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% \node[draw=none, above=1mm of gh, font=\scriptsize] {full first order};
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\end{tikzpicture}
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\caption{Evolution systems. Blue: second order systems; red: first order systems. Solid arrows: direct modifications; dashed arrows: relation. Bidirectional arrows: equivalence between systems.}
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\caption{Blue: second order systems; red: first order systems. Solid arrows: direct modifications; dashed arrows: relation. Bidirectional arrows: equivalence between systems.}
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\end{figure}
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\begin{itemize}
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\item Z4 and GH are said to be equivalent. They damps the momentum constraint and the Hamiltonian constraint respectively. They evolve the physical metric, and thus not compatible with the moving puncture method.
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