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Aside from a few simple exceptions, the corresponding $0$-statement also holds, that is, there exists $c>0$ such that whenever $p\\leq cn^{-1/m_2(H)}$ the random graph $G_{n,p}$ is a.a.s. not $H$-Ramsey.\n  We show that near this threshold, even when $G_{n,p}$ is not $H$-Ramsey, it is often extremely close to being $H$-Ramsey"},"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":"1908.02991","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-08T09:52:25Z","cross_cats_sorted":[],"title_canon_sha256":"0f9338db2efd8906675d6d6b9f90939c9a61f1701523a88c9f9991587949ff85","abstract_canon_sha256":"5220c740d346f7f8edce46eca2f68a6a4a6359c2c455f761304d6cdd4c59ac6b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:47:11.726978Z","signature_b64":"LO7olzePH8UiTMBvISprleRY3ljk6/OOMjtrb7+/GcTtXizZ3A+VetHTkNv7xv4crrVRIU/oidMHvhmghDZRAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8738e4a191cbb31dcca147a4300b8fa53bc503fe297695b174104c8d63f7021","last_reissued_at":"2026-07-05T01:47:11.726528Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:47:11.726528Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ramsey games near the critical threshold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David Conlon, Joonkyung Lee, Shagnik Das, Tam\\'as M\\'esz\\'aros","submitted_at":"2019-08-08T09:52:25Z","abstract_excerpt":"A well-known result of R\\\"odl and Ruci\\'nski states that for any graph $H$ there exists a constant $C$ such that if $p \\geq C n^{- 1/m_2(H)}$, then the random graph $G_{n,p}$ is a.a.s. $H$-Ramsey, that is, any $2$-colouring of its edges contains a monochromatic copy of $H$. Aside from a few simple exceptions, the corresponding $0$-statement also holds, that is, there exists $c>0$ such that whenever $p\\leq cn^{-1/m_2(H)}$ the random graph $G_{n,p}$ is a.a.s. not $H$-Ramsey.\n  We show that near this threshold, even when $G_{n,p}$ is not $H$-Ramsey, it is often extremely close to being $H$-Ramsey"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02991","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.02991/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1908.02991","created_at":"2026-07-05T01:47:11.726589+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.02991v3","created_at":"2026-07-05T01:47:11.726589+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.02991","created_at":"2026-07-05T01:47:11.726589+00:00"},{"alias_kind":"pith_short_12","alias_value":"VBZY4SQZDS5T","created_at":"2026-07-05T01:47:11.726589+00:00"},{"alias_kind":"pith_short_16","alias_value":"VBZY4SQZDS5TDXGK","created_at":"2026-07-05T01:47:11.726589+00:00"},{"alias_kind":"pith_short_8","alias_value":"VBZY4SQZ","created_at":"2026-07-05T01:47:11.726589+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/VBZY4SQZDS5TDXGKCR5EGAFY7J","json":"https://pith.science/pith/VBZY4SQZDS5TDXGKCR5EGAFY7J.json","graph_json":"https://pith.science/api/pith-number/VBZY4SQZDS5TDXGKCR5EGAFY7J/graph.json","events_json":"https://pith.science/api/pith-number/VBZY4SQZDS5TDXGKCR5EGAFY7J/events.json","paper":"https://pith.science/paper/VBZY4SQZ"},"agent_actions":{"view_html":"https://pith.science/pith/VBZY4SQZDS5TDXGKCR5EGAFY7J","download_json":"https://pith.science/pith/VBZY4SQZDS5TDXGKCR5EGAFY7J.json","view_paper":"https://pith.science/paper/VBZY4SQZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.02991&json=true","fetch_graph":"https://pith.science/api/pith-number/VBZY4SQZDS5TDXGKCR5EGAFY7J/graph.json","fetch_events":"https://pith.science/api/pith-number/VBZY4SQZDS5TDXGKCR5EGAFY7J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VBZY4SQZDS5TDXGKCR5EGAFY7J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VBZY4SQZDS5TDXGKCR5EGAFY7J/action/storage_attestation","attest_author":"https://pith.science/pith/VBZY4SQZDS5TDXGKCR5EGAFY7J/action/author_attestation","sign_citation":"https://pith.science/pith/VBZY4SQZDS5TDXGKCR5EGAFY7J/action/citation_signature","submit_replication":"https://pith.science/pith/VBZY4SQZDS5TDXGKCR5EGAFY7J/action/replication_record"}},"created_at":"2026-07-05T01:47:11.726589+00:00","updated_at":"2026-07-05T01:47:11.726589+00:00"}