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   [
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   [
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   [
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   [
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   [
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    195,
    204,
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   ],
   [
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    152,
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    196,
    233,
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   [
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   ],
   [
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   [
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   ]
  ]
 },
 "distance": {
  "d": 12,
  "X": {
   "value": 12,
   "confidence": "exact",
   "witness": [
    8,
    12,
    44,
    48,
    55,
    60,
    61,
    64,
    72,
    84,
    88,
    92
   ]
  },
  "Z": {
   "value": 12,
   "confidence": "exact",
   "witness": [
    51,
    61,
    68,
    71,
    72,
    80,
    91,
    145,
    146,
    150,
    157,
    164
   ]
  }
 },
 "provenance": {
  "authors": [
   "@yifanhong"
  ],
  "origin": "submission",
  "novelty": "known_parameters",
  "construction": "Balanced/lifted product over Z_12 semidirect-product_7 Z_4, with weight-3 group-ring entries a=1+x^8y+x^7y^2, b=1+x^2+x^5y, c=1+x^4y+x^2y^3, d=1+x^4+x^9; reproduced from arXiv:2607.27644v1.",
  "model": "GPT 5.6 Sol",
  "references": [
   "arXiv:2607.27644v1"
  ],
  "date": "2026-08-02",
  "notes": "Published in Table 1 of arXiv:2607.27644v1; fresh QDistEvol witnesses reproduced for this contribution."
 },
 "family": "balanced-product"
}