Classification conjecture for Hermitian non-Kähler ALF gravitational instantons

Let $(\mathcal{M}, g_{ab})$ be a Hermitian, non-Kähler, ALF gravitational instanton, meaning a complete Ricci-flat Riemannian four-manifold with the stated Hermitian, non-Kähler, and asymptotically locally flat properties. Classification conjecture. $(\mathcal{M}, g_{ab})$ is one of the Euclidean Kerr, Chen-Teo, or Taub-bolt gravitational instantons. The conjecture is motivated by the classification of known Hermitian gravitational instantons and by the result that a Hermitian, non-Kähler ALF instanton with a 2-torus in its isometry group belongs to this list; the general case remains open.