Sarnak's extremal height conjecture for flat tori

Let $T$ be an $n$-dimensional flat torus of volume $1$, represented by a lattice in Euclidean space. Let the height of $T$ be $\zeta'(0)$, equivalently the negative logarithm of its zeta-regularized determinant, and let the minimal vector of a lattice be a nonzero lattice vector of shortest length. Sarnak's conjecture. Among all $n$-dimensional flat tori of volume $1$, the height is minimized by the torus corresponding to the lattice with the longest minimal vector. This conjecture proposes that the global extremum of the determinant is governed by the geometry of the shortest lattice vector; the source records known low-dimensional extremal results but does not state a general resolution.