From a54bd981ba9b3404fb3ee214e35ea66e8f566ff1 Mon Sep 17 00:00:00 2001
From: Yingjie Wang <phywyj@gmail.com>
Date: Fri, 10 Apr 2026 01:41:28 -0400
Subject: [PATCH] update: auto commit

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

diff --git a/report.tex b/report.tex
index d54f62c..199d8e4 100644
--- a/report.tex
+++ b/report.tex
@@ -772,6 +772,17 @@ $}
 
   \end{frame}
 
+  \begin{frame}{Searching for a first order Z4c}{old workflow: by hand}
+    We have several new constraints:
+    \begin{gather*}
+      \constraintA{_i} \definedby \dlapse{_i} - \Partial{_i} \lapse \qc
+      \constraintB{^i_j} \definedby \dshift{^i_j} - \Partial{_j} \shift{^i} \qc
+      \constraintC*{_i} \definedby \dchi*{_i} - \spaceD*{_i} \ln(\chi) \qc
+      \constraintD*{_i_j_k} \definedby \dsmetric*{_i_j_k} - \Partial{_i}
+      \smetric*{_j_k}
+    \end{gather*}
+  \end{frame}
+
   \begin{frame}{References}
     \printbibliography
   \end{frame}