{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ABCVUUNFAIRFO3E7ET6KPMVN7Q","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":"7948371eb4419729e14d0dfe7cafdaa69e972f63223a427770bd54cc6f1103bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-08T09:25:10Z","title_canon_sha256":"5be34a914d7fff7977ffcc2e07f0315fa9a6db733b88162aa8ca2fedc1998364"},"schema_version":"1.0","source":{"id":"1602.02501","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.02501","created_at":"2026-05-18T00:23:09Z"},{"alias_kind":"arxiv_version","alias_value":"1602.02501v2","created_at":"2026-05-18T00:23:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.02501","created_at":"2026-05-18T00:23:09Z"},{"alias_kind":"pith_short_12","alias_value":"ABCVUUNFAIRF","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"ABCVUUNFAIRFO3E7","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"ABCVUUNF","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:84089ad405ddec6a613b192ee68049b575ce9664fb7474faec29ef729c0aea5f","target":"graph","created_at":"2026-05-18T00:23:09Z","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":"For a given graph $F$ we consider the family of (finite) graphs $G$ with the Ramsey property for $F$, that is the set of such graphs $G$ with the property that every two-colouring of the edges of $G$ yields a monochromatic copy of $F$. For $F$ being a triangle Friedgut, R\\\"odl, Ruci\\'nski, and Tetali (2004) established the sharp threshold for the Ramsey property in random graphs. We obtained a simpler proof of this result which extends to a more general class of graphs $F$ including all cycles.\n  The proof is based on Friedgut's criteria (1999) for sharp thresholds, and on the recently develop","authors_text":"Fabian Schulenburg, Mathias Schacht","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-08T09:25:10Z","title":"Sharp thresholds for Ramsey properties of strictly balanced nearly bipartite graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02501","kind":"arxiv","version":2},"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:f08e851b4a2949db1e1dd9f148ee3cca21097c6b77b802a96368f9b2f433aa0f","target":"record","created_at":"2026-05-18T00:23:09Z","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":"7948371eb4419729e14d0dfe7cafdaa69e972f63223a427770bd54cc6f1103bd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-08T09:25:10Z","title_canon_sha256":"5be34a914d7fff7977ffcc2e07f0315fa9a6db733b88162aa8ca2fedc1998364"},"schema_version":"1.0","source":{"id":"1602.02501","kind":"arxiv","version":2}},"canonical_sha256":"00455a51a50222576c9f24fca7b2adfc03c6a1008cc0cc40686e73316987e8e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"00455a51a50222576c9f24fca7b2adfc03c6a1008cc0cc40686e73316987e8e5","first_computed_at":"2026-05-18T00:23:09.578232Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:09.578232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TMXTnT6p1Ww9DqNfsAnAOFfP4wtRwZDEEJBG060hViuFf63IDtanRBCAbKGu802h3CpNU/7jqc/K9+LJEECeCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:09.578814Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.02501","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f08e851b4a2949db1e1dd9f148ee3cca21097c6b77b802a96368f9b2f433aa0f","sha256:84089ad405ddec6a613b192ee68049b575ce9664fb7474faec29ef729c0aea5f"],"state_sha256":"dc46dbcfacafeae37ddf41b882d488fc4ae79abac2de95eaaab41839a399c047"}