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 "distance": {
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   "confidence": "upper_bound",
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 "provenance": {
  "authors": [
   "@MathysRennela"
  ],
  "construction": "Construction I of arXiv:2610.19451, N=31",
  "origin": "submission",
  "date": "2026-10-17",
  "model": "Beam 1.0"
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 "family": "other",
 "circuit": {
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   "Z": {
    "value": 3,
    "confidence": "upper_bound",
    "witness": [
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   },
   "X": {
    "value": 3,
    "confidence": "upper_bound",
    "witness": [
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   }
  },
  "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 (7 X + 7 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)"
 }
}