The scalar-curvature extension conjecture for Ricci flow in all dimensions

Theorem 1.1: for some $q\ge10$ there is a smooth Ricci flow on the closed manifold $S^2\times S^{q+1}$ with $\sup|R|<\infty$ and $\max_M|\mathrm{Rm}|\to\infty$ at the finite maximal time; a corollary gives two-sided power-law curvature blowup with arbitrarily large exponents in one fixed dimension. This refutes the unrestricted all-dimensions conjecture. It relies on Stolarski's construction and gives no explicit dimension; it does not touch dimension four, which the companion proves true.

Theorem 1.1: for some $q\ge10$ there is a smooth Ricci flow on the closed manifold $S^2\times S^{q+1}$ with $\sup|R|<\infty$ and $\max_M|\mathrm{Rm}|\to\infty$ at the finite maximal time; a corollary gives two-sided power-law curvature blowup with arbitrarily large exponents in one fixed dimension. This refutes the unrestricted all-dimensions conjecture. It relies on Stolarski's construction and gives no explicit dimension; it does not touch dimension four, which the companion proves true.