Migliore–Miro-Roig conjecture on ghost terms in resolutions of generic forms

Let $S=k[x_1,\ldots,x_n]$, and let $I\subset S$ be generated by $d>n$ generic forms of the same degree. A redundant term in a minimal free resolution means a free summand occurring in two different homological degrees with the same internal shift.

Migliore–Miro-Roig conjecture. The minimal free resolution of $S/I$ has no redundant term. Consequently, the minimal free resolution is the minimum one consistent with the Hilbert function.

The conjecture concerns whether generic equal-degree generators can produce ghost terms in their minimal resolutions. The source gives no resolution status.