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   ],
   [
    85,
    93,
    114,
    139,
    156,
    163,
    180,
    190,
    198
   ],
   [
    84,
    106,
    115,
    138,
    157,
    162,
    181,
    191,
    199
   ],
   [
    87,
    95,
    116,
    141,
    158,
    165,
    182,
    192,
    200
   ],
   [
    86,
    108,
    117,
    140,
    159,
    164,
    183,
    193,
    201
   ],
   [
    89,
    97,
    118,
    143,
    160,
    167,
    184,
    194,
    202
   ],
   [
    88,
    110,
    119,
    142,
    161,
    166,
    185,
    195,
    203
   ],
   [
    91,
    99,
    120,
    127,
    145,
    162,
    186,
    196,
    204
   ],
   [
    90,
    112,
    121,
    126,
    144,
    163,
    187,
    197,
    205
   ],
   [
    93,
    101,
    122,
    129,
    147,
    164,
    188,
    198,
    206
   ],
   [
    92,
    114,
    123,
    128,
    146,
    165,
    189,
    199,
    207
   ],
   [
    95,
    103,
    124,
    131,
    149,
    166,
    190,
    200,
    208
   ],
   [
    94,
    116,
    125,
    130,
    148,
    167,
    191,
    201,
    209
   ]
  ]
 },
 "distance": {
  "d": 12,
  "X": {
   "value": 12,
   "confidence": "exact",
   "witness": [
    95,
    104,
    116,
    119,
    128,
    130,
    142,
    149,
    153,
    155,
    158,
    165
   ]
  },
  "Z": {
   "value": 12,
   "confidence": "exact",
   "witness": [
    53,
    59,
    70,
    75,
    82,
    126,
    130,
    134,
    136,
    140,
    155,
    158
   ]
  }
 },
 "provenance": {
  "authors": [
   "@yifanhong"
  ],
  "origin": "submission",
  "novelty": "known_parameters",
  "construction": "Balanced/lifted product over Z_21 semidirect-product_8 Z_2, with weight-3 group-ring entries a=1+xy+x^3y, b=1+x^12+x^17, c=1+x^4y+x^15y, d=1+x^9y+x^18y; reproduced from arXiv:2607.27644v1.",
  "model": "GPT 5.6 Sol",
  "references": [
   "arXiv:2607.27644v1"
  ],
  "date": "2026-08-02",
  "notes": "Published in Table 8 (Appendix A) of arXiv:2607.27644v1; fresh QDistEvol witnesses reproduced for this contribution."
 },
 "family": "balanced-product"
}