{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XAXRCEJDEDR33S4DKATBYAWPTM","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":"fa935865aa730f4bb81b73dcfe9920ec25294045c04955fe74c6a64ebcaf5279","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-25T19:17:09Z","title_canon_sha256":"983194c3b4e7b7bcead3375f623fcf253e7a07b731ab7ccf4b439bdd6db34ca9"},"schema_version":"1.0","source":{"id":"1310.7004","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7004","created_at":"2026-05-18T01:33:24Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7004v3","created_at":"2026-05-18T01:33:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7004","created_at":"2026-05-18T01:33:24Z"},{"alias_kind":"pith_short_12","alias_value":"XAXRCEJDEDR3","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XAXRCEJDEDR33S4D","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XAXRCEJD","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:b3f6d297152abad47a1dc11b7683f2eda0f9d64d4788744177972fc15aff5bbf","target":"graph","created_at":"2026-05-18T01:33:24Z","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":"We prove polynomial upper bounds of geometric Ramsey numbers of pathwidth-2 outerplanar triangulations in both convex and general cases. We also prove that the geometric Ramsey numbers of the ladder graph on $2n$ vertices are bounded by $O(n^{3})$ and $O(n^{10})$, in the convex and general case, respectively. We then apply similar methods to prove an $n^{O(\\log(n))}$ upper bound on the Ramsey number of a path with $n$ ordered vertices.","authors_text":"Josef Cibulka, Marek Kr\\v{c}\\'al, Pavel Valtr, Pu Gao, Tom\\'a\\v{s} Valla","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-25T19:17:09Z","title":"On the Geometric Ramsey Number of Outerplanar Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7004","kind":"arxiv","version":3},"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:f1c1e27f15e92350fba6bbdf14713721d7a27be4826aed9672f0a482e67e517d","target":"record","created_at":"2026-05-18T01:33:24Z","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":"fa935865aa730f4bb81b73dcfe9920ec25294045c04955fe74c6a64ebcaf5279","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-25T19:17:09Z","title_canon_sha256":"983194c3b4e7b7bcead3375f623fcf253e7a07b731ab7ccf4b439bdd6db34ca9"},"schema_version":"1.0","source":{"id":"1310.7004","kind":"arxiv","version":3}},"canonical_sha256":"b82f11112320e3bdcb8350261c02cf9b37becfac34bb8681f44ed9311a417449","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b82f11112320e3bdcb8350261c02cf9b37becfac34bb8681f44ed9311a417449","first_computed_at":"2026-05-18T01:33:24.563994Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:24.563994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Iq74U+Q3IC/QWVfcGkO7Zd1NGXS7In2f4kN+ZaSFXtMn8DnICWtQzYRcJcJk/Mdw8s6S+IWfyKiWpIcCFI8ZCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:24.564539Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.7004","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1c1e27f15e92350fba6bbdf14713721d7a27be4826aed9672f0a482e67e517d","sha256:b3f6d297152abad47a1dc11b7683f2eda0f9d64d4788744177972fc15aff5bbf"],"state_sha256":"aa5063cfe30a6ea2133b8ef33647e370cfba3c714737b6a9de29e38d6ac5bec5"}