From af0266508e235d9e187bdcfa5453f0d6e7c209f2 Mon Sep 17 00:00:00 2001
From: Yingjie Wang <phywyj@gmail.com>
Date: Fri, 10 Apr 2026 01:48:11 -0400
Subject: [PATCH] update: auto commit

---
 report.tex | 24 ++++++++++++++----------
 1 file changed, 14 insertions(+), 10 deletions(-)

diff --git a/report.tex b/report.tex
index c72905f..9f46ee7 100644
--- a/report.tex
+++ b/report.tex
@@ -807,16 +807,20 @@ $}
     $}
     \]
     these are closed, but not damping.
-    % \[
-    % \scalebox{0.8}{$\displaystyle
-    % \begin{aligned}
-    %   \pt \constraintA{_i} &= \dots - c_1 \constraintA{_i},\\
-    %   \pt \constraintB{^i_j} &= \dots - c_2 \constraintB{^i_j},\\
-    %   \pt \constraintC*{_i} &= \dots - c_3 \constraintC*{_i},\\
-    %   \pt \constraintD*{_i_j_k} &= \dots - c_4 \constraintD*{_i_j_k},
-    % \end{aligned}
-    % $}
-    % \]
+  \end{frame}
+
+  \begin{frame}{Searching for a first order Z4c}{old workflow: by hand}
+    The most simple way to damp the constraints:
+    \[
+    \scalebox{0.8}{$\displaystyle
+    \begin{aligned}
+      \pt \constraintA{_i} &= \dots - c_1 \constraintA{_i},\\
+      \pt \constraintB{^i_j} &= \dots - c_2 \constraintB{^i_j},\\
+      \pt \constraintC*{_i} &= \dots - c_3 \constraintC*{_i},\\
+      \pt \constraintD*{_i_j_k} &= \dots - c_4 \constraintD*{_i_j_k},
+    \end{aligned}
+    $}
+    \]
   \end{frame}
 
   \begin{frame}{References}