Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Moon in a puddle and the four-vertex theorem   We present a proof of the Moon in a puddle theorem, and use its key lemma to
prove a generalization of the four-vertex theorem.

32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin