Huisken's genericity conjecture for mean curvature flow

Consider mean curvature flow with generic initial data, meaning initial data outside an appropriate exceptional subset. A spherical singularity has spherical tangent model, and a cylindrical singularity has cylindrical tangent model. Huisken's genericity conjecture. Mean curvature flow with generic initial data only encounters spherical and cylindrical singularities. The source notes partial implications in dimensions four and five from a generic strong multiplicity-one statement, while the general conjecture remains open.