in log energy. The trend of wider pulse width for lower energy is fitted with a power law, as suggested by @2005ApJ...627..324N. \[Rob\_FWHM\_Energy\]](Rob_FWHM_Energy.pdf)

![The spectral evolution of fitted [$E_{\rm peak}$]{} values during the first 3 s of GRB130427A is presented as the ‘continental divide’ (dashed line) on top of a $\nu {\cal F}_{\nu}$ contour plot. Because [$E_{\rm peak}$]{}  represents the peak of each $\nu {\cal F}_{\nu}$ spectrum (arranged in time from bottom to top), the levels of increasing intensity form closed contours. The peak intensity clearly comes later than the highest [$E_{\rm peak}$]{}, which is found at the start of the burst. \[GRB130427A\_Horiz\_Contour\]](GRB130427A_Horiz_Contour.pdf)

The high intensity of this initial simulation allows us to examine the results with high temporal resolution. In particular, we can bin the fitted [$E_{\rm peak}$]{} values according to number of occurrences in log energy, the result is shown in Figure \[ephisto\]. We have simulated a larger sample of spectra by using the time-resolved spectral fits from fifty simulations of bursts of varying brightness and different rise and decay parameters (Figure \[sim\_ep\_histo\]). The spectra were drawn from the set of simulations described below in Section \[asymsection\], all binned to the same signal-to-noise criterion. Thus, the brightest simulated 