Energy spectra at the shocks in the lab frame (moving with the shock) (blue) and in the stationary shock frame (orange). The resulting spectral slope and time evolution are the same. Error bars are obtained from the Monte Carlo error in each bin and proportional to $\sqrt{N}$, where N is the number of independent candidates in the respective bin. The discrepancy mainly is due to the time integration in the case of the stationary profile.