A topological proof of the non-degeneracy of harmonic structures on Sierpinski Gaskets

We present a direct proof of the non-degeneracy of the harmonic structures on the level-$n$ Sierpinski gaskets for any $n\ge 2$, which was conjectured by Hino in [H1,H2] and confirmed to be true by Tsougkas [T] very recently using Tutte’s spring theorem.