The scalar-curvature extension conjecture for Ricci flow in dimension four

Theorem 1.1: a smooth Ricci flow on a closed four-manifold with $\sup_{M\times[0,T)}|R|<\infty$, $T<\infty$, extends smoothly past $T$; Corollary: at a finite maximal time $\limsup\max R=+\infty$. This removes the $H_2$ hypothesis of Bamler-Zhang and gives smooth continuation rather than an orbifold flow. The companion proves $E=o(M)$ for the renormalized Einstein-Hilbert functional on degenerating trees of Ricci-flat spaces. It is specific to dimension four; in high dimension the family's other paper shows the statement is false.

Theorem 1.1: a smooth Ricci flow on a closed four-manifold with $\sup_{M\times[0,T)}|R|<\infty$, $T<\infty$, extends smoothly past $T$; Corollary: at a finite maximal time $\limsup\max R=+\infty$. This removes the $H_2$ hypothesis of Bamler-Zhang and gives smooth continuation rather than an orbifold flow. The companion proves $E=o(M)$ for the renormalized Einstein-Hilbert functional on degenerating trees of Ricci-flat spaces. It is specific to dimension four; in high dimension the family's other paper shows the statement is false.