Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Logical Construction of the Ionization Energy Theory and the Origin of
  Physical Categories   Logical proofs and definitions are developed to establish (i) the
energy-level spacings, \xi for each chemical element (from the periodic table
of chemical elements) can be converted to the ionization energies, (ii) both
\xi and the ionization energies are unique, and (iii) the averaged ionization
energies of any quantum matter is proportional to the averaged ionization
energies of its constituent chemical elements, if and only if \xi not = 0 and
\xi is not an irrelevant constant. Physical sets are then constructed such that
they are members of a specific physical class where each class belongs to a
specific physical category, P. However, there is not a single
structure-preserving functor from one energy-level spacing physical category,
P(\xi) to another P'(\xi). Therefore, the existence of many P(\xi) imply the
existence of different categories of physical systems and quantum matter.

32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio