Alon–Powierski–Savery–Scott–Wilmer's n-dijoin conjecture

Let $n\in\mathbb{N}$ and let $D_1,\dots,D_n$ be oriented graphs. Write $[D_1,\dots,D_n]$ for their n-join, obtained by taking their disjoint union and orienting every arc between distinct parts from the earlier part to the later part. Let $\operatorname{inv}(D)$ denote the inversion number of an oriented graph.

Alon–Powierski–Savery–Scott–Wilmer's n-dijoin conjecture. If

$$\operatorname{inv}(D_i)\leq 2$$

for every $i$, then

$$\operatorname{inv}([D_1,\dots,D_n])=\sum_{i=1}^n\operatorname{inv}(D_i).$$

The paper says that this conjecture is resolved by its results, which prove the asserted additivity for n-joins whose constituent oriented graphs all have inversion number at most $2$.