Munteanu–Sung–Wang curvature-decay dichotomy for steady gradient Ricci solitons

Let $(M,g,f)$ be a complete non Ricci flat steady gradient Ricci soliton with $|\operatorname{Rm}|\to 0$ as $x\to\infty$, where $r$ denotes the distance function on $M$. Munteanu–Sung–Wang's curvature-decay conjecture. There is a positive constant $C$ such that, outside a compact set of $M$, either

$$C^{-1}r^{-1}\leq |\operatorname{Rm}|\leq Cr^{-1};$$

or

$$C^{-1}e^{-r}\leq |\operatorname{Rm}|\leq Ce^{-r}.$$

The conjecture proposes that non-Ricci-flat steady gradient Ricci solitons with curvature tending to zero have precisely either linear or exponential curvature decay. The paper presents it as a conjecture raised by Munteanu, Sung, and Wang; the supplied material gives no evidence that it has been resolved.