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In this section we discuss observational and theoretical constraints on boundary conditions and input values for the model, most notably $P(z)$, $\dot M$, $v_\infty$, and $\omega(z=0)$. Table~\ref{tab:fiducial} shows the values we adopt for our fiducial model. They are discussed in more detail in the following sections. We vary the parameters individually to show how each of them affects the solution of the ODE.   \begin{table}  \label{tab:fiducial}  \caption{Vaues \caption{Values  for fidicual model} \begin{tabular}{cc}  \hline\hline  parameter & value\\