ELUCID -- Exploring the Local Universe with the reConstructed Initial
  Density field. II: Reconstruction diagnostics, applied to numerical halo
  catalogs
  The ELUCID project aims to build a series of realistic cosmological
simulations that reproduce the spatial and mass distribution of the galaxies as
observed in the Sloan Digital Sky Survey (SDSS). This requires powerful
reconstruction techniques to create constrained initial conditions. We test the
reconstruction method by applying it to several $N$-body simulations. We use 2
medium resolution simulations from each of which three additional constrained
$N$-body simulations were produced. We compare the resulting friend of friend
catalogs by using the particle indexes as tracers, and quantify the quality of
the reconstruction by varying the main smoothing parameter. The cross
identification method we use proves to be efficient, and the results suggest
that the most massive reconstructed halos are effectively traced from the same
Lagrangian regions in the initial conditions. Preliminary time dependence
analysis indicates that high mass end halos converge only at a redshift close
to the reconstruction redshift. This suggests that, for earlier snapshots, only
collections of progenitors may be effectively cross-identified.
