The normality Gröbner-basis conjecture for projectively normal toric varieties

Let $I$ be a toric ideal defining a projectively normal $r$-dimensional toric variety. The normality Gröbner-basis conjecture. The ideal $I$ has a Gröbner basis consisting of binomials of degree at most $r$. This is a general conjecture about projectively normal toric varieties. Its status is presented in the source as open; its restriction to toric varieties arising from matroids neither implies nor is implied by White's conjecture.