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  "X": {
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   "confidence": "upper_bound",
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 "provenance": {
  "authors": [
   "@FarLab"
  ],
  "construction": "2BGA (two-block group algebra) code on group ab(9,3,2) (|G|=54); H_X=[L(a)|R(b)], H_Z=[R(b)^T|L(a)^T] with a = [0, 35, 45], b = [0, 2, 6, 47] as element indices of the Cayley table (identity = 0; table convention in the note)",
  "origin": "submission",
  "date": "2026-10-17",
  "model": "Claude Opus 5.5",
  "search_budget": {
   "candidates_screened": 27029048,
   "ris_trials_per_side": 30000000,
   "cpu_hours": 3,
   "tool": "research/kit 2BGA sweep + gf2_fast on Brev n2d-highcpu-64"
  }
 },
 "family": "bivariate-bicycle",
 "circuit": {
  "d_circ": {
   "Z": {
    "value": 12,
    "confidence": "upper_bound",
    "witness": [
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   },
   "X": {
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    "confidence": "upper_bound",
    "witness": [
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   }
  },
  "rounds": 12,
  "stim_version": "1.16.0",
  "notes": "Interleaved two-block extraction (Bravyi et al. arXiv:2308.07915 Table 5 style): joint reset and measurement layers, 8 CX layers per round; X-check term slots [6, 1, 7, 2, 3, 5, 4], Z-check term slots [0, 6, 1, 3, 4, 2, 5] over terms A_0..A_2, B_0..B_3; terms recovered from H alone by a commuting permutation decomposition; 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)"
 }
}