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 "distance": {
  "d": 12,
  "X": {
   "value": 12,
   "confidence": "upper_bound",
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    "found_by": [
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    "date": "2026-10-12",
    "found_at_samples": 4000,
    "survived_samples": 4000,
    "tool": "research/kit/surrogate.lightest_logical",
    "seeds": [
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   "confidence": "upper_bound",
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 "provenance": {
  "authors": [
   "Rajpurohit, Rajendra Prasad",
   "Lalitha, V.",
   "Garani, Shayan Srinivasa",
   "@MathysRennela"
  ],
  "construction": "Coset lifted product (CLP) code of arXiv:2610.12782, Definition III.1, 1x1 over 2x2 layout: a protograph A over F_2[G] acting by the LEFT coset action of G on the cosets G/H, and a protograph B over F_2[N_G(H)] acting by the RIGHT coset action of the normaliser on the same cosets. G = SmallGroup(336,188), H = <f1*f3, f2, f5> (non-normal, core free), m = [G:H], n = 4m = 168. Elements are named by the polycyclic generating sequence f_1,...,f_r of SmallGroup(336,188), as in the paper's Appendix A. CSS commutation is automatic (L(g) and R(n) commute for every g in G and n in N_G(H), so each block of H_X H_Z^T is L R + R L = 0 over F_2); no search for it is needed. n, k and the check weight 7 reproduce the paper's Table I exactly. Literature baseline seeded from the published parameters: this entry is a REPRODUCTION built from the paper's printed data, not a new construction and not a new parameter set. The paper certifies d = 12 by integer program; this entry carries witness-backed upper bounds from our own randomized GF(2) search, which is a weaker claim.",
  "references": [
   "arXiv:2610.12782",
   "arXiv:2606.17268"
  ],
  "date": "2026-10-12",
  "notes": "Literature baseline: a reproduction of the published parameters in arXiv:2610.12782 (Table I), not a new construction and not a new parameter set. The group, subgroup and protographs are the paper's Appendix A data, rebuilt from GAP SmallGroup(l,i); n, k and the check weight reproduce the paper exactly. Reproduced by Space Bunny Alpha 1.0. The distance here is a witness-backed upper bound from our own randomized GF(2) search, a weaker claim than the paper's integer-program certification. See the accompanying note for the full reproduction recipe.",
  "origin": "baseline",
  "novelty": "known_parameters",
  "model": "Space Bunny Alpha 1.0"
 },
 "family": "2bga-coset"
}