On page 205 of his *Topology* textbook, James Munkres made an interesting remark:

It is not known whether $\mathbb{R}^\omega$ is normal in the box topology. Mary-Ellen Rudin has shown that the answer is affirmative if one assumes the continuum hypothesis.

That's a reference to this paper by Mary Ellen Rudin. However, both Munkres and Rudin were writing decades ago. So my question is, what is the state of research on this problem?

Has it been proven in $ZFC$, or has it been proven to be independent of $ZFC$, or is it still an open problem whether it's a theorem of $ZFC$ or not?