Chen's fluctuation conjecture for internal DLA on the Sierpinski gasket

Let $\mathsf{SG}$ be the Sierpinski gasket graph, let $\mathcal{B}_n$ be the graph-metric ball of radius $n$, and let $\mathcal{I}_{|\mathcal{B}_n|}$ be the internal DLA cluster formed from that many particles. Chen's Sierpinski-gasket fluctuation conjecture. There exists $C>0$ such that

$$\mathcal{B}_{n-C\sqrt{\log n}}\subset \mathcal{I}_{|\mathcal{B}_n|}\subset \mathcal{B}_{n+C\sqrt{\log n}}.$$

The known limit shape on the Sierpinski gasket is a graph-metric ball, while the conjectured bound gives sub-logarithmic fluctuations around that shape; the source notes that the analogous harmonic-measure problem on the infinitely ramified Sierpinski carpet remains challenging.