files / problems / hilbert16-degree-8 / compute / q1 / certs / dn_nbhd.json

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{
 "what": "Exhaustive one-split add/drop/swap neighbourhood of every published 22-oval Haas collection (the 38 of arXiv:2602.06888v3 Table 1). Parent dn_sweep.py mode nbhd.",
 "evals": 28861,
 "distinct_schemes": 38,
 "new": 0,
 "hits_on_open_nests": 0,
 "best_score": 6.0,
 "best_scheme": "<17 u 1<2 u 1<1>>>",
 "schemes": [
  "<10 u 1<11>>",
  "<10 u 1<2 u 1<8>>>",
  "<10 u 1<6 u 1<4>>>",
  "<11 u 1<6 u 1<3>>>",
  "<12 u 1<1> u 2<3>>",
  "<12 u 2<1> u 1<5>>",
  "<13 u 1<1> u 1<6>>",
  "<13 u 1<2> u 1<5>>",
  "<13 u 1<3> u 1<4>>",
  "<13 u 1<6 u 1<1>>>",
  "<14 u 1<7>>",
  "<16 u 3<1>>",
  "<17 u 1<1> u 1<2>>",
  "<17 u 1<2 u 1<1>>>",
  "<18 u 1<3>>",
  "<5 u 1<10 u 1<5>>>",
  "<5 u 1<14 u 1<1>>>",
  "<5 u 1<1> u 1<14>>",
  "<5 u 1<2> u 1<13>>",
  "<5 u 1<3> u 1<12>>",
  "<5 u 1<4> u 1<11>>",
  "<5 u 1<5> u 1<10>>",
  "<5 u 1<7> u 1<8>>",
  "<6 u 1<10 u 1<4>>>",
  "<6 u 1<15>>",
  "<6 u 1<6 u 1<8>>>",
  "<7 u 1<10 u 1<3>>>",
  "<8 u 1<1> u 1<3> u 1<7>>",
  "<8 u 1<1> u 2<5>>",
  "<8 u 2<1> u 1<9>>",
  "<8 u 2<3> u 1<5>>",
  "<9 u 1<10 u 1<1>>>",
  "<9 u 1<1> u 1<10>>",
  "<9 u 1<2> u 1<9>>",
  "<9 u 1<3> u 1<8>>",
  "<9 u 1<4> u 1<7>>",
  "<9 u 1<5> u 1<6>>",
  "<9 u 1<6 u 1<5>>>"
 ],
 "open_nests_in_scope": false,
 "note": "The two open (19,3) nests are not one add, drop, or swap from any published M-collection. Collection-distance at least 2. Not an obstruction."
}