2 problems

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Fejes Toth's conjecture on the densest binary disk packing near ratio $\sqrt{2}-1$
Fejes Toth's conjecture. The packing in Figure has maximum density among disks with two radii whose ratio is slightly greater than $\sqrt{2}-1$ .
Conjectureopenbinary-packings disk-packings packing-densityarXiv posted 2 days ago
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Densest binary sphere packing conjecture at ratio $\sqrt{2}-1$
Binary sphere packing conjecture. The most dense packing has density $0.793$ , achieved when the large spheres are centered at the face-centered cubic lattice.
Conjectureopenbinary-packings packing-density sphere-packingsarXiv posted 2 days ago

Fejes Toth's conjecture on the densest binary disk packing near ratio 2−1\sqrt{2}-12​−1