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 },
 "distance": {
  "d": 25,
  "X": {
   "value": 25,
   "confidence": "exact",
   "witness": [
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  },
  "Z": {
   "value": 25,
   "confidence": "exact",
   "witness": [
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  }
 },
 "provenance": {
  "authors": [
   "@seunomonije"
  ],
  "construction": "Generalized bicycle on the circulant ring Z_107: H_X = [B^T | A^T], H_Z = [A | B] with A = circ(a), B = circ(b), a = [0, 9, 13, 21, 27, 59], b = [0, 1]. Found by search over GB polynomial supports; distance proven exact by exhaustive DFS refutation (EMPTY at W = 24, 316,311,844,431 nodes).",
  "origin": "submission",
  "novelty": "unknown",
  "model": "exhaustive verification (exhaustive-qec verifier 0.1.0)",
  "date": "2026-08-14",
  "notes": "Distance certified exhaustively, not estimated. Full method, evidence and a re-runnable notebook: https://github.com/qernelkit/verifiable-qec-experiments/blob/main/experiments/qldpc_challenge/qldpc_challenge.ipynb"
 },
 "family": "generalized-bicycle"
}