From 93cd56980bf69408b99d99edf7b5759367580e06 Mon Sep 17 00:00:00 2001
From: Yingjie Wang <phywyj@gmail.com>
Date: Fri, 10 Apr 2026 01:43:14 -0400
Subject: [PATCH] update: auto commit

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

diff --git a/report.tex b/report.tex
index 57a9fa6..3f74f09 100644
--- a/report.tex
+++ b/report.tex
@@ -781,6 +781,17 @@ $}
       \constraintD*{_i_j_k} \definedby \dsmetric*{_i_j_k} - \Partial{_i}
       \smetric*{_j_k}
     \end{gather*}
+    constraint dynamics:
+    \[
+    \scalebox{0.8}{$\displaystyle
+    \begin{aligned}
+      \pt \constraintA{_i} &= \dots - c_1 \constraintA{_i},\\
+      \pt \constraintB{^i_j} &= \dots - c_2 \constraintB{^i_j},\\
+      \pt \constraintC*{_i} &= \dots - c_3 \constraintC*{_i},\\
+      \pt \constraintD*{_i_j_k} &= \dots - c_4 \constraintD*{_i_j_k},
+    \end{aligned}
+    $}
+    \]
   \end{frame}
 
   \begin{frame}{References}