Shown below are $Q^2$ vs.$W$ plots for the 4- and 5-pass data sets. Displayed on each is a phase space boundary (the red curve) inside which cross section spectra are needed to carry out the radiative corrections to our data (shown in black). Also shown are the data for the E01-012 and E94-010 experiments in blue and green, respectively. The vertical line indicates the pion production threshold. The upper boundary indicates a line for which $E_s$ (incoming electron energy) is a constant. The lower bound is calculated by varying the quantity $E_{s}^{min}$ (see Mo and Tsai, Rev. Mod. Phys. 41, 205 1969), defined by:
$E_s^{min}(E_p) = \frac{m_{\pi}^2 + 2Mm_{\pi} + 2ME_p}{2M - 2E_p(1 - \cos \theta)}$,
where $m_{\pi}$ is the pion mass, $M$ is the nucleon mass, $E_p$ is the scattered electron energy and $\theta$ is the scattering angle of the electron. $E_s^{min}$ is varied from the above value (evaluated using the smallest $E_p$ value in the data set) up to the $E_s$ value for the data set which needs the radiative corrections in steps of 1 MeV.