result is that the highest energy photons are all confined to a very short time window very close to the GBM trigger time. Of course, real detectors are limited to counting photons, where the continuum model must break down. We note that there is a cluster of 3 Fermi LAT high-energy ($> 100$ MeV) photons in a 0.1 s window at or just before the GBM trigger time of GRB130427A, followed by a gap of 5 s.

![The spectral lag in seconds for the simulated pulse in Figure \[Sim\_EP\_Fit\] is plotted against the average energy of 9 spectral data bins of roughly equal width in log energy. Some of the BGO detector bins overlap in energy with those of the NaI, which accounts for the odd spacing. The binning is the same as can be seen in Figure \[Rob\_FWHM\_Energy\]. The lowest energy bin serves as the reference against which the lag of the higher energy bins is calculated and thus has zero lag by definition. \[Rob\_energy\_dep\_synthetic\_Suzanne\]](Rob_energy_dep_synthetic_Suzanne.pdf)

![The pulse widths in different energy bands in seconds for the simulated pulse in Figure \[Sim\_EP\_Fit\] is plotted against the average energy of each of the 9 spectral data bins of roughly equal width 