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   [
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    113,
    161,
    213,
    277
   ],
   [
    6,
    62,
    94,
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    102,
    114,
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    214,
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   ],
   [
    7,
    63,
    95,
    99,
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    163,
    215,
    277
   ],
   [
    8,
    76,
    80,
    104,
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   ],
   [
    9,
    77,
    81,
    105,
    109,
    129,
    141,
    217,
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   ],
   [
    10,
    78,
    82,
    106,
    110,
    130,
    142,
    218,
    278
   ],
   [
    11,
    79,
    83,
    107,
    111,
    131,
    143,
    219,
    278
   ],
   [
    16,
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    84,
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    120,
    148,
    220,
    279
   ],
   [
    17,
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    85,
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    149,
    221,
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   ],
   [
    18,
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    222,
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   ],
   [
    19,
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    87,
    107,
    111,
    123,
    151,
    223,
    279
   ]
  ]
 },
 "distance": {
  "d": 16,
  "X": {
   "value": 16,
   "confidence": "upper_bound",
   "witness": [
    44,
    47,
    128,
    131,
    144,
    147,
    156,
    159,
    164,
    167,
    180,
    183,
    208,
    211,
    216,
    219
   ]
  },
  "Z": {
   "value": 16,
   "confidence": "upper_bound",
   "witness": [
    45,
    47,
    73,
    75,
    81,
    83,
    97,
    99,
    157,
    159,
    193,
    195,
    205,
    207,
    213,
    215
   ]
  }
 },
 "provenance": {
  "authors": [
   "@FarLab"
  ],
  "construction": "[[4,2,2]] distance amplification of [[56,12,8]] (arXiv:2609.37231, central truncation of the CSS tensor product of codes/56-12-8.json with the [[4,2,2]] code, G_X = G_Z = [1111]; n = 4 n_base + m_X + m_Z, k = 2 k_base, d = 2 d_base by the paper's Eq. 3)",
  "origin": "submission",
  "date": "2026-09-30",
  "model": "Claude Fable 5.1",
  "notes": "Base code: codes/56-12-8.json ([[56,12,8]], by @MathysRennela); this entry is its [[4,2,2]] tensor amplification per arXiv:2609.37231, which is that paper's construction applied to a board code, not a new construction. Dedup gate: no exact or WL-equivalent board entry; checked, not equivalent. Base distance is certified exact (certs/56-12-8.json), so the theorem gives d = 16 exactly; filed as upper_bound.",
  "references": [
   "arXiv:2609.37231",
   "arXiv:1512.07081"
  ]
 },
 "family": "other"
}