Tao's finite-time singularity conjecture for incompressible Euler flow

Let $(M,\mathsf{g})$ be a closed, compact Riemannian manifold without boundary, and let $(u,p)$ be a smooth solution of the incompressible Euler equations on $M$. Tao's conjecture. There exists a choice of $(M,\mathsf{g})$ and a smooth solution $(u,p)$ that cannot be extended indefinitely forwards in time. The conjecture asks whether smooth incompressible Euler flow can develop a finite-time singularity on some closed Riemannian manifold; related finite-time breakdown results are known for weaker regularity and in computationally assisted settings, but the asserted smooth example remains unresolved.