{"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/on-the-structure-of-bad-science-matrices","title":"On the Structure of Bad Science Matrices","arxiv_id":"2408.00933","date":"2024-08-01","proceeding":null,"authors":["Alex Albors","Hisham Bhatti","Lukshya Ganjoo","Raymond Guo","Dmitriy Kunisky","Rohan Mukherjee","Alicia Stepin","Tony Zeng"],"abstract":"The bad science matrix problem consists in finding, among all matrices $A \\in \\mathbb{R}^{n \\times n}$ with rows having unit $\\ell^2$ norm, one that maximizes $\\beta(A) = \\frac{1}{2^n} \\sum_{x \\in \\{-1, 1\\}^n} \\|Ax\\|_\\infty$. Our main contribution is an explicit construction of an $n \\times n$ matrix $A$ showing that $\\beta(A) \\geq \\sqrt{\\log_2(n+1)}$, which is only 18% smaller than the asymptotic rate. We prove that every entry of any optimal matrix is a square root of a rational number, and we find provably optimal matrices for $n \\leq 4$.","url_abs":"https://arxiv.org/abs/2408.00933v2","url_pdf":"https://arxiv.org/pdf/2408.00933v2.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":"on-the-structure-of-bad-science-matrices","repo_url":"https://github.com/alexalbors7/bad-science-matrix-optimization","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":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}