Ouaki–Pitman conjecture on the concave-majorant transform of Brownian motion

Let $B$ be a one-dimensional Brownian motion on $[0,\infty)$ and let $K$ be its almost surely existing concave majorant on $[0,\infty)$. Ouaki–Pitman conjecture. The process $2K-B$ has the law of the $\operatorname{BES}(5)$ process. This conjecture is the analogue for concave majorants of Pitman’s $2M-B$ theorem, which identifies the corresponding transform using the running maximum with the $\operatorname{BES}(3)$ process. The source gives no resolution of the conjecture.