{"paper":{"title":"Generating non-jumps from a known one","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Caihong Yang, Heng Li, Jianfeng Hou, Yixiao Zhang","submitted_at":"2022-08-01T12:14:02Z","abstract_excerpt":"Let $r\\ge 2$ be an integer. The real number $\\alpha\\in [0,1]$ is a jump for $r$ if there exists a constant $c > 0$ such that for any $\\epsilon >0$ and any integer $m \\geq r$, there exists an integer $n_0(\\epsilon, m)$ satisfying any $r$-uniform graph with $n\\ge n_0(\\epsilon, m)$ vertices and density at least $\\alpha+\\epsilon$ contains a subgraph with $m$ vertices and density at least $\\alpha+c$. A result of Erd\\H{o}s, Stone and Simonovits implies that every $\\alpha\\in [0,1)$ is a jump for $r=2$. Erd\\H{o}s asked whether the same is true for $r\\ge 3$. Frankl and R\\\"{o}dl gave a negative answer b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.00794","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/2208.00794/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"}