  We prove that the harmonic extension matrices for the level-k Sierpinski
Gasket are invertible for every k>2. This has been previously conjectured to be
true by Hino in [6] and [7] and tested numerically for k<50. We also give a
necessary condition for the non-degeneracy of the harmonic structure for
general finitely ramified self-similar sets based on the vertex connectivity of
their first graph approximation.
