The square-root logarithmic fluctuation conjecture for IDLA on the Sierpinski gasket

Let $SG$ be the graphical Sierpinski gasket, let $o$ be its source vertex, and let $B_o(n)$ denote the graph-metric ball of radius $n$ centered at $o$. Write $\mathcal{I}(|B_o(n)|)$ for the IDLA cluster formed from $|B_o(n)|$ particles. IDLA fluctuation conjecture. There exists $C>0$ such that

$$B_o(n-C\sqrt{\log n})\subset \mathcal{I}(|B_o(n)|)\subset B_o(n+C\sqrt{\log n})$$

for all $n$, with probability $1$. The conjecture is motivated by simulations, while the paper's stated status is unresolved.