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  ]
 },
 "distance": {
  "d": 6,
  "X": {
   "value": 6,
   "confidence": "upper_bound",
   "witness": [
    0,
    2,
    3,
    5,
    6,
    16
   ]
  },
  "Z": {
   "value": 6,
   "confidence": "upper_bound",
   "witness": [
    0,
    10,
    11,
    13,
    14,
    64
   ]
  }
 },
 "provenance": {
  "authors": [
   "@hirobumii"
  ],
  "construction": "G=C16, product x+y modulo16. L_g[t,u]=1 iff u=g+t; R_h[t,u]=1 iff u=t+h. A is1x4 with support triples[[0, 1, 2], [0, 1, 8], [0, 2, 6], [0, 3, 7]]; B is1x4 with support triples[[0, 1, 2], [0, 1, 8], [0, 4, 9], [0, 4, 10]]; sum the corresponding left or right permutation matrices overF2. Sixteen VV(k,j) blocks indexed4*k+j precede one CC block, eachsize16. X(j) places A(k) on VV(k,j) and B(j) on CC. Z(k) places B(j)^T on VV(k,j) and A(k)^T on CC. All64 original rows in each sector are independent and retained.",
  "references": [
   "https://arxiv.org/abs/2111.03654",
   "https://arxiv.org/abs/2607.28795"
  ],
  "date": "2026-10-17",
  "notes": "Displayed presentation: maximum check weight 15, maximum qubit degree 24, 128 checks and total incidence 1920.",
  "model": "GPT-6 Astra + GPT-6.1 Sol (recorded multi-agent configuration)"
 },
 "family": "lifted-product"
}