Consider a metric space $(X,d)$ with a distinguished selection of geodesics, i.e. a geodesic bicombing $\sigma:X\times X\times [0,1]\rightarrow X$. We call a geodesic bicombing *conical* if it satisfies the following "convexity-type condition"
$$
d(\sigma_{xy}(t), \sigma_{x^\prime y^\prime}(t))\leq (1-t)d(x,x^\prime)+t d(y,y^\prime)
$$
for all $x,x',y,y'\in X$ and $t\in [0,1]$.

If $(X,d)$ is a complete, separable, contractible Gromov ($\delta$) hyperbolic intrinsic metric space, for some $\delta>0$, then does $(X,d)$ admit a conical geodesic bicombing?

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