  SCORCH (Simulations and Constructions of the Reionization of Cosmic Hydrogen)
is a new project to study the Epoch of Reionization (EoR). In this first paper,
we probe the connection between observed high-redshift galaxies and simulated
dark matter halos to better understand the abundance and evolution of the
primary source of ionizing radiation. High-resolution N-body simulations are
run to quantify the abundance of dark matter halos as a function of mass $M$,
accretion rate $\dot{M}$, and redshift $z$. A new fit for the halo mass
function $dn/dM$ is $\approx 20\%$ more accurate at the high-mass end where
bright galaxies are expected to reside. A novel approach is used to fit the
halo accretion rate function $dn/d\dot{M}$ in terms of the halo mass function.
Abundance matching against the observed galaxy luminosity function is used to
estimate the luminosity-mass relation and the luminosity-accretion-rate
relation. The inferred star formation efficiency is not monotonic with $M$ nor
$\dot{M}$, but reaches a maximum value at a characteristic mass $\sim 2 \times
10^{11}\ M_\odot$ and a characteristic accretion rate $\sim 6 \times 10^2\
M_\odot/{\rm yr}$ at $z \approx 6$. We find a universal EoR
luminosity-accretion-rate relation and construct a fiducial model for the
galaxy luminosity function. The Schechter parameters evolve such that
$\phi_\star$ decreases, $M_\star$ is more positive (fainter), and $\alpha$ is
more negative (steeper) at higher redshifts. We forecast for the upcoming James
Webb Space Telescope and show that with apparent magnitude limit $m_{\rm AB}
\approx 31\ (32)$, it can observe $\gtrsim 11\ (24)$ unlensed galaxies per
square degree per unit redshift at least down to $M_\star$ at $z \lesssim 13\
(14)$.
