Reality or Mirage? Observational Test and Implications for the Claimed
  Extremely Magnified Quasar at $z = 6.3$
  In the last two decades, approximately 200 quasars have been discovered at
$z>6$, hosting active super-massive black holes with masses $M_{\bullet}
\gtrsim 10^9 M_{\odot}$. While these sources reflect only the tip of the
iceberg of the black hole mass distribution, their detection challenges
standard growth models. The most massive $z>6$ black hole that was inferred
thus far (J0100+2802, $M_{\bullet} \approx 1.2\times 10^{10} M_{\odot}$) was
recently claimed to be lensed, with a magnification factor $\mu=450$. Here, we
perform a consistency check of this claim, finding that the detection of such
source requires a bright-end slope $\beta \geq 3.7$ for the intrinsic quasar
luminosity function, $\Phi(L) \propto L^{-\beta}$. Commonly used values of
$\beta \sim 2.8$ are rejected at $>3\sigma$. If the claim is confirmed, it is
very unlikely that all the remaining $51$ sources in the SDSS sample are not
magnified. Furthermore, it suffices that $\gtrsim 25\%$ of the remaining
sources are lensed for the intrinsic luminosity function to differ
significantly (i.e., $>3\sigma$) from the observed one. The presence of
additional extremely magnified sources in the sample would lower the
requirement to $\sim 4\%$. Our results urge the community to perform more
extended multi-wavelength searches targeting $z>6$ lensed quasars, also among
known samples. This effort could vitally contribute to solving the open problem
of the growth of the brightest $z\sim 7$ quasars.
