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 },
 "distance": {
  "d": 10,
  "X": {
   "value": 10,
   "confidence": "upper_bound",
   "witness": [
    1,
    19,
    33,
    44,
    48,
    61,
    79,
    93,
    104,
    108
   ]
  },
  "Z": {
   "value": 10,
   "confidence": "upper_bound",
   "witness": [
    0,
    16,
    32,
    45,
    48,
    180,
    196,
    212,
    225,
    228
   ]
  }
 },
 "provenance": {
  "authors": [
   "@hirobumii"
  ],
  "construction": "G=A5, even permutations of(0,1,2,3,4) in lexicographic order, composition a*b sends i to a[b[i]]. Set row-action L_g[t,u]=1 iff u=g*t, R_h[t,u]=1 iff u=t*h. A=[[I,I,I],[I,L_16,L_26]], B=[[I,I,I],[I,R_17,R_25]]. X(i,j) has A(i,k) on VV(k,j) and B(l,j) on CC(i,l); Z(k,l) has transpose(B(l,j)) on VV(k,j) and transpose(A(i,k)) on CC(i,l). Keep the lexicographically first independent rows in each sector. Full matrices have360 rows per sector, ranks358 each.",
  "references": [
   "https://arxiv.org/abs/2111.03654",
   "https://arxiv.org/abs/2607.28795",
   "https://arxiv.org/abs/2607.27644",
   "https://arxiv.org/abs/1611.07164"
  ],
  "date": "2026-10-17",
  "notes": "Displayed presentation: maximum check weight 5, maximum qubit degree 6, 716 checks and total incidence 3580.",
  "model": "GPT-6 Astra + GPT-6.1 Sol (recorded multi-agent configuration)"
 },
 "family": "lifted-product"
}