Global rigidity conjecture for higher-rank Anosov actions on infranilmanifolds

Let $r\geq 2$. An irreducible Anosov genuine $\mathbb{Z}^r$-action is an Anosov genuine action by $\mathbb{Z}^r$ on a compact infranilmanifold satisfying the stated irreducibility condition. The action is $C^\infty$-conjugate to another action if there is a $C^\infty$ diffeomorphism intertwining the two actions.

Infranilmanifold global rigidity conjecture. All irreducible Anosov genuine $\mathbb{Z}^r$-actions on compact infranilmanifolds should be $C^\infty$-conjugate to actions by affine automorphisms.

This is presented as a natural weaker form of the preceding global rigidity conjecture. The source says that the conjecture is widely open and notes that irreducibility is not a crucial issue in view of the cited work and the paper's main theorem.