# Reference for the result that the systol map from Teichmuller space to curve complex is coarsely Lipschitz

Let $\mathcal{T}(S)$ denotes the Teichmuller space of a finite type surface $S$ equipped with Teichmuller metric and $\mathcal{C}(S)$ denotes the curve complex. Define a map $$\phi:\mathcal{T}(S)\rightarrow \mathcal{C}(S),$$ by taking a hyperbolic metric to one of its systols. I read somewhere that this map is coarsely Lipschitz. Can anyone please give a proper reference of this result.

PS: Please mention the theorem not just the paper.