{"paper":{"title":"On $3$-graphs with vanishing codegree Tur\\'{a}n density","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ander Lamaison, Haotian Yang, Hong Liu, Laihao Ding, Shuaichao Wang","submitted_at":"2024-07-11T17:55:01Z","abstract_excerpt":"For a $k$-uniform hypergraph (or simply $k$-graph) $F$, the codegree Tur\\'{a}n density $\\pi_{\\mathrm{co}}(F)$ is the supremum over all $\\alpha$ such that there exist arbitrarily large $n$-vertex $F$-free $k$-graphs $H$ in which every $(k-1)$-subset of $V(H)$ is contained in at least $\\alpha n$ edges. Recently, it was proved that for every $3$-graph $F$, $\\pi_{\\mathrm{co}}(F)=0$ implies $\\pi_{\\therefore}(F)=0$, where $\\pi_{\\therefore}(F)$ is the uniform Tur\\'{a}n density of $F$ and is defined as the supremum over all $d$ such that there are infinitely many $F$-free $k$-graphs $H$ satisfying tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.08771","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/2407.08771/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"}