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  "d": 5,
  "X": {
   "value": 5,
   "confidence": "upper_bound",
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   "confidence": "upper_bound",
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 "provenance": {
  "authors": [
   "@Xo1otl"
  ],
  "construction": "contributed via qldpc submit",
  "origin": "submission",
  "date": "2026-08-20",
  "model": "Claude Opus 5",
  "notes": "The m=3 case of this parameterization is the board's dense-packing column [[101,5,5]], [[197,5,7]], [[325,5,9]], [[485,5,11]], [[677,5,13]], which it reproduces exactly; [[101,5,5]] is this code's direct m=3 neighbour. This entry is the m=4 rung at d=5 and is not equivalent to any of them: n and k both differ. Pareto scope stated honestly: frontier in the 8 layout-restricted cells; in the 4 unrestricted cells [[112,8,5]] (weight 4, no layout) dominates it. Mutually non-dominated with the other ladder rungs on the board. Distance is a witness-backed upper bound from 20000 RIS trials per side, not a certified exact distance."
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 "circuit": {
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    "confidence": "upper_bound",
    "witness": [
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    "confidence": "upper_bound",
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  "rounds": 5,
  "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/measure layers; CX layers are a proper edge coloring of each Tanner graph (4 X + 4 Z CX layers per round, schedule seed 0; hook-aware orders: every CNOT order suffix needs >= d-1 further data errors to complete a logical, layered by min-conflicts search). Screened by RIS on ker(H_dem) and an observable-constrained seeded BP+OSD search; witnesses validated in GF(2).",
  "contributed_by": {
   "by": [
    "@vprusso"
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   "date": "2026-09-18",
   "method": "generic CSS memory schedule: one ancilla per check, CX layers from a bipartite edge coloring, CNOT orders filtered by a hook-error criterion; screened by RIS on ker(H_dem) and an observable-constrained seeded BP+OSD search"
  }
 }
}