\begin{align*}
\sup_{(p,t) \in M \times [0,T)} |\operatorname{Rm}(g(t))|_{g(t)} < \infty,
\end{align*}
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then there exists $\varepsilon > 0$ and a smooth Ricci flow $\tilde g: [0,T+\varepsilon) \to \Gamma(S^2T^*M)$ such that $\tilde g(t)=g(t)$ for every $t \in [0,T)$.