The finite SU(3)-invariant AC shrinker conjecture for fixed negative parameter

Fix $\lambda<0$ and consider the 4-dimensional space of local $\textup{SU}(3)$-invariant shrinkers, together with the complete AC shrinkers among them on $\Lambda^2_-\mathbb{CP}^2$. Fixed-parameter SU(3)-invariant finiteness conjecture. For fixed $\lambda<0$, there are finitely many complete $\textup{SU}(3)$-invariant AC shrinkers. The expected finiteness follows from the intersection of the codimension-2 space of AC shrinker ends with the codimension-2 space of smoothly-closing solutions; it remains open.