Hamilton's conjecture on compact shrinking Ricci solitons with positive curvature operator

Let $M$ be a compact Riemannian manifold with a gradient shrinking Ricci soliton metric $g$, so that for some function $f$ and $\tau>0$,

$$R_{ij}+\nabla_i\nabla_j f=\frac{1}{2\tau}g_{ij}.$$

The metric has positive curvature operator if its curvature operator is positive definite. Hamilton's conjecture. A compact gradient shrinking Ricci soliton with positive curvature operator must be Einstein, meaning that its Ricci tensor is a constant multiple of the metric. The conjecture connects positivity of the curvature operator with rigidity of compact shrinking Ricci solitons. The source does not provide evidence of a resolution.