The Type I pointwise scalar-curvature conjecture for shrinking Ricci flows

Let $\{g(t)\}_{t\in [0,T)}$ be the solution of the Ricci flow on a closed Riemannian manifold $M^n$ with $n\geq 3$, and suppose that

$$\operatorname{diam}_{g(t)}\to 0$$

as $t\to T$. Type I scalar-curvature conjecture. There exists a point $x\in M$ such that

$$\liminf_{t\to T} (T-t)R(x,t)<\infty.$$

This conjecture asserts that scalar curvature cannot be of Type II at every point of a closed manifold that shrinks to a point under the Ricci flow. The preceding proposition proves the corresponding volume upper bound under a pointwise Type I assumption at one point, but the conjectured existence of such a point remains open.