Younsi–Ransford monotonicity conjecture for analytic capacity ratios

Let $E_r$ and $F_r$ be the unions of disks determined by points $z_1,\dots,z_n$ and $w_1,\dots,w_m$, respectively, with $0<r<\delta/2$, and define

$$R(r):=\frac{\gamma(E_r\cup F_r)}{\gamma(E_r)+\gamma(F_r)}.$$

Younsi–Ransford conjecture. For all $z_1,\dots,z_n,w_1,\dots,w_m$, the function $R(r)$ is decreasing on $0<r<\delta/2$.

Numerical experiments suggest this monotonicity, alongside the conjectured subadditivity of analytic capacity, but no resolution is given here.