Sturmfels' degree bound conjecture for graded normal configurations

Let ${\mathcal A}\subset\mathbb Z^d$ be a finite graded, normal configuration, and let $I_{\mathcal A}$ be its toric ideal. Write $\dim({\mathcal A})=d$ for the Krull dimension of the associated toric ring. Sturmfels' degree bound conjecture. The ideal $I_{\mathcal A}$ has a Gröbner basis whose elements have degree at most

$$d=\dim({\mathcal A}).$$

This conjecture predicts a uniform degree bound for Gröbner bases of toric ideals arising from graded normal configurations. The source gives no resolution status.