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 "distance": {
  "d": 10,
  "X": {
   "value": 10,
   "confidence": "upper_bound",
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 "provenance": {
  "authors": [
   "@FarLab"
  ],
  "construction": "2BGA (two-block group algebra) code on group ab(5,3,2) (|G|=30); H_X=[L(a)|R(b)], H_Z=[R(b)^T|L(a)^T] with a = [0, 3, 6, 20], b = [0, 9, 12, 14] 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",
  "notes": "WL-signature match with 60-6-9 (coprime BB on Z_5 x Z_6, the same abelian group Z_30 as Z_5 x Z_3 x Z_2 here) is a collision, not an equivalence: a SAT search with verify/sat_certify.py (selector encoding, 600 s per solve) returned UNSAT for logicals of weight <= 9 on both the X and the Z side of this code, so no weight-9 logical exists here, while 60-6-9 carries a verified weight-9 witness; a permutation-equivalent code would share it. Distance is nevertheless filed as upper_bound; a 3 x 20M fresh-seed gf2_fast ladder found nothing below 10.",
  "search_budget": {
   "candidates_screened": 3044305,
   "ris_trials_per_side": 60000000,
   "cpu_hours": 3,
   "tool": "research/kit/search.py-style sweep + gf2_fast on Brev n2d-highcpu-64"
  }
 },
 "family": "bivariate-bicycle",
 "circuit": {
  "d_circ": {
   "Z": {
    "value": 6,
    "confidence": "upper_bound",
    "witness": [
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    ]
   },
   "X": {
    "value": 5,
    "confidence": "upper_bound",
    "witness": [
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    ]
   }
  },
  "rounds": 10,
  "stim_version": "1.16.0",
  "notes": "Interleaved two-block extraction (Bravyi et al. arXiv:2308.07915 Table 5 style): joint reset and measurement layers, 9 CX layers per round; X-check term slots [2, 7, 6, 1, 3, 5, 8, 4], Z-check term slots [6, 1, 2, 7, 4, 3, 0, 5] over terms A_0..A_3, 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) Z-basis d_circ witness revised from 8 to 6: the CI refutation gate (PR #3682) found a lighter undetected fault set; its witness is the one recorded."
 }
}