Classification conjecture for irreducible 4-manifolds of trisection genus three

Let a 4-manifold be a smooth 4-dimensional manifold, and call it irreducible if each summand of any connected-sum decomposition is either the manifold itself or a homotopy 4-sphere. The trisection genus of a 4-manifold is the minimum genus of a trisection of it. A spin of a lens space is the 4-manifold obtained by spinning a lens space, and a Gluck twist is the operation performed along a specific 2-knot.

Trisection-genus-three classification 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 an enumeration of irreducible 4-manifolds at the next low trisection genus beyond the known classifications in genera at most two. Its status is not specified in the source.