The Montgomery–Yang problem for pseudofree circle actions on the 5-sphere

A pseudofree circle action is an action of $\mathbb{S}^1$ on a manifold that is free except for finitely many non-free orbits. Consider an action

$$\mathbb{S}^1 \times \mathbb{S}^5 \rightarrow \mathbb{S}^5.$$

Montgomery–Yang problem. Every pseudofree $\mathbb{S}^1$-action on $\mathbb{S}^5$ has at most $3$ non-free orbits.

The problem is the five-dimensional case of the Montgomery–Yang question on the number of exceptional orbits of pseudofree circle actions on spheres. It had remained unsolved since its formulation in the source; the source provides no resolution status beyond that.