{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:NLAB6DR3SA27SNOINI77LY67EE","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":"0bb64293689d3423fdf9602abe05cd4aa5c0a6926524543a81f054c133b36572","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-09-30T22:20:42Z","title_canon_sha256":"8e2cfc6ad492a9fd454ee2c178e3dd5a2dbcca3024a10495944d3af6336da478"},"schema_version":"1.0","source":{"id":"1910.00136","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.00136","created_at":"2026-06-23T03:14:26Z"},{"alias_kind":"arxiv_version","alias_value":"1910.00136v2","created_at":"2026-06-23T03:14:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.00136","created_at":"2026-06-23T03:14:26Z"},{"alias_kind":"pith_short_12","alias_value":"NLAB6DR3SA27","created_at":"2026-06-23T03:14:26Z"},{"alias_kind":"pith_short_16","alias_value":"NLAB6DR3SA27SNOI","created_at":"2026-06-23T03:14:26Z"},{"alias_kind":"pith_short_8","alias_value":"NLAB6DR3","created_at":"2026-06-23T03:14:26Z"}],"graph_snapshots":[{"event_id":"sha256:7d653b3993928889b90071347a5e2cf0614cab9943a8af2661e6e9cf4744a735","target":"graph","created_at":"2026-06-23T03:14:26Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1910.00136/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given graphs $F,H$ and $G$, we say that $G$ is $(F,H)_v$-Ramsey if every red/blue vertex colouring of $G$ containsa red copy of $F$ or a blue copy of $H$. Results of {\\L}uczak, Ruci\\'nski and Voigt, and Kreuter determine the threshold for the property that the random graph $G(n,p)$ is $(F,H)_v$-Ramsey. In this paper we consider the sister problem in the setting of \\emph{randomly perturbed graphs}. In particular, we determine how many random edges one needs to add to a dense graph to ensure that with high probability the resulting graph is $(F,H)_v$-Ramsey for all pairs $(F,H)$ that involve at ","authors_text":"Andrew Treglown, Patrick Morris, Shagnik Das","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-09-30T22:20:42Z","title":"Vertex Ramsey properties of randomly perturbed graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.00136","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":"sha256:68c381c479f278eaa0133334632e49812e278256cb6b52de02d66d8ac85c3a7d","target":"record","created_at":"2026-06-23T03:14:26Z","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":"0bb64293689d3423fdf9602abe05cd4aa5c0a6926524543a81f054c133b36572","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-09-30T22:20:42Z","title_canon_sha256":"8e2cfc6ad492a9fd454ee2c178e3dd5a2dbcca3024a10495944d3af6336da478"},"schema_version":"1.0","source":{"id":"1910.00136","kind":"arxiv","version":2}},"canonical_sha256":"6ac01f0e3b9035f935c86a3ff5e3df211ddaa36b9c170d25c63c070a3d20930f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ac01f0e3b9035f935c86a3ff5e3df211ddaa36b9c170d25c63c070a3d20930f","first_computed_at":"2026-06-23T03:14:26.580423Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T03:14:26.580423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sjgWbt9e0ciAuAL2OJPvufHWwJnAbodsv7tAqBwOuwTySCJTcayzFLU4Az5uuItRSo7doCPFb0Y/H9K6XTH3Bg==","signature_status":"signed_v1","signed_at":"2026-06-23T03:14:26.580929Z","signed_message":"canonical_sha256_bytes"},"source_id":"1910.00136","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68c381c479f278eaa0133334632e49812e278256cb6b52de02d66d8ac85c3a7d","sha256:7d653b3993928889b90071347a5e2cf0614cab9943a8af2661e6e9cf4744a735"],"state_sha256":"93d47be560f3881e7bec46bb3d61f1bf96d7756c2dfc0ffdee3d2afbb1769cb5"}