{"paper":{"title":"A Salem-Spencer-Type Construction for Large Subsets of Integer Grids with No Isosceles Right Triangles","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Gyula K\\'arolyi, Jozsef Solymosi","submitted_at":"2026-07-24T18:08:11Z","abstract_excerpt":"Let $F(n)$ be the largest size of a subset of $\\{0,1,\\ldots,n-1\\}^2$ containing no nondegenerate isosceles right triangle. We give a modified Salem--Spencer-type construction over the Gaussian integers showing that $F(n)=\\Omega(n^{1.3})$. The best known upper bound is $F(n)\\ll n^2/(\\log n)^{1+c}$ for some absolute constant $c>0$, so there is still a large gap between the bounds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.22828","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.22828/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}