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 "distance": {
  "d": 10,
  "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(7,7) (|G|=49); H_X=[L(a)|R(b)], H_Z=[R(b)^T|L(a)^T] with a = [0, 29, 39, 44, 47], b = [0, 8, 11, 34, 37] as element indices of the Cayley table (identity = 0; table convention in the note)",
  "origin": "submission",
  "date": "2026-10-17",
  "model": "Claude Fable 5.1",
  "search_budget": {
   "candidates_screened": 9400000,
   "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": 6,
    "confidence": "upper_bound",
    "witness": [
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     40846,
     42036,
     42063,
     42564,
     43120
    ]
   },
   "X": {
    "value": 5,
    "confidence": "upper_bound",
    "witness": [
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     11138,
     11732,
     11909,
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    ]
   }
  },
  "rounds": 10,
  "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 + 12 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) X-basis d_circ witness revised from 10 to 6: the CI refutation gate (PR #3737) found a lighter undetected fault set; its witness is the one recorded. X-basis d_circ revised from 6 to 5: a deeper run of the CI gate's own circuit search (verify/gate_changed.py's ris_dem on the committed memory_x circuit, 21,900 trials, seed 957080627) found a lighter undetected logical fault set. Z-basis d_circ witness revised from 10 to 6: a deeper run of the CI gate's own circuit search (verify/gate_changed.py's ris_dem on the committed memory_z circuit, 21,900 trials, seed 1684224377) found a lighter undetected logical fault set found a lighter undetected fault set; its witness is the one recorded."
 }
}