{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:VWBZ6AB4W45RL46THSXEYEBQ5O","short_pith_number":"pith:VWBZ6AB4","schema_version":"1.0","canonical_sha256":"ad839f003cb73b15f3d33cae4c1030eb80a4851a3ca53bae3d0a4a8fa1aa018d","source":{"kind":"arxiv","id":"1412.5085","version":1},"attestation_state":"computed","paper":{"title":"On Erd\\H{o}s-Ko-Rado for random hypergraphs I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Arran Hamm, Jeff Kahn","submitted_at":"2014-12-16T17:10:17Z","abstract_excerpt":"A family of sets is intersecting if no two of its members are disjoint, and has the Erd\\H{o}s-Ko-Rado property (or is EKR) if each of its largest intersecting subfamilies has nonempty intersection.\n  Denote by $\\mathcal{H}_k(n,p)$ the random family in which each $k$-subset of $\\{1\\dots n\\}$ is present with probability $p$, independent of other choices. A question first studied by Balogh, Bohman and Mubayi asks: \\[ \\mbox{for what $p=p(n,k)$ is $\\mathcal{H}_k(n,p)$ likely to be EKR?} \\] Here, for fixed $c<1/4$, and $k< \\sqrt{cn\\log n}$ we give a precise answer to this question, characterizing th"},"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":"1412.5085","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-16T17:10:17Z","cross_cats_sorted":[],"title_canon_sha256":"eb38da4200feb7ea039f4b30030322b4e8c511f0d2be5b1fc1128b03e996d031","abstract_canon_sha256":"03148281489315e553a1cc6d29cae50a8c367933f99f069c9de8216285badb8d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:09.680388Z","signature_b64":"JTqxbk+gSyydfO7ky/ulgJg4rtJDRaYzSV8W+aygMZL13BJvJXlmopagrbMPrAsLdSpnCdCeLCvIii/UAhbrBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad839f003cb73b15f3d33cae4c1030eb80a4851a3ca53bae3d0a4a8fa1aa018d","last_reissued_at":"2026-05-18T02:31:09.679706Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:09.679706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Erd\\H{o}s-Ko-Rado for random hypergraphs I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Arran Hamm, Jeff Kahn","submitted_at":"2014-12-16T17:10:17Z","abstract_excerpt":"A family of sets is intersecting if no two of its members are disjoint, and has the Erd\\H{o}s-Ko-Rado property (or is EKR) if each of its largest intersecting subfamilies has nonempty intersection.\n  Denote by $\\mathcal{H}_k(n,p)$ the random family in which each $k$-subset of $\\{1\\dots n\\}$ is present with probability $p$, independent of other choices. A question first studied by Balogh, Bohman and Mubayi asks: \\[ \\mbox{for what $p=p(n,k)$ is $\\mathcal{H}_k(n,p)$ likely to be EKR?} \\] Here, for fixed $c<1/4$, and $k< \\sqrt{cn\\log n}$ we give a precise answer to this question, characterizing th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5085","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":"1412.5085","created_at":"2026-05-18T02:31:09.679787+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.5085v1","created_at":"2026-05-18T02:31:09.679787+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5085","created_at":"2026-05-18T02:31:09.679787+00:00"},{"alias_kind":"pith_short_12","alias_value":"VWBZ6AB4W45R","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_16","alias_value":"VWBZ6AB4W45RL46T","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_8","alias_value":"VWBZ6AB4","created_at":"2026-05-18T12:28:54.890064+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/VWBZ6AB4W45RL46THSXEYEBQ5O","json":"https://pith.science/pith/VWBZ6AB4W45RL46THSXEYEBQ5O.json","graph_json":"https://pith.science/api/pith-number/VWBZ6AB4W45RL46THSXEYEBQ5O/graph.json","events_json":"https://pith.science/api/pith-number/VWBZ6AB4W45RL46THSXEYEBQ5O/events.json","paper":"https://pith.science/paper/VWBZ6AB4"},"agent_actions":{"view_html":"https://pith.science/pith/VWBZ6AB4W45RL46THSXEYEBQ5O","download_json":"https://pith.science/pith/VWBZ6AB4W45RL46THSXEYEBQ5O.json","view_paper":"https://pith.science/paper/VWBZ6AB4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.5085&json=true","fetch_graph":"https://pith.science/api/pith-number/VWBZ6AB4W45RL46THSXEYEBQ5O/graph.json","fetch_events":"https://pith.science/api/pith-number/VWBZ6AB4W45RL46THSXEYEBQ5O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VWBZ6AB4W45RL46THSXEYEBQ5O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VWBZ6AB4W45RL46THSXEYEBQ5O/action/storage_attestation","attest_author":"https://pith.science/pith/VWBZ6AB4W45RL46THSXEYEBQ5O/action/author_attestation","sign_citation":"https://pith.science/pith/VWBZ6AB4W45RL46THSXEYEBQ5O/action/citation_signature","submit_replication":"https://pith.science/pith/VWBZ6AB4W45RL46THSXEYEBQ5O/action/replication_record"}},"created_at":"2026-05-18T02:31:09.679787+00:00","updated_at":"2026-05-18T02:31:09.679787+00:00"}