Hermitian classification conjecture for non-Kähler ALF instantons

Let $(\mathcal{M},g_{ab})$ be a non-Kähler ALF Hermitian instanton. The Kerr, Chen--Teo, Taub-bolt, and Taub--NUT families are the named families of instantons, with the Taub--NUT metric understood with the orientation opposite to its hyperkähler orientation.

Hermitian classification conjecture. $(\mathcal{M},g_{ab})$ is one of Kerr, Chen--Teo, Taub-bolt, or Taub--NUT with the orientation opposite to the hyperkähler orientation.

This conjecture is presented as a rigidity statement toward classification of non-Kähler Hermitian ALF instantons. The source notes that toric ALF Hermitian instantons have been classified, while the general case remains open.