Horizon Run 3: Topology as a Standard Ruler
  We study the Physically Self Bound Cold Dark Matter Halo distribution which
we associate with the massive galaxies within the Horizon Run 3 to estimate the
accuracy in determination of the cosmological distance scale measured by the
topology analysis. We apply the routine "Contour 3D" to 108 Mock Survey of
$\pi$ steradians out to redshift z = 0.6, which effectively correspond to the
SDSS-III BOSS survey, and compare the topology with that of a Gaussian Random
Phase Field. We find that given three separate smoothing lengths $\lambda =$
15, 21, and 34 $h^{-1}{\rm Mpc}$, the least $\chi^2$ fit genus per unit volume
g yields a 1.7 % fractional uncertainty in smoothing length and angular
diameter distance to $z = 0.6$. This is an improvement upon former calibrations
of and presents a competitive error estimate with next BAO scale techniques. We
also present three dimensional graphics of the Horizon Run 3 spherical mock
survey to show a wealth of large-scale structures of the universe that are
predicted in surveys like BOSS.
