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 },
 "distance": {
  "d": 6,
  "X": {
   "value": 6,
   "confidence": "upper_bound",
   "witness": [
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   ]
  },
  "Z": {
   "value": 6,
   "confidence": "upper_bound",
   "witness": [
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   ]
  }
 },
 "provenance": {
  "authors": [
   "@FarLab"
  ],
  "construction": "lifted product over the order-30 group metacyclic(15,2,11)[0] (research/kit builders), base matrices A = [[[0, 23], [0, 2, 16]]], B = [[[0, 5], [0, 13]]] (entries = group-element index supports)",
  "origin": "submission",
  "date": "2026-10-17",
  "model": "Claude Opus 5.5",
  "search_budget": {
   "candidates_screened": 81800,
   "ris_trials_per_side": 4000000,
   "cpu_hours": 4.5,
   "tool": "research/kit/search.py + gf2_fast on Brev n2d-highcpu-64"
  }
 },
 "family": "lifted-product",
 "circuit": {
  "d_circ": {
   "Z": {
    "value": 4,
    "confidence": "upper_bound",
    "witness": [
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     11861,
     13635,
     13643
    ]
   },
   "X": {
    "value": 5,
    "confidence": "upper_bound",
    "witness": [
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     24273,
     24664,
     26673,
     27320
    ]
   }
  },
  "rounds": 6,
  "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 (8 X + 9 Z CX layers per round, coloring candidate 0); 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)"
 }
}