Multiplier-group subgroup conjecture for algebraic quasiperiodic flows

Let $T^n$ be the $n$-torus, let $\phi$ be a quasiperiodic flow on $T^n$ generated by a constant vector field $X$, and let $F$ be a real algebraic number field of degree $n$ over $\mathbb{Q}$. Suppose that there is a nonzero real number $\vartheta$ such that the components of $\vartheta X$ form a basis of $F$ over $\mathbb{Q}$. The multiplier-group subgroup conjecture. The multiplier group of $\phi$ is a subgroup of the group of units of the ring of integers in $F$. This conjecture concerns the arithmetic structure of the smooth-conjugacy invariant associated with a quasiperiodic flow; the paper later says that the conjecture is reformulated and proved, so its resolution should be checked against the cited theorem.