tt-separatedness conjecture for abelian varieties

Let $X$ be an abelian variety. A smooth projective variety is tt-separated when the relevant Fourier–Mukai copies in its triangular spectrum are pairwise disjoint. Abelian tt-separatedness conjecture. Every abelian variety is tt-separated. The source proves this for simple abelian varieties and presents the general assertion as an expectation; no resolution is given.