The nonexistence conjecture for gentile acute tetrahedra

An acute tetrahedron is a tetrahedron whose dihedral angles are all acute. A gentile tetrahedron is a tetrahedron that can be subdivided into finitely many smaller figures, each similar to the original tetrahedron, without requiring the pieces to be mutually congruent.

Gentile acute tetrahedra conjecture. There are no gentile acute tetrahedra.

This is stated as stronger than the conjectured nonexistence of reptile acute tetrahedra. The paper gives no resolution, so the conjecture remains open.