Uniqueness conjecture for trisections of the 4-sphere

A trisection of a closed 4-manifold is a decomposition into three 4-dimensional 1-handlebodies whose pairwise intersections are 3-dimensional handlebodies and whose triple intersection is a closed surface. A stabilization is the connected sum of a trisection diagram with one of the genus-1 trisection diagrams of $S^4$; the reverse operation is a destabilization. Two trisections of the same closed 4-manifold are isotopic if an isotopy of the manifold carries each sector of one trisection to the corresponding sector of the other. The trisection uniqueness conjecture. Each trisection of $S^4$ is isotopic to the genus-0 trisection or its stabilization. This is a 4-dimensional analogue of Waldhausen's theorem, which states that each genus-$g$ Heegaard splitting of $S^3$ is isotopic to the stabilization of the genus-0 Heegaard splitting. The supplied status evidence indicates that the conjecture is disproved: a counterexample may be obtained from trisection diagrams of a 4-manifold diffeomorphic to $S^4$, since isotopic trisections are diffeomorphic.