Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fast neutrino flavor instability and neutrino flavor lepton number
  crossings   In this paper, we show the equivalency between the existence of fast neutrino
flavor instability and that of neutrino flavor lepton number (NFLN) crossings,
which indicates that an NFLN angular distribution takes both signs. The
veracity of this proposition has been uncertain and sometimes controversial
despite its indispensability in the flavor evolutions of dense neutrinos. This
study clarifies that the occurrence of an NFLN crossing is both necessary and
sufficient for fast instability.

20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph