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 },
 "distance": {
  "d": 4,
  "X": {
   "value": 4,
   "confidence": "upper_bound",
   "witness": [
    48,
    49,
    52,
    53
   ]
  },
  "Z": {
   "value": 4,
   "confidence": "upper_bound",
   "witness": [
    240,
    241,
    244,
    245
   ]
  }
 },
 "provenance": {
  "authors": [
   "@MathysRennela"
  ],
  "construction": "Distance-amplified code: one [[4,2,2]] tensor-product amplification step (central three-term truncation of the chain-complex tensor product, arXiv:2609.37231 Eq. 1/Eq. 12-15) applied to the board's [[68,34,2]] 2BGA entry, using a sparse independent-row presentation of its checks: n' = 4n + m_X + m_Z = 306, k' = 2k = 68, check weight w' = w+1 = 7. X/Z witnesses are the base witnesses tensored with the weight-2 [[4,2,2]] logical on the central register (weights 4/4); a 100000-trial fast-backend search (seed 5000) found nothing lighter (min weight 4). Base provenance: 2BGA (arXiv:2306.16400) on SmallGroup(34,2), from github.com/QEC-pages/2BGA-codes @ 403d194c3f98f0cadc236aecbc4a8b6139ccf23c, abelian.zip, diswtabelian_wt6wtL2_order34_k34.txt, line 1. nonidentity supports a=[2], b=[2, 3, 4].",
  "references": [
   "arXiv:2609.37231"
  ],
  "date": "2026-09-30",
  "notes": "Constructed and packaged with the Space Bunny Alpha 1.0 model.",
  "model": "Space Bunny Alpha 1.0"
 },
 "family": "distance-amplified"
}
