From 6882462126e1ab95e57bb8d87f96e0332cc8d751 Mon Sep 17 00:00:00 2001
From: Yingjie Wang <phywyj@gmail.com>
Date: Thu, 9 Apr 2026 21:22:10 -0400
Subject: [PATCH] update: auto commit

---
 report.tex | 7 ++++++-
 1 file changed, 6 insertions(+), 1 deletion(-)

diff --git a/report.tex b/report.tex
index 99d139c..ab3f5b7 100644
--- a/report.tex
+++ b/report.tex
@@ -321,7 +321,7 @@
       \begin{cases}
         \Partial{t}{\phi} = \pi, \\
         \Partial{t}{\pi} = \tensor{\delta}{^i^j} \Partial{i} \tensor{\psi}{_j},\\
-        \Partial{t}{\tensor{\psi}{_i}} = \Partial{i} \pi - \gamma \mathcal{C}_i,
+        \Partial{t}{\tensor{\psi}{_i}} = \Partial{i} \pi - \gamma \left( \tensor{\psi}{_i} - \Partial{i} \phi \right),
       \end{cases}
     \end{equation}
     where $\gamma > 0$ is a constant. Then the evolution of the constraints becomes
@@ -331,6 +331,11 @@
     which means that the constraint violation will decay exponentially with time, and thus the system is more stable for numerical simulations.
   \end{frame}
 
+  \begin{frame}{Towards first order Z4c}{constraints during the reduction}
+    We have to check if the constraint damping term will change the hyperbolicity of the system. The new principal symbol matrix is
+    
+  \end{frame}
+
   \begin{frame}{Existing first order formulations}
     \subsection{Existing first order formulations}
     \begin{itemize}