Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantitative towers in finite difference calculus approximating the
  continuum   Multivector fields and differential forms at the continuum level have
respectively two commutative associative products, a third composition product
between them and various operators like $\partial$, $d$ and $*$ which are used
to describe many nonlinear problems. The point of this paper is to construct
consistent direct and inverse systems of finite dimensional approximations to
these structures and to calculate combinatorially how these finite dimensional
models differ from their continuum idealizations. In a Euclidean background
there is an explicit answer which is natural statistically.

3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph