The interval conjecture for degrees in quantum Schubert products

Let $X$ be the Grassmannian, and let $\sigma_{\lambda}$ and $\sigma_{\mu}$ be Schubert classes indexed by Young diagrams. Write $d_{\min}$ and $d_{\max}$ for the smallest and largest degrees of $q$ occurring with nonzero coefficient in the quantum product $\sigma_{\lambda}*\sigma_{\mu}$. Interval conjecture. The product $\sigma_{\lambda}*\sigma_{\mu}$ involves $q^d$ for every integer $d$ satisfying

$$d\in [d_{\min},d_{\max}].$$

The claim predicts that the degrees appearing in a quantum Schubert product form an interval, addressing the problem of determining precisely which powers of $q$ occur. The source gives computational evidence but no resolution, so the conjecture remains open.