files / problems / hilbert16-degree-8 / compute / q7 / certs / q7_summary.json

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{
 "search": "q7: leftover odd size-5 and tractable even components",
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   "<18 u 1<3>>",
   "<5 u 1<1> u 1<14>>",
   "<5 u 1<2> u 1<13>>",
   "<6 u 1<15>>",
   "<9 u 1<10 u 1<1>>>",
   "<9 u 1<1> u 1<10>>",
   "<9 u 1<2> u 1<9>>"
  ]
 },
 "even_components": {
  "what": "Component sizes for q5's pinned even add/drop/swap BFS. Five nonempty fixed-odd components are counted exactly. The all-even component is additional, so the sum is a certified lower bound on the full BFS closure, not a lower bound on real schemes.",
  "split_count": 1254,
  "even_split_count": 1065,
  "fixed_odd_components": 6,
  "exact_nonempty_component_collections": 538188419044,
  "all_even_component_collections_at_least": 249665706104,
  "full_bfs_collections_at_least": 787854125148,
  "lower_bound_reason": "Removing the fixed odd splits injects every even clique from a nonempty-odd component into the all-even component.",
  "full_bfs_complete": false,
  "components": [
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    "complete": true,
    "memo_states": 144
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   {
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    "compatible_even_splits": 340,
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    "complete": true,
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   {
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   {
    "seeds": [
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    "compatible_even_splits": 60,
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    "complete": true,
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   {
    "seeds": [
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    "odd_splits": [
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    "compatible_even_splits": 321,
    "collections": 88755852384,
    "complete": true,
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   {
    "seeds": [
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    "odd_splits": [],
    "compatible_even_splits": 1065,
    "collections": null,
    "complete": false,
    "why_incomplete": "The all-even component is larger than the already huge nonempty-odd components; it is not needed for the certified lower bound on the BFS closure size."
   }
  ]
 },
 "even_enumerated": [
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   "what": "All compatible even-split subsets with the odd splits of a published (19,3) collection held fixed.",
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   "seconds": 6.643,
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  {
   "what": "All compatible even-split subsets with the odd splits of a published (19,3) collection held fixed.",
   "seed": "<12v1<1>v2<3>>",
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   "compatible_even_splits": 108,
   "evals": 20436160,
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   "schemes": [
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  {
   "what": "All compatible even-split subsets with the odd splits of a published (19,3) collection held fixed.",
   "seed": "<17v1<2v1<1>>>",
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   "compatible_even_splits": 60,
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  {
   "what": "All compatible even-split subsets with the odd splits of a published (19,3) collection held fixed.",
   "seed": "<5v1<1>v1<14>>",
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   "compatible_even_splits": 49,
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  {
   "what": "All compatible even-split subsets with the odd splits of a published (19,3) collection held fixed.",
   "seed": "<5v1<5>v1<10>>",
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  {
   "what": "All compatible even-split subsets with the odd splits of a published (19,3) collection held fixed.",
   "seed": "<6v1<6v1<8>>>",
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  {
   "what": "All compatible even-split subsets with the odd splits of a published (19,3) collection held fixed.",
   "seed": "<8v2<1>v1<9>>",
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   "compatible_even_splits": 44,
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   "complete": true,
   "seconds": 93.745,
   "schemes": [
    "<8 u 2<1> u 1<9>>",
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  {
   "what": "All compatible even-split subsets with the odd splits of a published (19,3) collection held fixed.",
   "seed": "<9v1<2>v1<9>>",
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   "schemes": [
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  },
  {
   "what": "All compatible even-split subsets with the odd splits of a published (19,3) collection held fixed.",
   "seed": "<9v1<5>v1<6>>",
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   "compatible_even_splits": 39,
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  }
 ],
 "NEW_candidates": [],
 "NEW_candidates_ovals": {},
 "candidate_cert_file": null
}