Asymptotic existence conjecture for pure Betti diagrams

Let ${\bf d}$ be a degree sequence, and let $\pi({\bf d})$ denote the smallest integer diagram on the ray $t\pi({\bf d})$ for $t>0$. Such integer diagrams are $m\pi({\bf d})$ for $m\in\mathbb N$. Asymptotic existence conjecture for pure Betti diagrams. For every degree sequence ${\bf d}$ there is an integer $m_0$ such that, for $m\geq m_0$, the diagram $m\pi({\bf d})$ is the Betti diagram of a module.

This asks whether every ray generated by a pure diagram contains actual Betti diagrams after sufficiently large integral scaling. The supplied text gives examples and notes that the problem is harder, but does not state whether the conjecture has been resolved.