deletions | additions       diff --git a/In_the_next_section_we__.tex b/In_the_next_section_we__.tex  index fcaf953..ec8d688 100644  --- a/In_the_next_section_we__.tex  +++ b/In_the_next_section_we__.tex 
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\end{equation*}  The shaded contour plot in Figure \ref{fig:integration_path} illustrates this $\rho(\Gamma_{\rm act}, P_{\rm act})$ distribution.   The expression blows up as $P_{\rm act} \rightarrow P_{\rm min}$ because such shallow dips are only observed for statistically impossible central encounters ($b = 0$). If we assume $P_{\rm min} \ll P_{\rm obs}$ for any observed values, then we can approximate avoid the singularity by approximating  $\left[ P_{\rm min}/\left( P_{\rm act} - P_{\rm min} \right) \right]^{3/2} \approx P_{\rm min}^{3/2}\ P_{\rm act}^{-3/2}$ and incorporate collecting  $P_{\rm min}^{3/2}$ into with  the suite of other  constants at the beginning of Equation \ref{eqn:convert_from_observed_to_actual_density}.