{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:ABCVUUNFAIRFO3E7ET6KPMVN7Q","short_pith_number":"pith:ABCVUUNF","schema_version":"1.0","canonical_sha256":"00455a51a50222576c9f24fca7b2adfc03c6a1008cc0cc40686e73316987e8e5","source":{"kind":"arxiv","id":"1602.02501","version":2},"attestation_state":"computed","paper":{"title":"Sharp thresholds for Ramsey properties of strictly balanced nearly bipartite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Fabian Schulenburg, Mathias Schacht","submitted_at":"2016-02-08T09:25:10Z","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"},"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":"1602.02501","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-08T09:25:10Z","cross_cats_sorted":[],"title_canon_sha256":"5be34a914d7fff7977ffcc2e07f0315fa9a6db733b88162aa8ca2fedc1998364","abstract_canon_sha256":"7948371eb4419729e14d0dfe7cafdaa69e972f63223a427770bd54cc6f1103bd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:09.578814Z","signature_b64":"TMXTnT6p1Ww9DqNfsAnAOFfP4wtRwZDEEJBG060hViuFf63IDtanRBCAbKGu802h3CpNU/7jqc/K9+LJEECeCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00455a51a50222576c9f24fca7b2adfc03c6a1008cc0cc40686e73316987e8e5","last_reissued_at":"2026-05-18T00:23:09.578232Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:09.578232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sharp thresholds for Ramsey properties of strictly balanced nearly bipartite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Fabian Schulenburg, Mathias Schacht","submitted_at":"2016-02-08T09:25:10Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02501","kind":"arxiv","version":2},"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":"1602.02501","created_at":"2026-05-18T00:23:09.578362+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.02501v2","created_at":"2026-05-18T00:23:09.578362+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.02501","created_at":"2026-05-18T00:23:09.578362+00:00"},{"alias_kind":"pith_short_12","alias_value":"ABCVUUNFAIRF","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_16","alias_value":"ABCVUUNFAIRFO3E7","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_8","alias_value":"ABCVUUNF","created_at":"2026-05-18T12:30:04.600751+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/ABCVUUNFAIRFO3E7ET6KPMVN7Q","json":"https://pith.science/pith/ABCVUUNFAIRFO3E7ET6KPMVN7Q.json","graph_json":"https://pith.science/api/pith-number/ABCVUUNFAIRFO3E7ET6KPMVN7Q/graph.json","events_json":"https://pith.science/api/pith-number/ABCVUUNFAIRFO3E7ET6KPMVN7Q/events.json","paper":"https://pith.science/paper/ABCVUUNF"},"agent_actions":{"view_html":"https://pith.science/pith/ABCVUUNFAIRFO3E7ET6KPMVN7Q","download_json":"https://pith.science/pith/ABCVUUNFAIRFO3E7ET6KPMVN7Q.json","view_paper":"https://pith.science/paper/ABCVUUNF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.02501&json=true","fetch_graph":"https://pith.science/api/pith-number/ABCVUUNFAIRFO3E7ET6KPMVN7Q/graph.json","fetch_events":"https://pith.science/api/pith-number/ABCVUUNFAIRFO3E7ET6KPMVN7Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ABCVUUNFAIRFO3E7ET6KPMVN7Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ABCVUUNFAIRFO3E7ET6KPMVN7Q/action/storage_attestation","attest_author":"https://pith.science/pith/ABCVUUNFAIRFO3E7ET6KPMVN7Q/action/author_attestation","sign_citation":"https://pith.science/pith/ABCVUUNFAIRFO3E7ET6KPMVN7Q/action/citation_signature","submit_replication":"https://pith.science/pith/ABCVUUNFAIRFO3E7ET6KPMVN7Q/action/replication_record"}},"created_at":"2026-05-18T00:23:09.578362+00:00","updated_at":"2026-05-18T00:23:09.578362+00:00"}