Hamilton's nonexistence conjecture for Type I-like ancient Ricci flows

A complete noncompact ancient solution to the Ricci flow is a Ricci flow $(\mathcal{M}^{n},g(t))$ defined for $-\infty<t<\omega$ on a complete noncompact manifold. It is Type-I like if

$$\sup_{\mathcal{M}^{n}\times(-\infty,0]}|t|\,|\operatorname{Rm}(x,t)|<\infty.$$

Assume the solution has bounded positive curvature operator. Hamilton's conjecture. There does not exist a complete noncompact ancient Type-I-like solution to the Ricci flow with bounded positive curvature operator.

The conjecture asserts that curvature cannot remain both bounded in the Type-I sense and positive on a complete noncompact ancient solution. In the paper's setting, the cited theorem proves the corresponding nonexistence conclusion in dimension three under bounded positive sectional curvature, so the status of the general conjecture is not resolved by that result.