On mutation invariance in Khovanov homology

We show that reduced Khovanov homology over any field is invariant under component-preserving Conway mutation. Our proof relies on strong geography restrictions for a certain Khovanov multicurve invariant associated with Conway tangles that we introduced in previous work [arXiv:1910.14584]. Applying ideas from homological mirror symmetry, we give a full classification of the components of this invariant.