Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The 3-ball is a local pessimum for packing   It was conjectured by Ulam that the ball has the lowest optimal packing
fraction out of all convex, three-dimensional solids. Here we prove that any
origin-symmetric convex solid of sufficiently small asphericity can be packed
at a higher efficiency than balls. We also show that in dimensions 4, 5, 6, 7,
8, and 24 there are origin-symmetric convex bodies of arbitrarily small
asphericity that cannot be packed using a lattice as efficiently as balls can
be.

20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int