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  ]
 },
 "distance": {
  "d": 4,
  "X": {
   "value": 4,
   "confidence": "upper_bound",
   "witness": [
    82,
    83,
    102,
    103
   ]
  },
  "Z": {
   "value": 4,
   "confidence": "upper_bound",
   "witness": [
    110,
    111,
    130,
    131
   ]
  }
 },
 "provenance": {
  "authors": [
   "@MathysRennela"
  ],
  "construction": "One amplification of [[36,24,2]] base by flagged [[4,2,2]] amplifier (arXiv:2609.37231).",
  "origin": "submission",
  "date": "2026-10-18",
  "model": "Beam 1.0"
 },
 "family": "other",
 "circuit": {
  "d_circ": {
   "Z": {
    "value": 2,
    "confidence": "upper_bound",
    "witness": [
     12611,
     12612
    ]
   },
   "X": {
    "value": 2,
    "confidence": "upper_bound",
    "witness": [
     9551,
     9552
    ]
   }
  },
  "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 (12 X + 13 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)"
 }
}