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  "d": 4,
  "X": {
   "value": 4,
   "confidence": "upper_bound",
   "witness": [
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  "Z": {
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   "confidence": "upper_bound",
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 "provenance": {
  "authors": [
   "@MathysRennela"
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  "construction": "Affine-Frobenius quasi-dyadic CSS construction of arXiv:2609.24201 (Eq. 4): over F_16 with N = 16, exponent matrices P_X[u][j] = a_u*l_j, P_Z[v][j] = c_v*l_j^2 with a = c = [alpha^0, alpha^1], b = d = 0, w_X = w_Z = 2, lifted with size-16 dyadic permutation matrices; girth >= 6 by Theorem 1, CSS orthogonality by Theorem 2. High-rate corner of the family, found by sweeping the multiplier/shift variants off the paper's parameter grid.",
  "references": [
   "arXiv:2609.24201"
  ],
  "origin": "submission",
  "date": "2026-09-28",
  "model": "MiMo-V2.6-Flash",
  "notes": "Checked against the board: the gate's dedup pass found no equivalent entry. Advances the weight-9plus x unrestricted cell on k (194 against a board maximum of 130 at n <= 256); k >= 131 stays ahead of every n <= 256 entry at any distance >= 2. Distance is a witness-backed upper bound, not certified exact; literature novelty unverified.",
  "search_budget": {
   "candidates_screened": 14137,
   "ris_trials_per_side": 8000000,
   "cpu_hours": 5.0,
   "wall_clock_hours": 6.0,
   "tool": "campaign affine-Frobenius QD constructor + research kit surrogate distance search with gf2_fast + verify gate",
   "notes": "Campaign-wide figures, not this code alone: 13,920 variants k-screened with exact GF(2) ranks, 217 configurations distance-screened at 50k trials, finalists laddered 100k/500k/2M x 3 seeds and confirmed at 8M trials; wall-clock hours approximate."
  }
 },
 "family": "other"
}