From 2c984734ce9f59ecde2305d9b3d35b79af700860 Mon Sep 17 00:00:00 2001
From: Yingjie Wang <phywyj@gmail.com>
Date: Fri, 10 Apr 2026 01:03:34 -0400
Subject: [PATCH] update: auto commit

---
 report.tex | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/report.tex b/report.tex
index b95d4ef..70b0245 100644
--- a/report.tex
+++ b/report.tex
@@ -690,9 +690,9 @@
   \pt \Theta ={} & \frac{1}{2} \lapse \left[ \Rscalar - \Ktf*{_i_j}
     \Ktf*{^i^j} + \frac{2}{3} \left( \hat{K} + 2 \Theta \right)^2
   \right] - \lapse \left[ 8 \pi \rho + \kappa_1 (2+\kappa_2) \Theta
-  \right] + \shift{^i} \Partial{_i} \Theta,
-  \pt \lapse &= - \mu_L \lapse^2 \hat{K} + \Ld{\beta} \lapse,\\
-  \pt \shift{^i} &= \mu_S \lapse^2 \Gam*{^i} - \eta \shift{^i} +
+  \right] + \shift{^i} \Partial{_i} \Theta,\\
+  \pt \lapse ={} & - \mu_L \lapse^2 \hat{K} + \Ld{\beta} \lapse,\\
+  \pt \shift{^i} ={} & \mu_S \lapse^2 \Gam*{^i} - \eta \shift{^i} +
   \shift{^j} \Partial{_j} \shift{^i}.
 \end{aligned}
 $}