Kronheimer–Mrowka's framed instanton and monopole Floer homology conjecture

Let $Y$ be a closed oriented $3$-manifold. Kronheimer–Mrowka's conjecture. The framed instanton homology and the tilde version of monopole Floer homology satisfy

$$HI^{\#}(Y)\simeq\widehat{HF}(Y)\otimes\mathbb{C}\simeq\widetilde{HM}(Y)\otimes\mathbb{C}.$$

This is a special case of the conjectural relationship between framed instanton homology, monopole Floer homology, and Heegaard Floer homology. The source provides no evidence that the conjecture has been resolved.