Fujita's Spectrum Conjecture for smooth polarized varieties

For each integer $n\geq 1$, let $S_n$ be the set of unnormalized spectral values of a smooth polarized $n$-fold. For a smooth polarized variety, these spectral values are the numerical invariants under consideration.

Fujita's Spectrum Conjecture. For every $\varepsilon>0$, the set

$$\{\mu\in S_n\mid \mu>\varepsilon\}$$

is a finite set of rational numbers.

This conjecture concerns the discreteness and rationality of spectral values of smooth polarized varieties. The supplied text does not state whether it has been resolved, so its status is recorded as open.