  Effective field theories that manifest UV/IR mode mixing in such a way as to
be valid for arbitrarily large volumes, can be used for gravitational,
non-black hole events to be accounted for. In formulating such theories with a
large number of particle species $N$, we employ constraints from the muon
$g-2$, higher-dimensional operator corrections due to the required UV and IR
cutoffs as well as the RG evolution in a conventional field-theoretical model
in curved space. While in general our bounds on $N$ do reflect $N \simeq
10^{32}$, a bound motivated by the solution to the hierarchy problem in alike
theories and obtained by the fact that strong gravity has not been seen in the
particle collisions, the bound from the muon $g-2$ turns out to be much
stronger, $N \lsim 10^{19}$. For systems on the verge of gravitational
collapse, this bound on $N$ is far too restrictive to allow populating a large
gap in entropy between those systems and that of black holes of the same size.
