# SCORCH I: The Galaxy-Halo Connection in the First Billion Years

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 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 and redshift *z*. A new fit for the halo mass function *dn*/*dM* is ≈20% more accurate at the high-mass end. A novel approach is used to fit the halo accretion rate function 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 but reaches a maximum value at a characteristic mass and a characteristic accretion rate at *z* ≈ 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 decreases, is fainter, and *α* is steeper at higher redshifts. We forecast for the upcoming *James Webb Space Telescope* and show that with apparent magnitude limit (32), it can observe (24) unlensed galaxies per square degree per unit redshift at least down to at *z* 13 (14).