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Table 3:
Summary statistics of the putative CK1 ground states and low-energy minima as identified by CMA-ES. The number of particles, energy, and the BOP values Q4, Q6, and are reported for all instances. For N=10, 14, 16, 22, 23, 25, multiple minima were identified. The putative ground states are labeled “A”, other minima “B” or “C”.
NEnergyQ4Q6
0.1084 −0.0931 
0.4630 0.3750 0.7408 −0.0463 
1.0583 0.5092 0.6285 0.0132 
1.1029 0.5619 0.4369 0.0076 
1.9838 0.6250 0.4556 0.0466 
3.1501 0.7638 0.3536 0.0132 
4.6241 0.5118 0.2861 0.0598 
6.3434 0.5092 0.6285 0.0132 
8.3580 0.1387 0.3561 −0.0342 
10A 10.6645 0.2574 0.3289 0.0407 
10B 10.6646 0.2740 0.3651 0.0254 
11 13.3828 0.0198 0.1129 0.1293 
12 16.1847 0.0415 −0.1698 
13 20.5410 0.0736 0.2470 −0.0032 
14A 25.1733 0.0771 0.2328 0.0131 
14B 25.1880 0.0729 0.2212 0.0111 
14C 25.2088 0.0278 0.0285 −0.0931 
15 30.9350 0.0332 0.1080 0.1196 
16A 38.4985 0.0464 0.0090 0.0931 
16B 38.5386 0.0615 0.2061 −0.0631 
17 47.3064 0.1044 0.0509 0.0931 
18 59.9795 0.0052 0.1623 −0.0931 
19 78.2895 0.0487 0.1009 0.1476 
20 94.1138 0.0630 0.1052 −0.0407 
21 122.3120 0.0173 0.1709 −0.0274 
22A 151.7772 0.0294 0.0043 0.0132 
22B 153.1696 0.0307 0.0481 0.0026 
23A 202.9820 0.0139 0.1418 −0.0329 
23B 203.0328 0.0145 0.1410 −0.0277 
24 236.1115 0.0164 0.0363 0.0132 
25A 314.0809 0.0047 0.1300 −0.0158 
25B 314.0909 0.0048 0.1299 −0.0176 
25C 321.7856 0.0235 0.1466 −0.0316 
NEnergyQ4Q6
0.1084 −0.0931 
0.4630 0.3750 0.7408 −0.0463 
1.0583 0.5092 0.6285 0.0132 
1.1029 0.5619 0.4369 0.0076 
1.9838 0.6250 0.4556 0.0466 
3.1501 0.7638 0.3536 0.0132 
4.6241 0.5118 0.2861 0.0598 
6.3434 0.5092 0.6285 0.0132 
8.3580 0.1387 0.3561 −0.0342 
10A 10.6645 0.2574 0.3289 0.0407 
10B 10.6646 0.2740 0.3651 0.0254 
11 13.3828 0.0198 0.1129 0.1293 
12 16.1847 0.0415 −0.1698 
13 20.5410 0.0736 0.2470 −0.0032 
14A 25.1733 0.0771 0.2328 0.0131 
14B 25.1880 0.0729 0.2212 0.0111 
14C 25.2088 0.0278 0.0285 −0.0931 
15 30.9350 0.0332 0.1080 0.1196 
16A 38.4985 0.0464 0.0090 0.0931 
16B 38.5386 0.0615 0.2061 −0.0631 
17 47.3064 0.1044 0.0509 0.0931 
18 59.9795 0.0052 0.1623 −0.0931 
19 78.2895 0.0487 0.1009 0.1476 
20 94.1138 0.0630 0.1052 −0.0407 
21 122.3120 0.0173 0.1709 −0.0274 
22A 151.7772 0.0294 0.0043 0.0132 
22B 153.1696 0.0307 0.0481 0.0026 
23A 202.9820 0.0139 0.1418 −0.0329 
23B 203.0328 0.0145 0.1410 −0.0277 
24 236.1115 0.0164 0.0363 0.0132 
25A 314.0809 0.0047 0.1300 −0.0158 
25B 314.0909 0.0048 0.1299 −0.0176 
25C 321.7856 0.0235 0.1466 −0.0316 
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