{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/computationally-assisted-proof-of-a-novel","title":"Computationally-assisted proof of a novel $\\mathsf{O}(3)\\times \\mathsf{O}(10)$-invariant Einstein metric on $S^{12}$","arxiv_id":"2412.01184","date":"2024-12-02","proceeding":null,"authors":["Timothy Buttsworth","Liam Hodgkinson"],"abstract":"We prove existence of a non-round Einstein metric $g$ on $S^{12}$ that is invariant under the usual cohomogeneity one action of $\\mathsf{O}(3)\\times\\mathsf{O}(10)$ on $S^{12}\\subset \\mathbb{R}^{13}= \\mathbb{R}^3\\oplus \\mathbb{R}^{10}$. The proof involves using several rigorous numerical analysis techniques to produce a Riemannian metric $\\hat{g}$ which approximately satisfies the Einstein condition to known high precision, and then demonstrating that $\\hat{g}$ can be perturbed into a true Einstein metric $g$.","url_abs":"https://arxiv.org/abs/2412.01184v1","url_pdf":"https://arxiv.org/pdf/2412.01184v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"computationally-assisted-proof-of-a-novel","repo_url":"https://github.com/liamhodg/O3O10","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}