Let $M$ be a compact smooth manifold without boundary, let $I\subset\mathbb{R}$ be an interval, and let $g:I\to\Gamma(S^2T^*M)$ be a smooth Ricci flow on $M$. Let $u:M\times I\to\mathbb{R}$ and $v:M\times I\to\mathbb{R}$ be smooth functions such that
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\begin{align*}
\partial_t u &= \Delta_{g(t)}u, & \partial_t v &= -\Delta_{g(t)}v+R_{g(t)}v.
\end{align*}
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Then, for every interior time $t\in\operatorname{int}(I)$,