{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:SBEYWIDKELX6QBEXYLWNCKDOT5","short_pith_number":"pith:SBEYWIDK","schema_version":"1.0","canonical_sha256":"90498b206a22efe80497c2ecd1286e9f5ab35bfb3d05707a1cf6f7321af6a320","source":{"kind":"arxiv","id":"1412.5822","version":2},"attestation_state":"computed","paper":{"title":"Bounding the Number of Hyperedges in Friendship $r$-Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Jason Semeraro, Karen Gunderson, Natasha Morrison","submitted_at":"2014-12-18T11:47:26Z","abstract_excerpt":"For $r \\ge 2$, an $r$-uniform hypergraph is called a friendship $r$-hypergraph if every set $R$ of $r$ vertices has a unique 'friend' - that is, there exists a unique vertex $x \\notin R$ with the property that for each subset $A \\subseteq R$ of size $r-1$, the set $A \\cup \\{x\\}$ is a hyperedge.\n  We show that for $r \\geq 3$, the number of hyperedges in a friendship $r$-hypergraph is at least $\\frac{r+1}{r} \\binom{n-1}{r-1}$, and we characterise those hypergraphs which achieve this bound. This generalises a result given by Li and van Rees in the case when $r = 3$.\n  We also obtain a new upper b"},"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":"1412.5822","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-18T11:47:26Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"c3640a851782687e6531bd1ff975849c8dbb92eca8d725ea228173e89dad5776","abstract_canon_sha256":"13894454ae884df28ad59886cce8dcbcb892811a4ba77e63b24cad3a0a8417df"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:33.343811Z","signature_b64":"Gc0VAVyqTSN90VzZjwA6oV1i+kDqFfNESVl2m8WH9dW40awgHuzknVtejNM5jUvMbSnBK/r63ryAZRo7S0huAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"90498b206a22efe80497c2ecd1286e9f5ab35bfb3d05707a1cf6f7321af6a320","last_reissued_at":"2026-05-18T02:17:33.343157Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:33.343157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounding the Number of Hyperedges in Friendship $r$-Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Jason Semeraro, Karen Gunderson, Natasha Morrison","submitted_at":"2014-12-18T11:47:26Z","abstract_excerpt":"For $r \\ge 2$, an $r$-uniform hypergraph is called a friendship $r$-hypergraph if every set $R$ of $r$ vertices has a unique 'friend' - that is, there exists a unique vertex $x \\notin R$ with the property that for each subset $A \\subseteq R$ of size $r-1$, the set $A \\cup \\{x\\}$ is a hyperedge.\n  We show that for $r \\geq 3$, the number of hyperedges in a friendship $r$-hypergraph is at least $\\frac{r+1}{r} \\binom{n-1}{r-1}$, and we characterise those hypergraphs which achieve this bound. This generalises a result given by Li and van Rees in the case when $r = 3$.\n  We also obtain a new upper b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5822","kind":"arxiv","version":2},"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":"1412.5822","created_at":"2026-05-18T02:17:33.343257+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.5822v2","created_at":"2026-05-18T02:17:33.343257+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5822","created_at":"2026-05-18T02:17:33.343257+00:00"},{"alias_kind":"pith_short_12","alias_value":"SBEYWIDKELX6","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_16","alias_value":"SBEYWIDKELX6QBEX","created_at":"2026-05-18T12:28:49.207871+00:00"},{"alias_kind":"pith_short_8","alias_value":"SBEYWIDK","created_at":"2026-05-18T12:28:49.207871+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/SBEYWIDKELX6QBEXYLWNCKDOT5","json":"https://pith.science/pith/SBEYWIDKELX6QBEXYLWNCKDOT5.json","graph_json":"https://pith.science/api/pith-number/SBEYWIDKELX6QBEXYLWNCKDOT5/graph.json","events_json":"https://pith.science/api/pith-number/SBEYWIDKELX6QBEXYLWNCKDOT5/events.json","paper":"https://pith.science/paper/SBEYWIDK"},"agent_actions":{"view_html":"https://pith.science/pith/SBEYWIDKELX6QBEXYLWNCKDOT5","download_json":"https://pith.science/pith/SBEYWIDKELX6QBEXYLWNCKDOT5.json","view_paper":"https://pith.science/paper/SBEYWIDK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.5822&json=true","fetch_graph":"https://pith.science/api/pith-number/SBEYWIDKELX6QBEXYLWNCKDOT5/graph.json","fetch_events":"https://pith.science/api/pith-number/SBEYWIDKELX6QBEXYLWNCKDOT5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SBEYWIDKELX6QBEXYLWNCKDOT5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SBEYWIDKELX6QBEXYLWNCKDOT5/action/storage_attestation","attest_author":"https://pith.science/pith/SBEYWIDKELX6QBEXYLWNCKDOT5/action/author_attestation","sign_citation":"https://pith.science/pith/SBEYWIDKELX6QBEXYLWNCKDOT5/action/citation_signature","submit_replication":"https://pith.science/pith/SBEYWIDKELX6QBEXYLWNCKDOT5/action/replication_record"}},"created_at":"2026-05-18T02:17:33.343257+00:00","updated_at":"2026-05-18T02:17:33.343257+00:00"}