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 "distance": {
  "d": 15,
  "X": {
   "value": 15,
   "confidence": "upper_bound",
   "witness": [
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   ]
  },
  "Z": {
   "value": 15,
   "confidence": "upper_bound",
   "witness": [
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  }
 },
 "provenance": {
  "authors": [
   "@FarLab"
  ],
  "construction": "bivariate bicycle on Z_7 x Z_10: A = x^0y^0 + x^2y^8 + x^3y^4 + x^4y^2, B = x^0y^0 + x^3y^3 + x^2y^0 + x^4y^5",
  "origin": "submission",
  "date": "2026-10-17",
  "model": "Claude Fable 5.1",
  "search_budget": {
   "candidates_screened": 3529,
   "ris_trials_per_side": 4000000,
   "cpu_hours": 6.5,
   "tool": "research/kit/search.py + gf2_fast on Brev n2d-highcpu-64"
  },
  "notes": "The Weisfeiler-Leman signature matches the board's [[140,10,10]] entry (a 2BGA on the metacyclic group Z_35 x| Z_2), but the two cannot be qubit permutations of each other: a permutation preserves logical weights, the board entry carries a weight-10 logical witness, and three fresh-seed runs of 4,000,000 gf2_fast RIS trials per side on this code (plus the qldpc submit 10,000,000-trial pass) found no logical below weight 15. This code is a bivariate bicycle code on the abelian torus Z_7 x Z_10."
 },
 "family": "bivariate-bicycle",
 "circuit": {
  "d_circ": {
   "Z": {
    "value": 15,
    "confidence": "upper_bound",
    "witness": [
     119004,
     119006,
     119020,
     119022,
     119040,
     119042,
     119053,
     119060,
     119068,
     119070,
     119078,
     119087,
     119089,
     119090,
     119109
    ]
   },
   "X": {
    "value": 15,
    "confidence": "upper_bound",
    "witness": [
     118692,
     118695,
     118755,
     118766,
     118808,
     118820,
     118822,
     118832,
     118939,
     118941,
     118985,
     119030,
     119053,
     119081,
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    ]
   }
  },
  "rounds": 15,
  "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 (10 X + 10 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)"
 }
}