Blow-up conjecture for inversion diameter

Let $G$ be a graph, let $t$ be a positive integer, let $\overline{K}_t$ be the edgeless graph on $t$ vertices, and let $G[\overline{K}_t]$ denote the blow-up of $G$ in which each vertex is replaced by an independent set of size $t$. Let $\mathcal{I}(G)$ be the inversion graph of $G$. Blow-up conjecture. For every graph $G$ and every positive integer $t$,

$$\operatorname{diam}(\mathcal{I}(G[\overline{K}_t])) \leqslant t\cdot\operatorname{diam}(\mathcal{I}(G)).$$

The conjecture seeks to generalise the paper's upper bound for complete multipartite graphs to blow-ups of arbitrary graphs.