{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:LOTSAHNE3UNQV6P364BOTCPFVL","short_pith_number":"pith:LOTSAHNE","schema_version":"1.0","canonical_sha256":"5ba7201da4dd1b0af9fbf702e989e5aaf9c58219b0039a237bbafd2d86fd7554","source":{"kind":"arxiv","id":"1808.04025","version":1},"attestation_state":"computed","paper":{"title":"Off-diagonal ordered Ramsey numbers of matchings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dhruv Rohatgi","submitted_at":"2018-08-13T00:00:52Z","abstract_excerpt":"For ordered graphs $G$ and $H$, the ordered Ramsey number $r_<(G,H)$ is the smallest $n$ such that every red/blue edge coloring of the complete graph on vertices $\\{1,\\dots,n\\}$ contains either a blue copy of $G$ or a red copy of $H$, where the embedding must preserve the relative order of vertices. One number of interest, first studied by Conlon, Fox, Lee, and Sudakov, is the \"off-diagonal\" ordered Ramsey number $r_<(M, K_3)$, where $M$ is an ordered matching on $n$ vertices. In particular, Conlon et al. asked what asymptotic bounds (in $n$) can be obtained for $\\max r_<(M, K_3)$, where the m"},"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":"1808.04025","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-13T00:00:52Z","cross_cats_sorted":[],"title_canon_sha256":"b4e10cfe2971b2a78c30a79b31ad95c418149564a9373e3f9625e299e0c39e4e","abstract_canon_sha256":"20cabbff5fce7c60723916a79586ddab687c93c79c7dc79a9bf09b37b919e440"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:19.059791Z","signature_b64":"n0Y4n276gwk/yFxfV/Bbz5i9FQmYsIcL4EdEybs6tNNqU6tpK5Uaiw3xBHNMWDFB+iRbpGTPx1ZpeZDrZOMFDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ba7201da4dd1b0af9fbf702e989e5aaf9c58219b0039a237bbafd2d86fd7554","last_reissued_at":"2026-05-18T00:08:19.059264Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:19.059264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Off-diagonal ordered Ramsey numbers of matchings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dhruv Rohatgi","submitted_at":"2018-08-13T00:00:52Z","abstract_excerpt":"For ordered graphs $G$ and $H$, the ordered Ramsey number $r_<(G,H)$ is the smallest $n$ such that every red/blue edge coloring of the complete graph on vertices $\\{1,\\dots,n\\}$ contains either a blue copy of $G$ or a red copy of $H$, where the embedding must preserve the relative order of vertices. One number of interest, first studied by Conlon, Fox, Lee, and Sudakov, is the \"off-diagonal\" ordered Ramsey number $r_<(M, K_3)$, where $M$ is an ordered matching on $n$ vertices. In particular, Conlon et al. asked what asymptotic bounds (in $n$) can be obtained for $\\max r_<(M, K_3)$, where the m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.04025","kind":"arxiv","version":1},"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":"1808.04025","created_at":"2026-05-18T00:08:19.059331+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.04025v1","created_at":"2026-05-18T00:08:19.059331+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.04025","created_at":"2026-05-18T00:08:19.059331+00:00"},{"alias_kind":"pith_short_12","alias_value":"LOTSAHNE3UNQ","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_16","alias_value":"LOTSAHNE3UNQV6P3","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_8","alias_value":"LOTSAHNE","created_at":"2026-05-18T12:32:37.024351+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/LOTSAHNE3UNQV6P364BOTCPFVL","json":"https://pith.science/pith/LOTSAHNE3UNQV6P364BOTCPFVL.json","graph_json":"https://pith.science/api/pith-number/LOTSAHNE3UNQV6P364BOTCPFVL/graph.json","events_json":"https://pith.science/api/pith-number/LOTSAHNE3UNQV6P364BOTCPFVL/events.json","paper":"https://pith.science/paper/LOTSAHNE"},"agent_actions":{"view_html":"https://pith.science/pith/LOTSAHNE3UNQV6P364BOTCPFVL","download_json":"https://pith.science/pith/LOTSAHNE3UNQV6P364BOTCPFVL.json","view_paper":"https://pith.science/paper/LOTSAHNE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.04025&json=true","fetch_graph":"https://pith.science/api/pith-number/LOTSAHNE3UNQV6P364BOTCPFVL/graph.json","fetch_events":"https://pith.science/api/pith-number/LOTSAHNE3UNQV6P364BOTCPFVL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LOTSAHNE3UNQV6P364BOTCPFVL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LOTSAHNE3UNQV6P364BOTCPFVL/action/storage_attestation","attest_author":"https://pith.science/pith/LOTSAHNE3UNQV6P364BOTCPFVL/action/author_attestation","sign_citation":"https://pith.science/pith/LOTSAHNE3UNQV6P364BOTCPFVL/action/citation_signature","submit_replication":"https://pith.science/pith/LOTSAHNE3UNQV6P364BOTCPFVL/action/replication_record"}},"created_at":"2026-05-18T00:08:19.059331+00:00","updated_at":"2026-05-18T00:08:19.059331+00:00"}