From be1572e9ca0b90260e537523a15511252789be41 Mon Sep 17 00:00:00 2001
From: Yingjie Wang <phywyj@gmail.com>
Date: Fri, 10 Apr 2026 01:56:05 -0400
Subject: [PATCH] update: auto commit

---
 report.tex | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/report.tex b/report.tex
index 17ef350..0368975 100644
--- a/report.tex
+++ b/report.tex
@@ -823,8 +823,9 @@ $}
     \]
     where $c_1$, $c_2$, $c_3$ and $c_4$ are positive constants that large enough (the lower bound can be calculated). Thus we have constraint damping.
 
-    \vspace{0.5cm}
+    \vspace{0.2cm}
     {\color{red} \textbf{Unfortunately, this naive system is not even weakly hyperbolic!}}
+    \vspace{0.2cm}
 
     We have to add some constraint terms that equals to zero, while contributes to the principal symbol, until the principal symbol matrix is diagonalizable with real eigenvalues. This is the most tricky part, and we have to do it by hand, which is very time consuming and error prone.
   \end{frame}