{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:UBJVYADDT7ZM5EUPE4F36NUXDI","short_pith_number":"pith:UBJVYADD","canonical_record":{"source":{"id":"1406.5793","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-23T02:19:31Z","cross_cats_sorted":[],"title_canon_sha256":"7ebf438412e569a8d31e4c1b96611466e210c8d90d7facf1362513257cfa4fbd","abstract_canon_sha256":"ee1c41233a62582ca1ba45e2bfebd998e0e89fc16872fc9e6040f6350ac08624"},"schema_version":"1.0"},"canonical_sha256":"a0535c00639ff2ce928f270bbf36971a3492b828419504f5c72f7e16a261d49a","source":{"kind":"arxiv","id":"1406.5793","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5793","created_at":"2026-05-18T01:08:44Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5793v3","created_at":"2026-05-18T01:08:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5793","created_at":"2026-05-18T01:08:44Z"},{"alias_kind":"pith_short_12","alias_value":"UBJVYADDT7ZM","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UBJVYADDT7ZM5EUP","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UBJVYADD","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:UBJVYADDT7ZM5EUPE4F36NUXDI","target":"record","payload":{"canonical_record":{"source":{"id":"1406.5793","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-23T02:19:31Z","cross_cats_sorted":[],"title_canon_sha256":"7ebf438412e569a8d31e4c1b96611466e210c8d90d7facf1362513257cfa4fbd","abstract_canon_sha256":"ee1c41233a62582ca1ba45e2bfebd998e0e89fc16872fc9e6040f6350ac08624"},"schema_version":"1.0"},"canonical_sha256":"a0535c00639ff2ce928f270bbf36971a3492b828419504f5c72f7e16a261d49a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:44.927540Z","signature_b64":"yZts60s33BiFQam4G4wsmJjfnl9/sPD465YBy6Xiis9z7olU9I5YIORqLftaVhxaMl87FlFMpsSD++TBiYn4CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0535c00639ff2ce928f270bbf36971a3492b828419504f5c72f7e16a261d49a","last_reissued_at":"2026-05-18T01:08:44.926863Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:44.926863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.5793","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:08:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YpeagNaxmfth8xlynaWlnSToP2apUrFOSp6Bmf303TNmIUhJrc/qQuuspfZ4WXFnI/EIXYiwFSlUdXuaG2VOBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T16:22:39.662619Z"},"content_sha256":"d7426834861440172355d41f3339c16011e77c0f7a8fefba9329ddec894be955","schema_version":"1.0","event_id":"sha256:d7426834861440172355d41f3339c16011e77c0f7a8fefba9329ddec894be955"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:UBJVYADDT7ZM5EUPE4F36NUXDI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Erd\\H{o}s-Ko-Rado for random hypergraphs II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Arran Hamm, Jeff Kahn","submitted_at":"2014-06-23T02:19:31Z","abstract_excerpt":"Denote by $\\mathcal{H}_k (n,p)$ the random $k$-graph in which each $k$-subset of $\\{1... n\\}$ is present with probability $p$, independent of other choices. More or less answering a question of Balogh, Bohman and Mubayi, we show: there is a fixed $\\varepsilon >0$ such that if $n=2k+1$ and $p> 1-\\varepsilon$, then w.h.p. (that is, with probability tending to 1 as $k\\rightarrow \\infty$), $\\mathcal{H}_k (n,p)$ has the \"Erd\\H{o}s-Ko-Rado property.\" We also mention a similar random version of Sperner's Theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5793","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:08:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HQYH2+in2jYwBebffhOhCFYiNVXXY0oppFFmxIoJvsbfoIA7vJfNUuD/u9hXgDXKZ2TGYWTSgauK/oXAlOKcCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T16:22:39.662963Z"},"content_sha256":"b13e5451771820e72b478d9695b466d85eb3854aecfeba3f2522d709a88b105f","schema_version":"1.0","event_id":"sha256:b13e5451771820e72b478d9695b466d85eb3854aecfeba3f2522d709a88b105f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UBJVYADDT7ZM5EUPE4F36NUXDI/bundle.json","state_url":"https://pith.science/pith/UBJVYADDT7ZM5EUPE4F36NUXDI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UBJVYADDT7ZM5EUPE4F36NUXDI/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T16:22:39Z","links":{"resolver":"https://pith.science/pith/UBJVYADDT7ZM5EUPE4F36NUXDI","bundle":"https://pith.science/pith/UBJVYADDT7ZM5EUPE4F36NUXDI/bundle.json","state":"https://pith.science/pith/UBJVYADDT7ZM5EUPE4F36NUXDI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UBJVYADDT7ZM5EUPE4F36NUXDI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:UBJVYADDT7ZM5EUPE4F36NUXDI","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":"ee1c41233a62582ca1ba45e2bfebd998e0e89fc16872fc9e6040f6350ac08624","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-23T02:19:31Z","title_canon_sha256":"7ebf438412e569a8d31e4c1b96611466e210c8d90d7facf1362513257cfa4fbd"},"schema_version":"1.0","source":{"id":"1406.5793","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5793","created_at":"2026-05-18T01:08:44Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5793v3","created_at":"2026-05-18T01:08:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5793","created_at":"2026-05-18T01:08:44Z"},{"alias_kind":"pith_short_12","alias_value":"UBJVYADDT7ZM","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UBJVYADDT7ZM5EUP","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UBJVYADD","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:b13e5451771820e72b478d9695b466d85eb3854aecfeba3f2522d709a88b105f","target":"graph","created_at":"2026-05-18T01:08:44Z","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":"Denote by $\\mathcal{H}_k (n,p)$ the random $k$-graph in which each $k$-subset of $\\{1... n\\}$ is present with probability $p$, independent of other choices. More or less answering a question of Balogh, Bohman and Mubayi, we show: there is a fixed $\\varepsilon >0$ such that if $n=2k+1$ and $p> 1-\\varepsilon$, then w.h.p. (that is, with probability tending to 1 as $k\\rightarrow \\infty$), $\\mathcal{H}_k (n,p)$ has the \"Erd\\H{o}s-Ko-Rado property.\" We also mention a similar random version of Sperner's Theorem.","authors_text":"Arran Hamm, Jeff Kahn","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-23T02:19:31Z","title":"On Erd\\H{o}s-Ko-Rado for random hypergraphs II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5793","kind":"arxiv","version":3},"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:d7426834861440172355d41f3339c16011e77c0f7a8fefba9329ddec894be955","target":"record","created_at":"2026-05-18T01:08:44Z","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":"ee1c41233a62582ca1ba45e2bfebd998e0e89fc16872fc9e6040f6350ac08624","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-23T02:19:31Z","title_canon_sha256":"7ebf438412e569a8d31e4c1b96611466e210c8d90d7facf1362513257cfa4fbd"},"schema_version":"1.0","source":{"id":"1406.5793","kind":"arxiv","version":3}},"canonical_sha256":"a0535c00639ff2ce928f270bbf36971a3492b828419504f5c72f7e16a261d49a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a0535c00639ff2ce928f270bbf36971a3492b828419504f5c72f7e16a261d49a","first_computed_at":"2026-05-18T01:08:44.926863Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:44.926863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yZts60s33BiFQam4G4wsmJjfnl9/sPD465YBy6Xiis9z7olU9I5YIORqLftaVhxaMl87FlFMpsSD++TBiYn4CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:44.927540Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.5793","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7426834861440172355d41f3339c16011e77c0f7a8fefba9329ddec894be955","sha256:b13e5451771820e72b478d9695b466d85eb3854aecfeba3f2522d709a88b105f"],"state_sha256":"15bd82b9c11e91c766e6cd50317c20d032b99e265d639d5396f12741481c5c9e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i4w3jCRsO0loj9gqSvDz9j2fSSkQbDnz5fbNYa45wgm/d/VDMz1+Z2DzCwTgzphAyPTJwiVlfMYnscluB01ZAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T16:22:39.664866Z","bundle_sha256":"ae54d2d5f60d8ecb2133a4aee84cb8895bd322b5d1a38183af94b5a305160c14"}}