{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:AQUY5ZKQAZL6YLLGZ2X3BKEMPX","short_pith_number":"pith:AQUY5ZKQ","schema_version":"1.0","canonical_sha256":"04298ee5500657ec2d66ceafb0a88c7dd20d0672924652d844744178b59b2dc7","source":{"kind":"arxiv","id":"1808.09963","version":1},"attestation_state":"computed","paper":{"title":"Improved Upper Bounds for Gallai-Ramsey Numbers of Odd Cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christian Bosse, Jingmei Zhang, Zi-Xia Song","submitted_at":"2018-08-29T22:41:16Z","abstract_excerpt":"A Gallai coloring of a complete graph is an edge-coloring such that no triangle has all its edges colored differently. A Gallai $k$-coloring is a Gallai coloring that uses $k$ colors. Given an integer $k\\ge1$ and a graph $H$, the Gallai-Ramsey number $GR_k(H)$ is the least positive integer $n$ such that every Gallai $k$-coloring of the complete graph $K_n$ contains a monochromatic copy of $H$. Gy\\'{a}rf\\'{a}s, S\\'{a}rk\\\"{o}zy, Seb\\H{o} and Selkow proved in 2010 that $GR_k (H) $ is exponential in $k$ if $H$ is not bipartite, linear in $k$ if $H$ is bipartite but not a star, and constant (does n"},"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":"1808.09963","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-08-29T22:41:16Z","cross_cats_sorted":[],"title_canon_sha256":"8f722131f83858270127d30c1352ee4d3764a9f15af5c4f72e04c7707a6427fc","abstract_canon_sha256":"182540f83927e2cb4cd36cbc6e2d2a8fa8cf4c133cf437591bd247d080eaac73"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:50.288130Z","signature_b64":"kA5kUlCqNaZYAMRJMsl2fdoTkUfnSk5fiLaXPdwSPX0WpVNEu0q2jyenTzu+AFbiEdGFrbS2PYvd3yrMgPt4Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04298ee5500657ec2d66ceafb0a88c7dd20d0672924652d844744178b59b2dc7","last_reissued_at":"2026-05-18T00:06:50.287207Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:50.287207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Improved Upper Bounds for Gallai-Ramsey Numbers of Odd Cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christian Bosse, Jingmei Zhang, Zi-Xia Song","submitted_at":"2018-08-29T22:41:16Z","abstract_excerpt":"A Gallai coloring of a complete graph is an edge-coloring such that no triangle has all its edges colored differently. A Gallai $k$-coloring is a Gallai coloring that uses $k$ colors. Given an integer $k\\ge1$ and a graph $H$, the Gallai-Ramsey number $GR_k(H)$ is the least positive integer $n$ such that every Gallai $k$-coloring of the complete graph $K_n$ contains a monochromatic copy of $H$. Gy\\'{a}rf\\'{a}s, S\\'{a}rk\\\"{o}zy, Seb\\H{o} and Selkow proved in 2010 that $GR_k (H) $ is exponential in $k$ if $H$ is not bipartite, linear in $k$ if $H$ is bipartite but not a star, and constant (does n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.09963","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":"1808.09963","created_at":"2026-05-18T00:06:50.287380+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.09963v1","created_at":"2026-05-18T00:06:50.287380+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.09963","created_at":"2026-05-18T00:06:50.287380+00:00"},{"alias_kind":"pith_short_12","alias_value":"AQUY5ZKQAZL6","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_16","alias_value":"AQUY5ZKQAZL6YLLG","created_at":"2026-05-18T12:32:13.499390+00:00"},{"alias_kind":"pith_short_8","alias_value":"AQUY5ZKQ","created_at":"2026-05-18T12:32:13.499390+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/AQUY5ZKQAZL6YLLGZ2X3BKEMPX","json":"https://pith.science/pith/AQUY5ZKQAZL6YLLGZ2X3BKEMPX.json","graph_json":"https://pith.science/api/pith-number/AQUY5ZKQAZL6YLLGZ2X3BKEMPX/graph.json","events_json":"https://pith.science/api/pith-number/AQUY5ZKQAZL6YLLGZ2X3BKEMPX/events.json","paper":"https://pith.science/paper/AQUY5ZKQ"},"agent_actions":{"view_html":"https://pith.science/pith/AQUY5ZKQAZL6YLLGZ2X3BKEMPX","download_json":"https://pith.science/pith/AQUY5ZKQAZL6YLLGZ2X3BKEMPX.json","view_paper":"https://pith.science/paper/AQUY5ZKQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.09963&json=true","fetch_graph":"https://pith.science/api/pith-number/AQUY5ZKQAZL6YLLGZ2X3BKEMPX/graph.json","fetch_events":"https://pith.science/api/pith-number/AQUY5ZKQAZL6YLLGZ2X3BKEMPX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AQUY5ZKQAZL6YLLGZ2X3BKEMPX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AQUY5ZKQAZL6YLLGZ2X3BKEMPX/action/storage_attestation","attest_author":"https://pith.science/pith/AQUY5ZKQAZL6YLLGZ2X3BKEMPX/action/author_attestation","sign_citation":"https://pith.science/pith/AQUY5ZKQAZL6YLLGZ2X3BKEMPX/action/citation_signature","submit_replication":"https://pith.science/pith/AQUY5ZKQAZL6YLLGZ2X3BKEMPX/action/replication_record"}},"created_at":"2026-05-18T00:06:50.287380+00:00","updated_at":"2026-05-18T00:06:50.287380+00:00"}