Finite universal Sagbi basis conjecture for the Grassmannian coordinate ring

Let $G(m,n)$ denote the Grassmannian, and let a universal Sagbi basis mean a finite generating set that is a Sagbi basis for every monomial order. Finite universal Sagbi basis conjecture. $G(m,n)$ has a finite universal Sagbi basis. The preceding results establish this experimentally in several cases for $m=3$, but the general assertion remains open.