Chromatic invariance conjecture for generalized Sierpiński gasket graphs

Let $G$ be a simple graph, let $t$ be a positive integer, and let $S[G,t]$ denote the generalized Sierpiński gasket graph based on $G$ at level $t$. Write $\chi(G)$ for the chromatic number of $G$. Chromatic invariance conjecture. For each graph $G$ and each integer $t\geq 1$,

$$\chi\left(S[G,t]\right)=\chi(G).$$

The paper proves this equality for $t=1,2$, for bipartite graphs, and gives the bound $\chi(G)\leq\chi(S[G,t])\leq\chi(G)+1$ for $t\geq3$; the conjecture remains open in the supplied text for arbitrary graphs and all $t\geq1$.