Hamilton's scalar-curvature blow-up conjecture for Ricci flow

Let $(M,g(t))_{t\in[0,T)}$ be a solution to Ricci flow on a closed smooth $n$-dimensional Riemannian manifold, with $T$ its maximal time. Hamilton's scalar-curvature blow-up conjecture. If $T<+\infty$, then

$$\limsup_{t\to T}\left(\max_M R_{g(t)}\right)=+\infty.$$

This conjecture asks whether scalar curvature alone must become unbounded at every finite-time Ricci-flow singularity. The source records stronger known criteria involving Riemann or Ricci curvature, while the optimal scalar-curvature condition remains unresolved.