Fröberg's conjecture on Hilbert series of generic ideals

Let $k[x_1,\dots,x_n]$ be a polynomial ring, and let $I=(f_1,\dots,f_r)$ be a generic ideal whose generators satisfy $\deg f_i=d_i$. For a power series $F(T)$, write $[F(T)]$ for its truncation at the first nonpositive coefficient. Fröberg's conjecture. The Hilbert series of $R/I$ is

$$\operatorname{H}_{R/I}(T)=\left[\frac{\prod_{i=1}^r(1-T^{d_i})}{(1-T)^n}\right].$$

The conjecture predicts the Hilbert series of a generic ideal from the degrees of its generators and is equivalent to the expected maximal-rank behavior of a generic sequence of forms. The surrounding discussion relates it to semi-regular sequences, for which the predicted Hilbert series is known; the conjectural assertion for generic ideals remains unresolved in the stated generality.