Lovász and Szegedy's finite-dimension conjecture for typical vertices

A graphon is a measurable symmetric function $W:[0,1]^2\to[0,1]$. It is finitely forcible if it is uniquely determined, up to weak isomorphism, by the densities of finitely many graphs. Each graphon has an associated topological space whose points correspond to types of vertices appearing in sequences of graphs converging to it; these points are called typical vertices. Lovász and Szegedy's finite-dimension conjecture. The space of typical vertices of every finitely forcible graphon has finite dimension. This conjecture was disproved by a counterexample construction, so the space of typical vertices of a finitely forcible graphon can have infinite dimension.