L2 decay conjecture for Sierpinski gasket sampling functions

Let $\psi_m$ be a sampling function on level $m$ of the Sierpinski gasket $SG$. L2 decay conjecture. There is a constant $c$, numerically around $1.1$, such that

$$\int_{SG} \left| \psi_m \right|^2 \le c3^{-m}.$$

Unlike the corresponding real-line sampling behavior, this conjecture predicts decay of the squared $L^2$ norm with the level. The stated bound is based on numerical calculations.