The dimension-reduction conjecture for four-dimensional steady Ricci soliton singularity models

Let $(M,g,f)$ be a $4$-dimensional steady gradient Ricci soliton singularity model. A soliton dimension reduces to $3$-manifolds if, along a sequence of points tending to infinity and after curvature rescaling, a subsequential limit is a product $(N^3\times\mathbb{R},g_N(t)+ds^2)$ with a nonflat three-dimensional Ricci flow.

Dimension-reduction conjecture. If $(M,g,f)$ is a $4$-dimensional steady gradient Ricci soliton singularity model, then it dimension reduces to $3$-manifolds.

The conjecture would ensure that every such four-dimensional singularity model falls within the paper's dimension-reduction framework; the source gives no resolution.