{"paper":{"title":"Hypergraph Erd\\H{o}s--Rogers functions with consecutive clique sizes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lin Niu, Qizhong Lin","submitted_at":"2026-07-11T04:13:38Z","abstract_excerpt":"For integers \\(k\\le s<t\\), let \\(f^{(k)}_{s,t}(n)\\) denote the largest integer \\(m\\) such that every \\(n\\)-vertex \\(K_t^{(k)}\\)-free \\(k\\)-graph contains a set of \\(m\\) vertices spanning no copy of \\(K_s^{(k)}\\). We give an affirmative answer to a problem of Conlon, Fox and Sudakov by proving that, for every fixed \\(s\\ge4\\), \\[\n  f^{(4)}_{s,s+1}(n)=(\\log n)^{o(1)} . \\] The key input is a new \\(3\\)-uniform estimate: for every fixed \\(s\\ge3\\), \\(f^{(3)}_{s,s+1}(n)=O(\\frac{\\log n}{\\log\\log n})\\). This improves the logarithmic upper bound of Dudek and Mubayi. The proof combines hypergraph containe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.10111","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/2607.10111/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"}