From b2dedc9c41936c695b794467e0fb57d481a41adb Mon Sep 17 00:00:00 2001
From: Yingjie Wang <phywyj@gmail.com>
Date: Thu, 9 Apr 2026 20:05:45 -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 70df743..dc8bcc8 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}\pdv{\phi}{x^i}{x^j} = 0,
+      \pdvt[2]{\phi} - \nabla^2 \phi = 0,
     \end{equation}
     we can introduce $\pi := \pdvt{\phi}$ and $\psi := \pdv{\phi}{x}$, and rewrite the wave equation as
     \begin{equation}