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The Erd{\\H o}s-Hajnal conjecture for rainbow triangles. J. Combin. Theory Ser. B, 111:75-125, 2015.] conjectured the value of the Gallai Ramsey numbers for complete graphs. Recently, this conjecture has been verified for the first open case, when $H = K_{4}$.\n  In this paper we attack the"},"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":"1901.03622","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-01-11T15:51:06Z","cross_cats_sorted":[],"title_canon_sha256":"89bff8cad70fcca12feff0bca1e558bdcef8a6cdc41527817c7de42847e16ee4","abstract_canon_sha256":"3a0356dd98c1665de776b3b972bd88312482a0a1b144466a10b1252f16c6bd4b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:30.829728Z","signature_b64":"dwvwhOT67F5EKtaFq4TVAeXHeBHOOPvz3akIMwaBQiZ1Xhea4mMjDxvCYn0XqdjESNHyGAnKD7WJkCtTIxTYBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b1905902fe4c68db8aedcaa3e5b5d372c7dc79cca4a68b63dce72d790222a7f","last_reissued_at":"2026-05-17T23:56:30.829361Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:30.829361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gallai-Ramsey number for $K_{5}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Colton Magnant, Ingo Schiermeyer","submitted_at":"2019-01-11T15:51:06Z","abstract_excerpt":"Given a graph $H$, the $k$-colored Gallai Ramsey number $gr_{k}(K_{3} : H)$ is defined to be the minimum integer $n$ such that every $k$-coloring of the edges of the complete graph on $n$ vertices contains either a rainbow triangle or a monochromatic copy of $H$. Fox et al. [J. Fox, A. Grinshpun, and J. Pach. The Erd{\\H o}s-Hajnal conjecture for rainbow triangles. J. Combin. Theory Ser. B, 111:75-125, 2015.] conjectured the value of the Gallai Ramsey numbers for complete graphs. Recently, this conjecture has been verified for the first open case, when $H = K_{4}$.\n  In this paper we attack the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.03622","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":"1901.03622","created_at":"2026-05-17T23:56:30.829417+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.03622v1","created_at":"2026-05-17T23:56:30.829417+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.03622","created_at":"2026-05-17T23:56:30.829417+00:00"},{"alias_kind":"pith_short_12","alias_value":"LMMQLEBP4TDI","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_16","alias_value":"LMMQLEBP4TDI3OFO","created_at":"2026-05-18T12:33:21.387695+00:00"},{"alias_kind":"pith_short_8","alias_value":"LMMQLEBP","created_at":"2026-05-18T12:33:21.387695+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/LMMQLEBP4TDI3OFO3SVD4W25G4","json":"https://pith.science/pith/LMMQLEBP4TDI3OFO3SVD4W25G4.json","graph_json":"https://pith.science/api/pith-number/LMMQLEBP4TDI3OFO3SVD4W25G4/graph.json","events_json":"https://pith.science/api/pith-number/LMMQLEBP4TDI3OFO3SVD4W25G4/events.json","paper":"https://pith.science/paper/LMMQLEBP"},"agent_actions":{"view_html":"https://pith.science/pith/LMMQLEBP4TDI3OFO3SVD4W25G4","download_json":"https://pith.science/pith/LMMQLEBP4TDI3OFO3SVD4W25G4.json","view_paper":"https://pith.science/paper/LMMQLEBP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.03622&json=true","fetch_graph":"https://pith.science/api/pith-number/LMMQLEBP4TDI3OFO3SVD4W25G4/graph.json","fetch_events":"https://pith.science/api/pith-number/LMMQLEBP4TDI3OFO3SVD4W25G4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LMMQLEBP4TDI3OFO3SVD4W25G4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LMMQLEBP4TDI3OFO3SVD4W25G4/action/storage_attestation","attest_author":"https://pith.science/pith/LMMQLEBP4TDI3OFO3SVD4W25G4/action/author_attestation","sign_citation":"https://pith.science/pith/LMMQLEBP4TDI3OFO3SVD4W25G4/action/citation_signature","submit_replication":"https://pith.science/pith/LMMQLEBP4TDI3OFO3SVD4W25G4/action/replication_record"}},"created_at":"2026-05-17T23:56:30.829417+00:00","updated_at":"2026-05-17T23:56:30.829417+00:00"}