Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strict Periodic Extreme Lattices   A lattice is called periodic extreme if it cannot locally be modified to
yield a better periodic sphere packing. It is called strict periodic extreme if
its sphere packing density is an isolated local optimum among periodic point
sets. In this note we show that a lattice is periodic extreme if and only if it
is extreme, that is, locally optimal among lattices. Moreover, we show that a
lattice is strict periodic extreme if and only if it is extreme and
non-floating.

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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph