Sturmfels conjecture on Graver basis degrees and true circuit degrees

Let $I_A$ be a toric ideal, and let the true degree of a circuit of $A$ mean the degree computed without dividing by the common factor $c$ in the circuit formula. Sturmfels's conjecture. The degree of any Graver basis element of $I_A$ is at most the maximum true degree of any circuit of $A$. This conjecture refines an earlier proposed degree bound that was disproved by a counterexample; the supplied source gives no evidence that the refined bound has been resolved.