Meier's conjecture on trisections of the 4-sphere

Let a trisection of a smooth, closed, connected $4$-manifold be a decomposition into three $4$-dimensional $1$-handlebodies meeting pairwise in $3$-dimensional handlebodies and all three in a closed surface. The standard $(0,0)$-trisection is the genus-zero trisection of $S^4$, and a stabilization is the standard operation that increases the trisection genus while preserving the underlying $4$-manifold.

Meier's conjecture. Every trisection of $S^4$ is either the $(0,0)$-trisection or a stabilization of the $(0,0)$-trisection.

This is a trisection-theoretic analogue of the assertion that all decompositions of the $4$-sphere are standard up to stabilization. The conjecture is presented as a specific case of the question about whether trisections arising from the Price-twist algorithm are stabilized, and its general status is not resolved in the supplied text.