{
 "schema_version": "0.1",
 "name": "[[18,4,4]] [[4,2,2]]-amplified [[4,2,2]] rotated toric code (2x2 torus)",
 "code_type": "CSS",
 "n": 18,
 "k": 4,
 "checks": {
  "X": [
   [
    0,
    4,
    8,
    12,
    17
   ],
   [
    1,
    5,
    9,
    13,
    17
   ],
   [
    2,
    6,
    10,
    14,
    17
   ],
   [
    3,
    7,
    11,
    15,
    17
   ],
   [
    0,
    1,
    2,
    3,
    16
   ],
   [
    4,
    5,
    6,
    7,
    16
   ],
   [
    8,
    9,
    10,
    11,
    16
   ],
   [
    12,
    13,
    14,
    15,
    16
   ]
  ],
  "Z": [
   [
    0,
    4,
    8,
    12,
    16
   ],
   [
    1,
    5,
    9,
    13,
    16
   ],
   [
    2,
    6,
    10,
    14,
    16
   ],
   [
    3,
    7,
    11,
    15,
    16
   ],
   [
    0,
    1,
    2,
    3,
    17
   ],
   [
    4,
    5,
    6,
    7,
    17
   ],
   [
    8,
    9,
    10,
    11,
    17
   ],
   [
    12,
    13,
    14,
    15,
    17
   ]
  ]
 },
 "distance": {
  "d": 4,
  "X": {
   "value": 4,
   "confidence": "upper_bound",
   "witness": [
    0,
    1,
    12,
    13
   ]
  },
  "Z": {
   "value": 4,
   "confidence": "upper_bound",
   "witness": [
    0,
    1,
    12,
    13
   ]
  }
 },
 "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 [[4,2,2]] rotated toric code (2x2 torus) entry, using a sparse independent-row presentation of its checks: n' = 4n + m_X + m_Z = 18, k' = 2k = 4, check weight w' = w+1 = 5. 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: Rotated toric code on the periodic 2x2 lattice: all plaquette checks, (i+j) even -> X; distance 2 (cycle lengths).",
  "references": [
   "arXiv:2609.37231",
   "arXiv:quant-ph/9707021"
  ],
  "date": "2026-09-30",
  "notes": "Constructed and packaged with the Space Bunny Alpha 1.0 model. Filed under the -b slug: the board's codes/18-4-4.json is a different [[18,4,4]] (twisted-torus bivariate-bicycle, arXiv:2503.03827, by Zijian Liang, Ke Liu, Hao Song, Yu-An Chen), with a 2D-local layout, whereas this entry is the [[4,2,2]] amplification of the [[4,2,2]] toric code and carries no layout. The trusted gate reports no exact and no Weisfeiler-Leman-equivalent board entry: exact_duplicate_of null, wl_equivalent_of null.",
  "model": "Space Bunny Alpha 1.0"
 },
 "family": "distance-amplified"
}