for some finite time $T < \infty$. Then there exist constants $\kappa = \kappa(g(0),T) > 0$ and $\rho = \rho(g(0),T) > 0$ such that the following holds.
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For every $t \in [0,T]$, every point $x \in M$, and every radius $r \in (0,\rho)$, if the geodesic ball $B_{g(t)}(x,r)$ satisfies the curvature bound