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 "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 [[27,11,3]] entry, using a sparse independent-row presentation of its checks: n' = 4n + m_X + m_Z = 124, k' = 2k = 22, 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 6/6); a 100000-trial fast-backend search (seed 5000) found nothing lighter (min weight 6). Base provenance: Reconstructed from qecdb.org record 67a4adf72916ddddf1688e1d (https://qecdb.org/codes/67a4adf72916ddddf1688e1d); the record's H field is read as binary symplectic rows and split by rowspace (rank(A|B) = rank(A) + rank(B)), keeping the lightest independent basis of each part; n, k and the check weight recomputed here, witnesses from the kit's random search at the trials below. Database description: hyperbolic_2d; database distance claim d=3 (lower 3, upper 3).",
  "references": [
   "arXiv:2609.37231"
  ],
  "date": "2026-09-30",
  "notes": ""
 },
 "family": "distance-amplified"
}