[[12, 25, 32, 36, 44], [0, 9, 30, 35, 45]]",
  "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"
}