{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:23CTWRJSFBKBREY2K5YE7GPRJC","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":"8a9f63c8b9c8b0cd1c0c84f195bf21f28fa1451e438da4928421447b5421c3a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-19T17:34:10Z","title_canon_sha256":"a37ae02522992434bfda8a97409f5cb9b02b6d012d2d47e6d278284deda41eaf"},"schema_version":"1.0","source":{"id":"1906.08234","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.08234","created_at":"2026-07-04T23:58:57Z"},{"alias_kind":"arxiv_version","alias_value":"1906.08234v2","created_at":"2026-07-04T23:58:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.08234","created_at":"2026-07-04T23:58:57Z"},{"alias_kind":"pith_short_12","alias_value":"23CTWRJSFBKB","created_at":"2026-07-04T23:58:57Z"},{"alias_kind":"pith_short_16","alias_value":"23CTWRJSFBKBREY2","created_at":"2026-07-04T23:58:57Z"},{"alias_kind":"pith_short_8","alias_value":"23CTWRJS","created_at":"2026-07-04T23:58:57Z"}],"graph_snapshots":[{"event_id":"sha256:89cd90a58b74019c395a5a57279fcf9fa89a46af2c99e600725aa0277a37c652","target":"graph","created_at":"2026-07-04T23:58:57Z","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/1906.08234/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"An edge-ordered graph is a graph with a linear ordering of its edges. Two edge-ordered graphs are equivalent if their is an isomorphism between them preserving the ordering of the edges. The edge-ordered Ramsey number $r_{edge}(H; q)$ of an edge-ordered graph $H$ is the smallest $N$ such that there exists an edge-ordered graph $G$ on $N$ vertices such that, for every $q$-coloring of the edges of $G$, there is a monochromatic subgraph of $G$ equivalent to $H$. Recently, Balko and Vizer announced that $r_{edge}(H;q)$ exists. However, their proof uses the Graham-Rothschild theorem and consequentl","authors_text":"Jacob Fox, Ray Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-19T17:34:10Z","title":"On edge-ordered Ramsey numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.08234","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:cdce4b0b5e54eb83588705bdedbb55756575675808df686221f0c58cc364a065","target":"record","created_at":"2026-07-04T23:58:57Z","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":"8a9f63c8b9c8b0cd1c0c84f195bf21f28fa1451e438da4928421447b5421c3a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-06-19T17:34:10Z","title_canon_sha256":"a37ae02522992434bfda8a97409f5cb9b02b6d012d2d47e6d278284deda41eaf"},"schema_version":"1.0","source":{"id":"1906.08234","kind":"arxiv","version":2}},"canonical_sha256":"d6c53b4532285418931a57704f99f148a41c1948396dc1330978390d070a5f20","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6c53b4532285418931a57704f99f148a41c1948396dc1330978390d070a5f20","first_computed_at":"2026-07-04T23:58:57.907770Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:58:57.907770Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2RwjXQXnMbyaNmzNSBnc/YZv9GXKW+ChrKntAoGuXeyWUevnXwjP7wXh2N6H8o68XmKWi8ID362trpFii30aDg==","signature_status":"signed_v1","signed_at":"2026-07-04T23:58:57.908175Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.08234","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cdce4b0b5e54eb83588705bdedbb55756575675808df686221f0c58cc364a065","sha256:89cd90a58b74019c395a5a57279fcf9fa89a46af2c99e600725aa0277a37c652"],"state_sha256":"c0dfc4f320623680b964a56e8f31e31a945665851132d9cf3df97a14fcf135a9"}