update: auto commit

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wyj committed 2026-04-10 01:22:33 -04:00
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@@ -712,7 +712,7 @@ $}
\] \]
and replace all the spatical derivatives of the original variables with the new auxiliary variables, we got this and replace all the spatical derivatives of the original variables with the new auxiliary variables, we got this
\[ \[
\scalebox{0.45}{$\displaystyle \scalebox{0.47}{$\displaystyle
\begin{aligned} \begin{aligned}
\pt \chi ={}&\frac{2}{3} \chi \left[ \alpha \left( \hat{K} + \pt \chi ={}&\frac{2}{3} \chi \left[ \alpha \left( \hat{K} +
2\Theta \right) - \dshift{^i_i} - \Gam*{^j_j_k} \shift{^k} \right] 2\Theta \right) - \dshift{^i_i} - \Gam*{^j_j_k} \shift{^k} \right]