{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HCDBUXA4SGDEAQZW3LPTYP2FKK","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":"a15c42b96d47fa36d5eedd7be482b8109428f1370e87bc5ba26be75a89bf86c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-04T11:35:19Z","title_canon_sha256":"c996fb3effb4a91f943a60ff354e6f6413450b974016d455a8d1b03b32eff117"},"schema_version":"1.0","source":{"id":"1610.00935","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.00935","created_at":"2026-05-18T01:03:12Z"},{"alias_kind":"arxiv_version","alias_value":"1610.00935v1","created_at":"2026-05-18T01:03:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.00935","created_at":"2026-05-18T01:03:12Z"},{"alias_kind":"pith_short_12","alias_value":"HCDBUXA4SGDE","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HCDBUXA4SGDEAQZW","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HCDBUXA4","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:154ad11c38bbe3aa09fd94b6cb4cbf8d280beb55a5cec0180a2503815041cc56","target":"graph","created_at":"2026-05-18T01:03:12Z","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 celebrated result of R\\\"odl and Ruci\\'nski states that for every graph $F$, which is not a forest of stars and paths of length $3$, and fixed number of colours $r\\ge 2$ there exist positive constants $c, C$ such that for $p \\leq cn^{-1/m_2(F)}$ the probability that every colouring of the edges of the random graph $G(n,p)$ contains a monochromatic copy of $F$ is $o(1)$ (the \"0-statement\"), while for $p \\geq Cn^{-1/m_2(F)}$ it is $1-o(1)$ (the \"1-statement\"). Here $m_2(F)$ denotes the $2$-density of $F$. On the other hand, the case where $F$ is a forest of stars has a coarse threshold which is","authors_text":"Angelika Steger, Henning Thomas, Luca Gugelmann, Nemanja \\v{S}kori\\'c, Rajko Nenadov, Yury Person","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-04T11:35:19Z","title":"Symmetric and asymmetric Ramsey properties in random hypergraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00935","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":"sha256:06041e19e404b64df5c365866a3caedbd9d401251a6b795cd98d57bc4bb52cef","target":"record","created_at":"2026-05-18T01:03:12Z","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":"a15c42b96d47fa36d5eedd7be482b8109428f1370e87bc5ba26be75a89bf86c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-04T11:35:19Z","title_canon_sha256":"c996fb3effb4a91f943a60ff354e6f6413450b974016d455a8d1b03b32eff117"},"schema_version":"1.0","source":{"id":"1610.00935","kind":"arxiv","version":1}},"canonical_sha256":"38861a5c1c9186404336dadf3c3f4552bf84a2160c6e126318c8441aef6a5115","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"38861a5c1c9186404336dadf3c3f4552bf84a2160c6e126318c8441aef6a5115","first_computed_at":"2026-05-18T01:03:12.876431Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:12.876431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G5kBqrhImxnfsU4wxQLjZP4LKZhOnPXgksvU6elAw0N1AVD9mYo1T9CW78EOoz0YnKZ3WiUPLts5td0/ygH5DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:12.876954Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.00935","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:06041e19e404b64df5c365866a3caedbd9d401251a6b795cd98d57bc4bb52cef","sha256:154ad11c38bbe3aa09fd94b6cb4cbf8d280beb55a5cec0180a2503815041cc56"],"state_sha256":"48542f2e6187361b421f7888d05b5e7b5e2251f08d863af44f17b1f95be8c1d7"}