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 "name": "Cornucopia [[144,76,4]]",
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 "distance": {
  "d": 4,
  "X": {
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   "confidence": "upper_bound",
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 "provenance": {
  "authors": [
   "@mathysrennela"
  ],
  "construction": "Cornucopia code (Lu, Li & Deng, arXiv:2608.02773; block-convolutional CSS construction with the check matrices given in the Methods of arXiv:2610.19073): q=4, n=36q=144 data qubits in twelve 3x4 tiles L0..L5,R0..R5 plus nine 3x4 X-check and nine 3x4 Z-check tiles; HX=[A_(j-i)|B_(j-i)], HZ=[B^-1_(i-j)|A^-1_(i-j)] with the coordinate permutations A_p,B_p:(r,c)|->(rho(p,r),c+s[p]) on Z_3 x Z_4, row maps rho_A(0)=r+1, rho_A(1)=2r+2, rho_B(2)=r+1, rho_B(3)=2r+2 (identity otherwise), and column shifts sA=[0,2,2,0,3,1], sB=[3,3,1,0,1,0]. These shifts were found by a random shift search; the paper publishes instances only at q=7,16,25,29,49,64,79. Weight-12 checks, k=18q+4=76.",
  "origin": "submission",
  "date": "2026-10-15",
  "model": "MiMo-V2.6-Flash",
  "search_budget": {
   "candidates_screened": 1200,
   "ris_trials_per_side": 100000,
   "tool": "OpenCode agent, MiMo-V2.6-Flash",
   "notes": "uniform random shift search, 3-stage RIS ladder (100/4000/100000 trials), see research note"
  },
  "references": [
   "arXiv:2608.02773",
   "arXiv:2610.19073"
  ]
 },
 "family": "other",
 "circuit": {
  "d_circ": {
   "Z": {
    "value": 3,
    "confidence": "upper_bound",
    "witness": [
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     22068,
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    ]
   },
   "X": {
    "value": 3,
    "confidence": "upper_bound",
    "witness": [
     22062,
     22063,
     22764
    ]
   }
  },
  "rounds": 4,
  "stim_version": "1.16.0",
  "notes": "Generic sequential two-block extraction: one ancilla per check, X checks then Z checks each round with joint reset and measurement layers; CX layers are a proper edge coloring of each Tanner graph (13 X + 13 Z CX layers per round, coloring candidate 1); generated by qldpc submit (research/circuit_autogen.py, seed 0), the first of up to 6 candidates whose RIS screen at 2 rounds found nothing below d; witnesses from RIS on ker(H_dem) at twice the gate's trial budget, validated in GF(2)"
 }
}