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The local Tur\\'an density about property $(q,p)$ in $r$-uniform hypergraphs is defined as $t_{r}(q,p)=\\lim_{n\\to \\infty}T_{r}(n,q,p)/\\binom{n}{r}$. Frankl, Huang and R\\\"odl [J. Comb. Theory, Ser. A, 177 (2021)] showed that $\\lim_{p\\to\\infty}t_{r}(ap+1,p+1)=\\frac{1}{a^{r-1}}$ for positive integer $a$"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2303.00427","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2023-03-01T11:31:28Z","cross_cats_sorted":[],"title_canon_sha256":"46b16642963310a4184e9f70c50e76891832e83d355187dbabf17c8d438f64e9","abstract_canon_sha256":"d8caf9d1c52a72c49aa242c23e27253f914e948aba7705b7d289743ca7cb4d70"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:47:09.131549Z","signature_b64":"dnmKcRyxncTwUWAwRNmJIDeGoXegvMBMDQjox5I3AvcURuhxi5HSuVeGEMdz+m9C0KXnXRQdYa31SW4DLNSpAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe21fda352d398e8019ac03101e2948b7557d9a29a0cde6afd86ef31bd62c189","last_reissued_at":"2026-07-05T05:47:09.131116Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:47:09.131116Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On local Tur\\'an density problems of hypergraphs","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Chunqiu Fang, Ge Song, Guorong Gao, Jie Ma","submitted_at":"2023-03-01T11:31:28Z","abstract_excerpt":"For integers $q\\ge p\\ge r\\ge2$, we say that an $r$-uniform hypergraph $H$ has property $(q,p)$, if for any $q$-vertex subset $Q$ of $V(H)$, there exists a $p$-vertex subset $P$ of $Q$ spanning a clique in $H$. Let $T_{r}(n,q,p)=\\min\\{ e(H): H\\subset \\binom{[n]}{r}, H \\text{~has property~} (q,p)\\}$. The local Tur\\'an density about property $(q,p)$ in $r$-uniform hypergraphs is defined as $t_{r}(q,p)=\\lim_{n\\to \\infty}T_{r}(n,q,p)/\\binom{n}{r}$. Frankl, Huang and R\\\"odl [J. Comb. Theory, Ser. 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