{"paper":{"title":"Uniform Tur\\'an density -- palette classification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ander Lamaison, Daniel Kr\\'al', Filip Ku\\v{c}er\\'ak, G\\'abor Tardos","submitted_at":"2025-05-22T22:37:36Z","abstract_excerpt":"In the 1980s, Erd\\H{o}s and S\\'os initiated the study of Tur\\'an hypergraph problems with a uniformity condition on the distribution of edges, i.e., determining density thresholds for the existence of a hypergraph H in a host hypergraph with edges uniformly distributed. In particular, Erd\\H{o}s and S\\'os asked to determine the uniform Tur\\'an densities of the hypergraphs $K_4^{(3)-}$ and $K_4^{(3)}$. After more than 30 years, the former was solved by Glebov, Kr\\'al' and Volec [Israel J. Math. 211 (2016), 349-366] and Reiher, R\\\"odl and Schacht [J. Eur. Math. Soc. 20 (2018), 1139-1159], while t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.17325","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/2505.17325/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"}