Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-maximal rank separable states are a set of measure 0 within the set
  of non-maximal rank states   This paper is being withdrawn due to an error in the proof. Hao Chen has
shown the author in the two qubit case that there is an open set of three
dimensional subspaces that are spanned by separable states. This means the
author's proof is in error. The problem is that homogeneity cannot be used and
so the Jacobian needs to be computed at all points

17
The categories of this paper are: q-fin
2
The categories of this paper are: math
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs