The generalized Waldhausen conjecture for strongly irreducible splittings

Let $M$ be a closed, orientable, atoroidal three-manifold. A Heegaard splitting is strongly irreducible if every compressing disk on one side intersects every compressing disk on the other side. The generalized Waldhausen conjecture. For each genus, $M$ contains only finitely many strongly irreducible Heegaard splittings, up to isotopy.

This conjecture is used to control the finitely many low-genus splittings after the paper proves that all sufficiently high-genus splittings have the disjoint curve property. The source reports that Jaco and Rubinstein claimed a solution, but does not establish the conjecture itself.