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$\implies$ we need to find a first order, strongly hyperbolic formulation of Einstein's equations with constraint damping and compatible with the moving puncture gauge condition.
\end{frame}
\begin{frame}{Towards first order Z4c}
\begin{frame}{Towards first order Z4c}{Hyperbolicity of first order systems}
\section{Towards first order Z4c}
\subsection{Hyperbolicity of first order systems}
Say we have a list of variables $u^I$, and a first order PDE system