From 6c628abc14b750efb7f65cff12af89b896c954bf Mon Sep 17 00:00:00 2001
From: Yingjie Wang <phywyj@gmail.com>
Date: Thu, 9 Apr 2026 20:08:59 -0400
Subject: [PATCH] update: auto commit

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

diff --git a/report.tex b/report.tex
index eae8b98..cf2fcff 100644
--- a/report.tex
+++ b/report.tex
@@ -255,7 +255,7 @@
   \begin{frame}{Towards first order Z4c}{First order reduction}
     We can introduce auxiliary variables to reduce a second order PDE system to a first order one. For example, for the wave equation on flat spacetime:
     \begin{equation}
-      \pdvt[2]{\phi} - \tensor{\delta}{^i^j} \Partial{i} \Partial{j} \phi = 0,
+      \Partial{t}^2 {\phi} - \tensor{\delta}{^i^j} \Partial{i} \Partial{j} \phi = 0,
     \end{equation}
     we can introduce $\pi := \Partial{t} \phi$ and $\tensor{\psi}{_i} := \Partial{_i} \phi$, and rewrite the wave equation as
     \begin{equation}