A liminf upper bound for the radii of univalence of harmonic derivatives

Let $f(z)=\sum_{k=1}^{\infty}a_k z^k+\overline{\sum_{k=1}^{\infty}b_kz^k}\in \mathcal{S}_{H}$. Let $R_f$ be the radius of convergence of $f$, let $R_n$ be the radius of univalence of $f^{(n)}$, and let $\alpha$ and $\beta$ denote the quantities defined in the preceding results. Liminf radius conjecture.

$$\liminf_{n\rightarrow \infty} n R_n\leq 2 \max\{\alpha,\beta\} R_f.$$

The conjecture proposes a sharper estimate for $R_n$ than the preceding inequality. Its status is not resolved in the supplied source.