{"id":"openai-math/Bounded-scalar-curvature-and-smooth-extension-of-four-dimensional-Ricci-flow","pdf":"https://github.com/openai/math/blob/main/preprints/Bounded-scalar-curvature-and-smooth-extension-of-four-dimensional-Ricci-flow-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Bounded-scalar-curvature-and-smooth-extension-of-four-dimensional-Ricci-flow-September-24-2026","tags":["ricci-flow","scalar-curvature","geometric-analysis"],"score":0,"title":"Bounded scalar curvature and smooth extension of four-dimensional Ricci flow","domain":"Differential geometry","family":"351","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.DG","summary":"We prove that a smooth Ricci flow on a closed real four-manifold extends on the same manifold through every finite time at which its scalar curvature remains uniformly bounded. This resolves the scalar-curvature extension problem in dimension four.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"Scalar curvature and finite-time Ricci-flow singularities"}