{"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/an-improved-example-for-an-autoconvolution","title":"An improved example for an autoconvolution inequality","arxiv_id":"2506.16750","date":"2025-06-20","proceeding":null,"authors":["Christopher Boyer","Zane Kun Li"],"abstract":"We give a nonnegative step function with 575 equally spaced intervals such that $$\\frac{\\|f \\ast f\\|_{L^{2}(\\mathbb{R})}^{2}}{\\|f \\ast f\\|_{L^{\\infty}(\\mathbb{R})}\\|f \\ast f\\|_{L^{1}(\\mathbb{R})}} \\geq 0.901564.$$ This improves upon a recent result of Deepmind's AlphaEvolve, which found a nonnegative step function with 50 equally space intervals for which the left hand side is $\\geq 0.8962$. Our function was found using simulated annealing and gradient based methods rather than using large language models.","url_abs":"https://arxiv.org/abs/2506.16750v1","url_pdf":"https://arxiv.org/pdf/2506.16750v1.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":"an-improved-example-for-an-autoconvolution","repo_url":"https://github.com/zkli-math/autoconvolutionholder","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2506.16750","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}