Moreno-Socías's conjecture for generic complete intersections

Let $R=K[x_1,\dots,x_n]$ and let $I=(f_1,\dots,f_n)$ be a generic ideal generated by $n$ generic homogeneous forms. Write $\operatorname{in}(I)$ for its initial ideal in the fixed graded reverse lexicographic order, and call a monomial ideal almost reverse lexicographic when it contains every larger monomial of the same degree as each of its minimal generators.

Moreno-Socías's conjecture for generic complete intersections. Then $\operatorname{in}(I)$ is almost reverse lexicographic.

This is the restriction to $n$ generators of the broader Moreno-Socías conjecture; the paper treats this case and proves it under additional degree conditions, while the general assertion remains open.