– 10 – function of redshift. Early-type galaxies at low redshifts have colors similar to stars and then become redder in [3.6] − [4.5] for z > 1 at roughly fixed [5.8] − [8.0], tracking along the left edge of the AGN wedge. They become red in [3.6] − [4.5] due to the flux “peak” near rest-frame wavelength of 1.6 µ m, which passes through the 4.5 µ m band at a redshift of 1.5– 2.1. Late-type galaxies at low redshift have red [5.8] − [8.0] colors at low redshift due to the polycyclic aromatic hydrocarbon (PAH) emission in the 8 µ m band, then move horizontally to bluer [5.8] − [8.0] along the bottom of the AGN wedge as the feature is redshifted out of the 8 µ m band, and finally follow the early-type galaxies up along the left edge of the selection region. Pure AGNs remain inside the AGN wedge except near z ∼ 4 . 5 where they make an excursion out of the AGN wedge when the H α line lies in the 3.6 µ m band. If we use an equal combination of an AGN and a host galaxy, defined by the total emission from 0.1 to 30 µ m, the combined SED is somewhat bluer. With further increases in the host luminosity relative to the AGN, the source drops below the bottom of the AGN wedge. In fact, the distribution of the IRAC colors for the XBo¨ otes X-ray sources does extend below the Stern et al. (2005) AGN wedge (Gorjian et al. 2008). Based on Gorjian et al. (2008), we define a “modified AGN wedge” that encompasses most X-ray sources. This modified AGN wedge is defined by [3 . 6] − [4 . 5] < 2 . 5 × ([5 . 8] − [8 . 0]) − 0 . 6 mag (left side), [3 . 6] − [4 . 5] > 2 . 5 × ([5 . 8] − [8 . 0]) − 3 . 5 mag (right side), and [3 . 6] − [4 . 5] > 0 . 2 × ([5 . 8] − [8 . 0]) + 0 . 08 mag (bottom). Because we are identifying AGN candidates based on their mid- IR variability, we should be able to identify them in this [3 . 6] − [4 . 5] blueward extension of the Stern et al. (2005) selection region despite any host contamination. The caveat, however, is that this blueward extension is dominated by false positives (galaxies) if used to select AGNs based solely on their mid-IR colors without additional information such as variability or X-ray emission. We also define a “stellar” box which should contain most normal stars. The edges of this box are defined by − 0 . 15 mag < [3 . 6] − [4 . 5] < 0 . 15 mag and − 0 . 15 mag < [5 . 8] − [8 . 0] < 0 . 15 mag. The coldest stars, reaching into the brown dwarf regime, become red in [3 . 6] − [4 . 5] due to methane absorption in the 3.6 µ m band, but have [5 . 8] − [8 . 0] colors near zero and thus stay to the left of the AGN wedge (Stern et al. 2007; Eisenhardt et al. 2010). Beyond these mid-IR color diagnostics, we also use the extensive multi-wavelength and spectroscopic data for the field to characterize the sources. We know that the variable sources must be dominated by AGNs and a small fraction of stars, so the basic check on our selection criteria is that our selection limits on σ$_{12}$ and r preferentially select sources with AGN signatures, without introducing large numbers of contaminating sources.