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  "X": {
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   "confidence": "upper_bound",
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 "provenance": {
  "authors": [
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  "construction": "2BGA (two-block group algebra) code on group ab(7,3,2) (|G|=42); H_X=[L(a)|R(b)], H_Z=[R(b)^T|L(a)^T] with a = [0, 17, 31, 37], b = [0, 19, 28, 30] 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"
  }
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 "family": "bivariate-bicycle",
 "circuit": {
  "d_circ": {
   "Z": {
    "value": 5,
    "confidence": "upper_bound",
    "witness": [
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   },
   "X": {
    "value": 7,
    "confidence": "upper_bound",
    "witness": [
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  },
  "rounds": 12,
  "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 (9 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) d_circ tightened before submission by a deeper run of the gate's DEM search (X 12->7, Z 12->6). Z-basis d_circ witness revised from 6 to 5: the CI refutation gate (PR #3791) found a lighter undetected fault set; its witness is the one recorded."
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}