The NuSTAR Extragalactic Survey of the James Webb Space Telescope North
  Ecliptic Pole Time-Domain Field
  We present the $NuSTAR$ extragalactic survey of the $James$ $Webb$ $Space$
$Telescope$ ($JWST$) North Ecliptic Pole (NEP) Time-Domain Field. The survey
covers a $\sim$0.16 deg$^2$ area with a total exposure of 681 ks acquired in a
total of nine observations from three epochs. The survey sensitivities at 20%
of the area are 2.39, 1.14, 2.76, 1.52, and 5.20 $\times$ 10$^{-14}$ erg
cm$^{-2}$ s$^{-1}$ in the 3-24, 3-8, 8-24, 8-16, and 16-24 keV bands,
respectively. The NEP survey is one of the most sensitive extragalactic surveys
with $NuSTAR$ so far. A total of 33 sources were detected above 95% reliability
in at least one of the five bands. We present the number counts, log$N$-log$S$,
measured in the hard X-ray 8-24 and 8-16 keV bands, uniquely accessible by
$NuSTAR$ down to such faint fluxes. We performed source detection on the
XMM-$Newton$ and $Chandra$ observations of the same field to search for soft
X-ray counterparts of each $NuSTAR$ detection. The soft band positions were
used to identify optical and infrared associations. We present the X-ray
properties (hardness ratio and luminosity) and optical-to-X-ray properties of
the detected sources. The measured fraction of candidate Compton-thick (N$\rm
_H\ge10^{24} cm^{-2}$) active galactic nuclei, derived from the hardness ratio,
is between 3% to 27%. As this survey was designed to have variability as its
primary focus, we present preliminary results on multi-epoch flux variability
in the 3-24 keV band.
