Meier's classification conjecture for genus-three trisections

A closed smooth $4$-manifold is said to admit a genus-three trisection when it admits a trisection of genus three. A $4$-manifold is a spun lens space when it is obtained by spinning a lens space, and a Gluck twist is the operation of regluing along the boundary of a tubular neighborhood of a $2$-knot. Meier's conjecture. Every irreducible $4$-manifold with trisection genus three is either the spin of a lens space, or a Gluck twist on a specific $2$-knot in the spin of a lens space. This conjecture proposes a classification of irreducible $4$-manifolds admitting genus-three trisections; the source gives no resolution of the conjecture.