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We prove that the harmonic extension matrices for the two dimensional level- Sierpiński gasket are invertible for every . This has been previously conjectured to be true by Hino in  and  and tested numerically for . 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.
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Konstantinos Tsougkas, Non-degeneracy of the harmonic structure on Sierpiński gaskets. J. Fractal Geom. 6 (2019), no. 2 pp. 143–156