Strong well-posedness conjecture for measure-valued drifts driven by fractional Brownian motion

Let $b$ be a finite signed measure on $\mathbb{R}$, let $H\in(0,1/2)$, and consider the stochastic differential equation

$$dX_t=b(X_t)\,dt+dB_t^H,$$

where $B^H$ is fractional Brownian motion with Hurst parameter $H$. Strong well-posedness conjecture. For every such $b$ and $H$, the equation has a unique strong solution. This conjecture would close the gap in the known strong well-posedness theory for measure-valued drifts: the result is established up to $H<(\sqrt{13}-3)/2$, while the remaining range up to $1/2$ is expected to hold but is described as a very hard challenge.