Nisnevich's conjecture on torsors over punctured regular local rings

Let $R$ be a regular local ring of dimension $d\geq 1$, let $m$ be its maximal ideal, and let $u\in m\setminus m^2$. Let $G$ be a strictly isotropic reductive group over $R$. Nisnevich's conjecture.

$$H^1_{Zar}(R_u,G)=1.$$

Nisnevich established the conjecture when $\dim R=2$ and $G$ is quasi-split. Fedorov proved it when $R$ contains an infinite field, and Česnavičius extended this to finite fields and to the case where only $G_{R/u}$ is strictly isotropic; the equicharacteristic case is completely settled, while the full mixed-characteristic statement remains open.