The degree-reduction conjecture for quantum Schubert structure constants

Let $d\geq 1$ be an integer, and let $\lambda$, $\mu$, and $\nu$ be Young diagrams indexing Schubert classes in the Grassmannian. Denote by $\langle\lambda,\mu,\nu\rangle_d$ the corresponding degree-$d$ quantum Schubert structure constant. Degree-reduction conjecture. If

$$\langle\lambda,\mu,\nu\rangle_d\neq 0,$$

then either there exists a Young diagram $\alpha\supseteq\nu$ such that

$$\langle\lambda,\mu,\alpha\rangle_{d-1}\neq 0,$$

or

$$\langle\lambda,\mu,\alpha\rangle_j=0$$

for every $\alpha\subseteq l\times k$ and every integer $j$ with $0\leq j\leq d-1$. This describes how a nonzero degree-$d$ invariant must either descend from a nonzero invariant in degree $d-1$ or be the first nonzero degree for the pair $(\lambda,\mu)$. The source presents this as a further conjectural strengthening after the interval claim; no resolution is supplied.