{"paper":{"title":"A tight bound for Green's arithmetic triangle removal lemma in vector spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jacob Fox, L\\'aszl\\'o Mikl\\'os Lov\\'asz","submitted_at":"2016-06-03T19:45:25Z","abstract_excerpt":"Let $p$ be a fixed prime. A triangle in $\\mathbb{F}_p^n$ is an ordered triple $(x,y,z)$ of points satisfying $x+y+z=0$. Let $N=p^n=|\\mathbb{F}_p^n|$. Green proved an arithmetic triangle removal lemma which says that for every $\\epsilon>0$ and prime $p$, there is a $\\delta>0$ such that if $X,Y,Z \\subset \\mathbb{F}_p^n$ and the number of triangles in $X \\times Y \\times Z$ is at most $\\delta N^2$, then we can delete $\\epsilon N$ elements from $X$, $Y$, and $Z$ and remove all triangles. Green posed the problem of improving the quantitative bounds on the arithmetic triangle removal lemma, and, in p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01230","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}