value for [$E_{\rm peak}$]{} from simulations of spectra of increasingly diminished intensity. Next, in section 3, we look at simulations of hard-to-soft pulses and the role of spectral evolution in the determination of average values of [$E_{\rm peak}$]{}. In section 4, we look at simulations of multiple, overlapping hard-to-soft pulses. Finally, we examine some intrinsic correlations that arise naturally in pulses with spectral evolution.

Limits on [$E_{\rm peak}$]{} Detectability
==========================================

By simulating $\sim15000$ different spectra via varying all Band function parameters on a spectral grid using GBM responses, we can study the efficiency of recovering $E_{\rm peak}$. Figure \[EpeakRecover\] shows the fraction of Band function fits that include the simulated true value of $E_{\rm peak}$ within the 1$\sigma$ uncertainty, marginalizing over all inputs of the amplitude, alpha, and beta. We find that $E_{\rm peak}$ can be reliably recovered between $\sim
20$ keV–40 MeV. Considering that the GBM bandpass is 8 keV–40 MeV, nearly all $E_{\rm peak}$ values that exist within the GBM band can be reliably recovered via spectral fitting. The low point at $~600$ keV represents a roughly 1 – 2 $\sigma$ fluctuation. Because the estimation and constraint of the Band function curvature is dependent on the low-energy index, 