Quasi-isometry conjecture for the electric curve-complex model

Let $\mathcal{CC}\hat{}$ be the electric model of the curve complex obtained from the Cayley graph of $B_n$ by coning off the stabilizers of round curves, and let $\mathcal C_{AL}(B_n)$ be the additional length complex. Define a map

$$\varphi\colon \mathcal{CC}\hat{}\longrightarrow \mathcal C_{AL}(B_n)$$

by the construction in the paper.

Electric-model quasi-isometry conjecture. The map $\varphi$ is a quasi-isometry.

The electric model is already known to be quasi-isometric to the curve complex, while the paper constructs $\varphi$ and proves its Lipschitz properties; the asserted quasi-isometry is not established there.