Analytic extension conjecture for semigroups generated by nonlinear resolvents

Let $G_r$ be the nonlinear resolvent associated with $r>0$, and let $q$ and $\gamma_r$ be the parameters defined in the paper. The semigroup generated by $G_r$ is considered with respect to the complex time parameter $t$. Analytic extension conjecture. For every $r>0$, the semigroup generated by $G_r$ can be analytically extended to the sector

$$\left\{t\in{\mathbb C}: \left|\arg t - \arg(1+rq)\right| < \frac{ \pi\gamma_r}{ 2}\right\}.$$

The paper proves analytic extension to a sector of opening $\pi\gamma_r$ for $r\geq r_0/\operatorname{Re}q$ and notes that $\gamma_r$ tends to $1$ as $r\to0^+$. The conjecture asks for this sectorial extension for every positive $r$, including the range not covered by the theorem.