The conjecture that every composite knot is persistently foliar

A composite knot is a nontrivial connected sum of knots, and a knot is persistently foliar if, for each boundary slope, its complement admits a co-oriented taut foliation meeting the boundary transversely in curves of that slope. Composite-knot persistence conjecture. Every composite knot is persistently foliar. The paper has already proved this when a summand is persistently foliar and, in particular, for several classes of composite knots; the general assertion remains open in the source.