Donaldson's cone-singularity conjecture along an anticanonical divisor

Let $X$ be a Fano manifold, let $Y\in |-K_X|$ be a general smooth Calabi–Yau hypersurface, and let $R(X)$ be the supremum of the parameters $t$ for which the continuity-method equation is solvable. For a parameter $\beta$, a cone-singularity solution $\omega_\beta$ means a Kähler–Einstein metric with cone angle $2\pi\beta$ along $Y$, satisfying

$$\operatorname{Ric}(\omega)=\beta\omega+(1-\beta)\{Y\}.$$

Donaldson's conjecture. There is a cone-singularity solution $\omega_\beta$ to this equation for every parameter $\beta\in(0,R(X))$. If $R(X)<1$, there is no solution for any parameter $\beta\in(R(X),1)$. This conjecture relates the greatest solvable cone angle parameter to the continuity threshold $R(X);$ the source does not state a resolution.