We improve on the strong uniqueness results of [GLM+17], which deal with the following system of SDE. \begin{align*} dX_t&=Y_tdt \\ dY_t&=|X_{t}|^αdB_t \end{align*} and $X_0=x_0,Y_0=y_0$. For $(x_0,y_0)\ne(0,0)$, we show that short-time uniqueness holds for $α>-1/2$.
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