Nonvanishing normal derivative conjecture for Green potentials on the Sierpinski gasket

For each integer $t\geq 0$, let $p_{t,1}$ be the relevant monomial on the Sierpinski gasket, let $G(x,y)$ be the Green function, and define

$$f_{t+1,1}(x):=-\int_{SG}G(x,y)p_{t,1}(y)\,dy.$$

Here $\partial_n$ denotes the normal derivative at the boundary point $q_0$.

Nonvanishing normal derivative conjecture. For every integer $t\geq 0$,

$$\partial_n f_{t+1,1}(q_0)\neq 0.$$

This conjecture is needed to extend results established for the cases $k=2,3$ to the family with $k=1$ of Sobolev orthogonal polynomials on the Sierpinski gasket. The source does not provide evidence that the claim has been resolved.