{"paper":{"title":"Strong counterexamples to Mubayi's supersaturation conjecture in every uniformity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Heng Li, Hong Liu, Jing Wang, Xizhi Liu","submitted_at":"2026-06-25T08:16:56Z","abstract_excerpt":"The classical supersaturation problem, originating in classical results of Rademacher and Erd\\H{o}s on complete graphs, asks for the minimum number of copies of an $r$-graph $\\mathcal{F}$ in an $n$-vertex $r$-graph with $\\ex(n,\\mathcal{F})+q$ edges. Mubayi conjectured that, for every stable non-$r$-partite $r$-graph $\\mathcal{F}$, this minimum is at least $q c(n,\\mathcal{F})$, where $c(n,\\mathcal{F})$ is the minimum number of copies created by adding one edge to the $n$-vertex extremal $\\mathcal{F}$-free $r$-graph. Ma and Yuan recently constructed infinitely many graph counterexamples, with ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.26735","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/2606.26735/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"}