{"id":"openai-math/Positive-scalar-curvature-forces-rational-inessentiality","pdf":"https://github.com/openai/math/blob/main/preprints/Positive-scalar-curvature-forces-rational-inessentiality-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Positive-scalar-curvature-forces-rational-inessentiality-September-23-2026","tags":["differential-geometry","scalar-curvature","algebraic-topology"],"score":0,"title":"Positive scalar curvature forces rational inessentiality","domain":"Differential geometry","family":"335","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.DG","summary":"We prove that every closed connected oriented smooth manifold admitting strictly positive scalar curvature is rationally inessential: its rational fundamental class maps to zero under the classifying map. No spin or fundamental-group hypothesis is needed, and there is no upper dimension bound. This proves the Gromov–Lawson aspherical conjecture; moreover, every nonnegative-scalar-curvature metric on a closed aspherical manifold is flat. We also show that every closed oriented smooth manifold of positive dimension with nonnegative scalar curvature has zero real simplicial volume, proving the…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":1,"published":"2026-09-23","reactions":{},"discussion":[{"url":"https://proofsandprompts.com/2026/10/08/100-reactions-to-100-solutions/#:~:text=This%20trick%20and%20these%20two%20papers%20now%20appear%20in%20OpenAI%E2%80%99s%20deeply%20creative%20solutions%20of%20problems%20207%20and%20335","date":"2026-10-08","kind":"web","site":"Proofs and Prompts","text":"This trick and these two papers now appear in OpenAI’s deeply creative solutions of problems 207 and 335 – problems so different, they could not be farther apart! I am stunned. What do I take away from this night? We cannot defensively narrow our focus to what we currently regard as human…","added":"2026-10-24","title":"100+ reactions to 100+ solutions"}],"formalized":false,"family_title":"Gromov’s integral scalar-curvature bound for simplicial volume"}