Degree-independence conjecture for Chow rings of open stable-map spaces

Let $X$ be any flag variety, and let $\mathcal M_{0,n}(X,\beta)$ be the open part of the moduli space of stable maps, parametrizing maps without boundary degenerations. Let the indecomposable classes of $X$ be the basic effective curve classes that cannot be written as sums of two nonzero effective classes. Degree-independence conjecture. The dimensions of the Chow rings of $\mathcal M_{0,n}(X,\beta)$ are independent of the degree $\beta$, provided that $\beta$ is a linear combination of the indecomposable classes with positive coefficients. This conjecture is motivated by computations cited in the paper, and no resolution is given in the supplied text.