{"id":"openai-math/A-power-saving-for-square-difference-free-sets","pdf":"https://github.com/openai/math/blob/main/preprints/A-power-saving-for-square-difference-free-sets-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-power-saving-for-square-difference-free-sets-September-24-2026","tags":["additive-combinatorics","number-theory","difference-sets"],"score":0,"title":"A power saving for square-difference-free sets","domain":"Combinatorics","family":"182","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.CO","summary":"We prove that there are absolute constants c > 0 and C < ∞ such that every set $`A\\subseteq\\{1,\\ldots,N\\}`$ with no nonzero square difference satisfies $`|A|\\le C N^{1-c}`$. This answers the fixed-power question posed by Green and Sawhney.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"Power savings for intersective polynomial differences and prime arguments"}