The five-dimensional Bessel-process conjecture for the concave majorant of Brownian motion

Let $B=(B_t)_{t\geq 0}$ be a standard one-dimensional Brownian motion, and let $K=(K_t)_{t\geq 0}$ be its almost surely unique concave majorant on $[0,\infty)$. Write $R_5$ for a five-dimensional Bessel process started from $0$. The five-dimensional Bessel-process conjecture. The process

$$(2K(t)-B(t))_{t\geq 0}$$

has the law of the radial part of a five-dimensional Brownian motion, equivalently, the law of $R_5$.

The conjecture is motivated by the fact that $2K(1)-B(1)$ has the same distribution as the one-dimensional marginal of $R_5$ at time $1$, together with several further matching properties. The process is also conjectured in the paper to have the distribution of $R_5$; the source provides no resolution.