{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:IM4NH33SCLJMQISAFPDEM6FUOX","short_pith_number":"pith:IM4NH33S","schema_version":"1.0","canonical_sha256":"4338d3ef7212d2c822402bc64678b475f35855949f0a170ad254ac22f5f95d02","source":{"kind":"arxiv","id":"1411.1480","version":2},"attestation_state":"computed","paper":{"title":"Closed Intersecting Families of finite sets and their applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kaushik Majumder","submitted_at":"2014-11-06T03:00:06Z","abstract_excerpt":"Paul Erd\\H{o}s and L\\'aszl\\'o Lov\\'asz established that any \\emph{maximal intersecting family of $k-$sets} has at most $k^{k}$ blocks. They introduced the problem of finding the maximum possible number of blocks in such a family. They also showed that there exists a maximal intersecting family of $k-$sets with approximately $(e-1)k!$ blocks. Later P\\'eter Frankl, Katsuhiro Ota and Norihide Tokushige used a remarkable construction to prove the existence of a maximal intersecting family of $k-$sets with at least $(\\frac{k}{2})^{k-1}$ blocks. In this article we introduce the notion of a \\emph{clo"},"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":"1411.1480","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-06T03:00:06Z","cross_cats_sorted":[],"title_canon_sha256":"ddf7e8237a4f341454351bc75ab1da37942222c63dce39c94a240108f3afaf9e","abstract_canon_sha256":"cb1d4827d3295c34807d33af42f3b630b02801113b7b3fe523d389e2f60109a9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:59.067836Z","signature_b64":"LEd9fcNuUfkV1EEqjo1wWWMmJ1xNEFuvc3/bNsQPTWImJzzgbbz0Fj9963mr+N66uO64kjJE7GGZBVnyJUgPDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4338d3ef7212d2c822402bc64678b475f35855949f0a170ad254ac22f5f95d02","last_reissued_at":"2026-05-18T02:31:59.067288Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:59.067288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Closed Intersecting Families of finite sets and their applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kaushik Majumder","submitted_at":"2014-11-06T03:00:06Z","abstract_excerpt":"Paul Erd\\H{o}s and L\\'aszl\\'o Lov\\'asz established that any \\emph{maximal intersecting family of $k-$sets} has at most $k^{k}$ blocks. They introduced the problem of finding the maximum possible number of blocks in such a family. They also showed that there exists a maximal intersecting family of $k-$sets with approximately $(e-1)k!$ blocks. Later P\\'eter Frankl, Katsuhiro Ota and Norihide Tokushige used a remarkable construction to prove the existence of a maximal intersecting family of $k-$sets with at least $(\\frac{k}{2})^{k-1}$ blocks. In this article we introduce the notion of a \\emph{clo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1480","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":"1411.1480","created_at":"2026-05-18T02:31:59.067380+00:00"},{"alias_kind":"arxiv_version","alias_value":"1411.1480v2","created_at":"2026-05-18T02:31:59.067380+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.1480","created_at":"2026-05-18T02:31:59.067380+00:00"},{"alias_kind":"pith_short_12","alias_value":"IM4NH33SCLJM","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"IM4NH33SCLJMQISA","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"IM4NH33S","created_at":"2026-05-18T12:28:33.132498+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/IM4NH33SCLJMQISAFPDEM6FUOX","json":"https://pith.science/pith/IM4NH33SCLJMQISAFPDEM6FUOX.json","graph_json":"https://pith.science/api/pith-number/IM4NH33SCLJMQISAFPDEM6FUOX/graph.json","events_json":"https://pith.science/api/pith-number/IM4NH33SCLJMQISAFPDEM6FUOX/events.json","paper":"https://pith.science/paper/IM4NH33S"},"agent_actions":{"view_html":"https://pith.science/pith/IM4NH33SCLJMQISAFPDEM6FUOX","download_json":"https://pith.science/pith/IM4NH33SCLJMQISAFPDEM6FUOX.json","view_paper":"https://pith.science/paper/IM4NH33S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1411.1480&json=true","fetch_graph":"https://pith.science/api/pith-number/IM4NH33SCLJMQISAFPDEM6FUOX/graph.json","fetch_events":"https://pith.science/api/pith-number/IM4NH33SCLJMQISAFPDEM6FUOX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IM4NH33SCLJMQISAFPDEM6FUOX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IM4NH33SCLJMQISAFPDEM6FUOX/action/storage_attestation","attest_author":"https://pith.science/pith/IM4NH33SCLJMQISAFPDEM6FUOX/action/author_attestation","sign_citation":"https://pith.science/pith/IM4NH33SCLJMQISAFPDEM6FUOX/action/citation_signature","submit_replication":"https://pith.science/pith/IM4NH33SCLJMQISAFPDEM6FUOX/action/replication_record"}},"created_at":"2026-05-18T02:31:59.067380+00:00","updated_at":"2026-05-18T02:31:59.067380+00:00"}