Castelnuovo–Mumford regularity bound for ideals

Let $R$ be a polynomial ring over a field, and let $I\subseteq R$ be an ideal with minimal homogeneous generators whose number and degrees are fixed. The regularity-bound conjecture. There is a bound on the Castelnuovo–Mumford regularity of $I$ depending only on the number of its minimal generators and the degrees of those generators. This is presented as an open question equivalent to Stillman's conjecture, with the equivalence attributed to Caviglia; it asks for a uniform regularity bound independent of the number of variables.