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Let $r$-uniform Berge theta hypergraph $\\Theta_{\\ell,t}^{B}$ be the $r$-uniform hypergraph consisting of $t$ internally disjoint Berge paths of length $\\ell$ with the same pair of endpoints. In this work, we determine the Tur\\'{a}n number of $3$-uniform Berge theta hypergraph when $\\ell=3$ and $t$ is relatively small. More precisely, we provide an explicit construction giving \\begin{align*} \\textup{ex}_{3}(n,\\Theta_{3,217}^{B})=\\Omega(n^{\\frac{4}{3}}). \\end{align*} This matches an ea"},"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":"1908.01459","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-05T04:07:33Z","cross_cats_sorted":[],"title_canon_sha256":"e2b4617f6fef5487bcf1bd9ba2529ea3cd1a566e87b6eb081aa11291bd641b0e","abstract_canon_sha256":"d84c21142298f415bf1243a1f5ee0f937b0412782235f8584191a7d709bd09d0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:16:36.073062Z","signature_b64":"KxWI1uzgiq/CGjVlkoEzYN5czwABLX3fHNRRaJUN4TdI/aApULHcrpw7tpBtYwWbC7nZVPCpvETe0+YLGZgjCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db068d15275c9e41ee11c81cd901bdaf587048365444bc84203599964d2f3445","last_reissued_at":"2026-07-05T00:16:36.072676Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:16:36.072676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"3-uniform hypergraphs with few Berge paths of length three between any two vertices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gennian Ge, Tao Zhang, Zixiang Xu","submitted_at":"2019-08-05T04:07:33Z","abstract_excerpt":"Recently, Berge theta hypergraphs have received special attention due to the similarity with Berge even cycles. 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