Ito's conjecture on the Fourier–Mukai and Serre spectra

Let $\mathcal T$ be a triangulated category with $\operatorname{FM} \mathcal T\neq\emptyset$.

Ito's conjecture. The Fourier–Mukai spectrum of $\mathcal T$ should coincide with its Serre spectrum:

$$\operatorname{Spc}^\mathsf{FM} \mathcal T = \operatorname{Spc}^\mathsf{Ser} \mathcal T.$$

The conjecture proposes that the Fourier–Mukai locus can be identified purely categorically through the Serre spectrum, which would allow reconstruction of all Fourier–Mukai partners in the setting described for abelian varieties. Its resolution is not indicated in the source.