From a600917fb7adaa1e3c0810ae8ab76348a1e06c19 Mon Sep 17 00:00:00 2001
From: Yingjie Wang <phywyj@gmail.com>
Date: Fri, 10 Apr 2026 02:26:30 -0400
Subject: [PATCH] update: auto commit

---
 report.tex | 11 +++++++++++
 1 file changed, 11 insertions(+)

diff --git a/report.tex b/report.tex
index 766d3e5..d8c4390 100644
--- a/report.tex
+++ b/report.tex
@@ -853,6 +853,17 @@ $}
     \end{figure}
   \end{frame}
 
+  \begin{frame}{Searching for a first order Z4c}{A new idea: start from FOCCZ4}
+    Another way to speed up is, maybe we can start from FOCCZ4:
+    \begin{itemize}
+      \item FOCCZ4 is already strongly hyperbolic
+      \item FOCCZ4 only differs from our naive first order reduction of Z4c by some constraint terms, to be specific, sone terms proportional to $\tensor{\tilde{Z}}{^i}$ or it's derivatives. We can remove these differing terms and watch how the hyperbolicity changes, and find out how to recover the hyperbolicity
+      \item We also add constraint damping terms, which will break the hyperbolicity, and then find out how to recover the hyperbolicity.
+    \end{itemize}
+
+    In short, we are looking for a series of hyprbolicity-preserving modifications to FOCCZ4, to get a first order reduction of Z4c with constraint damping. This is working in progress.
+  \end{frame}
+
   \begin{frame}{References}
     \printbibliography
   \end{frame}