{"paper":{"title":"Quasipolynomial bounds for the corners theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.NT"],"primary_cat":"math.CO","authors_text":"Anthony Ostuni, Mehtaab Sawhney, Michael Jaber, Shachar Lovett, Yang P. Liu","submitted_at":"2025-04-09T16:26:06Z","abstract_excerpt":"Let $G$ be a finite abelian group and $A$ be a subset of $G \\times G$ which is corner--free, meaning that there are no $x, y \\in G$ and $d \\in G \\setminus \\{0\\}$ such that $(x, y)$, $(x+d, y)$, $(x, y+d) \\in A$. We prove that \\[|A| \\le |G|^2 \\cdot \\exp(-(\\log |G|)^{\\Omega(1)}).\\] As a consequence, we obtain polynomial (in the input length) lower bounds on the nondeterministic communication complexity of Exactly-N in the 3-player Number-on-Forehead model. We also obtain the first \"reasonable'' lower bounds on the coloring version of the $3$-dimensional corners problem, as well as on the nondete"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.07006","kind":"arxiv","version":2},"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/2504.07006/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"}