Multiplier-group equality conjecture for real algebraic number fields

Let $F$ be a real algebraic number field of degree $n$ over $\mathbb{Q}$, and let $T^n$ denote the $n$-torus. The multiplier-group equality conjecture. There exists a quasiperiodic flow $\phi$ on $T^n$ whose multiplier group is exactly the group of units of the ring of integers in $F$. This asserts that every such number field occurs as the full multiplier group of an algebraic quasiperiodic flow. The paper later says that this conjecture is reformulated and proved, so it is treated as solved.