even higher accretion rate is required to produce the observed X-ray luminosities. However, the slope of the super-Eddington tail of the accretion rate distribution remains poorly constrained due to the limited samples of luminous, hard X-ray selected AGNs that enter our XLF, and thus the exact form of the bolometric correction does not have a substantial impact on our findings. ]{}]{}

In Figure \[fig:xlf\_modC\] we compare our prediction from model C with the observed XLF. With model C we are able to produce an XLF that is in good agreement with the observed data (considering the uncertainties in both our prediction and the observations). However, there are minor discrepancies between our observations and our model for the XLF. Our model underpredicts the number density of $L_\mathrm{X}\approx 10^{43.5-44.5}$[$\mathrm{erg\;s^{-1}}$]{} AGNs at $z\gtrsim0.7$, although the discrepancy is only at the $\sim 2\sigma$ level when considering the uncertainties in both the observed XLF and our model prediction (propagated from the SMF and measurements of the specific accretion rate distribution). In addition, the evolutionary behavior of our model is predominantly a density evolution. We do not reproduce the luminosity-dependent evolution found in a number of studies of the XLF, although our model prediction does provide 