{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:AZQSZBH5M7CDW3ZS2WD6HLIFU7","short_pith_number":"pith:AZQSZBH5","schema_version":"1.0","canonical_sha256":"06612c84fd67c43b6f32d587e3ad05a7fc53150c9b773c0b96d1bf25e0d27c5b","source":{"kind":"arxiv","id":"1803.01953","version":1},"attestation_state":"computed","paper":{"title":"Uniformity thresholds for the asymptotic size of extremal Berge-$F$-free hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Abhishek Methuku, Casey Tompkins, D\\'aniel Gr\\'osz","submitted_at":"2018-03-05T22:41:00Z","abstract_excerpt":"Let $F = (U,E)$ be a graph and $\\mathcal{H} = (V,\\mathcal{E})$ be a hypergraph. We say that $\\mathcal{H}$ contains a Berge-$F$ if there exist injections $\\psi:U\\to V$ and $\\varphi:E\\to \\mathcal{E}$ such that for every $e=\\{u,v\\}\\in E$, $\\{\\psi(u),\\psi(v)\\}\\subset\\varphi(e)$. Let $ex_r(n,F)$ denote the maximum number of hyperedges in an $r$-uniform hypergraph on $n$ vertices which does not contain a Berge-$F$.\n  For small enough $r$ and non-bipartite $F$, $ex_r(n,F)=\\Omega(n^2)$; we show that for sufficiently large $r$, $ex_r(n,F)=o(n^2)$. Let $thres(F) = \\min\\{r_0 :ex_r(n,F) = o(n^2) \\text{ fo"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1803.01953","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-03-05T22:41:00Z","cross_cats_sorted":[],"title_canon_sha256":"66b8bc9aab1bd6bcbe5d34450b25561dc61add60206bedc8cfd9f180ca9aa95d","abstract_canon_sha256":"534d0e98473c8b564295b1aac0fe858bf92917055f88bcac1d61ca7e94520796"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:56.222134Z","signature_b64":"5shIZlohalo1icx3AdenoCDc7cLTOj1Tr8+cyyGqjWdpSMBJ1h8Ez3qXReyspsmIOIZf0XH8cXOVZ+Rtp0EKCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06612c84fd67c43b6f32d587e3ad05a7fc53150c9b773c0b96d1bf25e0d27c5b","last_reissued_at":"2026-05-18T00:21:56.221584Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:56.221584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniformity thresholds for the asymptotic size of extremal Berge-$F$-free hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Abhishek Methuku, Casey Tompkins, D\\'aniel Gr\\'osz","submitted_at":"2018-03-05T22:41:00Z","abstract_excerpt":"Let $F = (U,E)$ be a graph and $\\mathcal{H} = (V,\\mathcal{E})$ be a hypergraph. We say that $\\mathcal{H}$ contains a Berge-$F$ if there exist injections $\\psi:U\\to V$ and $\\varphi:E\\to \\mathcal{E}$ such that for every $e=\\{u,v\\}\\in E$, $\\{\\psi(u),\\psi(v)\\}\\subset\\varphi(e)$. Let $ex_r(n,F)$ denote the maximum number of hyperedges in an $r$-uniform hypergraph on $n$ vertices which does not contain a Berge-$F$.\n  For small enough $r$ and non-bipartite $F$, $ex_r(n,F)=\\Omega(n^2)$; we show that for sufficiently large $r$, $ex_r(n,F)=o(n^2)$. Let $thres(F) = \\min\\{r_0 :ex_r(n,F) = o(n^2) \\text{ fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01953","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1803.01953","created_at":"2026-05-18T00:21:56.221667+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.01953v1","created_at":"2026-05-18T00:21:56.221667+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.01953","created_at":"2026-05-18T00:21:56.221667+00:00"},{"alias_kind":"pith_short_12","alias_value":"AZQSZBH5M7CD","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_16","alias_value":"AZQSZBH5M7CDW3ZS","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_8","alias_value":"AZQSZBH5","created_at":"2026-05-18T12:32:13.499390+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AZQSZBH5M7CDW3ZS2WD6HLIFU7","json":"https://pith.science/pith/AZQSZBH5M7CDW3ZS2WD6HLIFU7.json","graph_json":"https://pith.science/api/pith-number/AZQSZBH5M7CDW3ZS2WD6HLIFU7/graph.json","events_json":"https://pith.science/api/pith-number/AZQSZBH5M7CDW3ZS2WD6HLIFU7/events.json","paper":"https://pith.science/paper/AZQSZBH5"},"agent_actions":{"view_html":"https://pith.science/pith/AZQSZBH5M7CDW3ZS2WD6HLIFU7","download_json":"https://pith.science/pith/AZQSZBH5M7CDW3ZS2WD6HLIFU7.json","view_paper":"https://pith.science/paper/AZQSZBH5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.01953&json=true","fetch_graph":"https://pith.science/api/pith-number/AZQSZBH5M7CDW3ZS2WD6HLIFU7/graph.json","fetch_events":"https://pith.science/api/pith-number/AZQSZBH5M7CDW3ZS2WD6HLIFU7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AZQSZBH5M7CDW3ZS2WD6HLIFU7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AZQSZBH5M7CDW3ZS2WD6HLIFU7/action/storage_attestation","attest_author":"https://pith.science/pith/AZQSZBH5M7CDW3ZS2WD6HLIFU7/action/author_attestation","sign_citation":"https://pith.science/pith/AZQSZBH5M7CDW3ZS2WD6HLIFU7/action/citation_signature","submit_replication":"https://pith.science/pith/AZQSZBH5M7CDW3ZS2WD6HLIFU7/action/replication_record"}},"created_at":"2026-05-18T00:21:56.221667+00:00","updated_at":"2026-05-18T00:21:56.221667+00:00"}