{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:VWBZ6AB4W45RL46THSXEYEBQ5O","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"03148281489315e553a1cc6d29cae50a8c367933f99f069c9de8216285badb8d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-16T17:10:17Z","title_canon_sha256":"eb38da4200feb7ea039f4b30030322b4e8c511f0d2be5b1fc1128b03e996d031"},"schema_version":"1.0","source":{"id":"1412.5085","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.5085","created_at":"2026-05-18T02:31:09Z"},{"alias_kind":"arxiv_version","alias_value":"1412.5085v1","created_at":"2026-05-18T02:31:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5085","created_at":"2026-05-18T02:31:09Z"},{"alias_kind":"pith_short_12","alias_value":"VWBZ6AB4W45R","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VWBZ6AB4W45RL46T","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VWBZ6AB4","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:eb22767fbba5dd6a9fa6c78380cb55c3d0c1939fb67f944f2db0592228762220","target":"graph","created_at":"2026-05-18T02:31:09Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Arran Hamm, Jeff Kahn","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-16T17:10:17Z","title":"On Erd\\H{o}s-Ko-Rado for random hypergraphs I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5085","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:04312a5555e492750d4f4b67a10734e36b28e58ebbd70d8c0149e8c1281c7771","target":"record","created_at":"2026-05-18T02:31:09Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"03148281489315e553a1cc6d29cae50a8c367933f99f069c9de8216285badb8d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-16T17:10:17Z","title_canon_sha256":"eb38da4200feb7ea039f4b30030322b4e8c511f0d2be5b1fc1128b03e996d031"},"schema_version":"1.0","source":{"id":"1412.5085","kind":"arxiv","version":1}},"canonical_sha256":"ad839f003cb73b15f3d33cae4c1030eb80a4851a3ca53bae3d0a4a8fa1aa018d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad839f003cb73b15f3d33cae4c1030eb80a4851a3ca53bae3d0a4a8fa1aa018d","first_computed_at":"2026-05-18T02:31:09.679706Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:09.679706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JTqxbk+gSyydfO7ky/ulgJg4rtJDRaYzSV8W+aygMZL13BJvJXlmopagrbMPrAsLdSpnCdCeLCvIii/UAhbrBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:09.680388Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.5085","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04312a5555e492750d4f4b67a10734e36b28e58ebbd70d8c0149e8c1281c7771","sha256:eb22767fbba5dd6a9fa6c78380cb55c3d0c1939fb67f944f2db0592228762220"],"state_sha256":"728451ecdd1cc639097753df3813ef4383f68124b4b20a79995a9e069516c248"}