  In large-scale optical spectroscopic surveys, there are many objects found to
have multiple redshift measurements due to the weakness of their emission lines
and the different automatic identification algorithms used. These include some
suspicious high-redshift (z >= 5) active galactic nuclei (AGNs). Here we
present a method for inspecting the high-redshift identification of such
sources provided that they are radio-loud and have very long baseline
interferometry (VLBI) imaging observations of their milli-arcsec (mas) scale
jet structure available at multiple epochs. The method is based on the
determination of jet component proper motions, and the fact that the
combination of jet physics (the observed maximal values of the bulk Lorentz
factor) and cosmology (the time dilation of observed phenomena in the early
Universe) constrain the possible values of apparent proper motions. As an
example, we present the case of the quasar J2346+0705 that was reported with
two different redshifts, $z_{1} = 5.063$ and $z_{2} = 0.171$, in the
literature. We measured the apparent proper motions ($\mu$) of three components
identified in its radio jet by utilizing VLBI data taken from 2014 to 2018. We
obtained $\mu_{J1} = 0.334 \pm 0.099$ mas yr$^{-1}$, $\mu_{J2} = 0.116 \pm
0.029$ mas yr$^{-1}$, and $\mu_{J3} = 0.060 \pm 0.005$ mas yr$^{-1}$. The
maximal proper motion is converted to an apparent transverse speed of
$\beta_{\rm app} = 41.2\pm12.2\,c$. if the source is at redshift 5.063. This
value exceeds the blazar jet speeds known to date. This and other arguments
suggest that J2346+0705 is hosted by a low-redshift galaxy. Our method may be
applicable for other high-redshift AGN candidates lacking unambiguous
spectroscopic redshift determination or having photometric redshift estimates
only, but showing prominent radio jets allowing for VLBI measurements of fast
jet proper motions.
