{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:BFEUCWOYR3GWC7DZDW67ZAWNSI","short_pith_number":"pith:BFEUCWOY","canonical_record":{"source":{"id":"1905.12414","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2019-05-28T13:18:45Z","cross_cats_sorted":[],"title_canon_sha256":"002ce70b610e922e04eeacbef3521604ea1e4a13bb139cc3f7a685780f93eb47","abstract_canon_sha256":"6603a27b6ebc9fbac8543420edcf0bf42c87a13eac76d26d53f048ac9f1f63e1"},"schema_version":"1.0"},"canonical_sha256":"09494159d88ecd617c791dbdfc82cd920b4a0151c7ca6d32ec8c97e4f4c15860","source":{"kind":"arxiv","id":"1905.12414","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.12414","created_at":"2026-05-17T23:44:44Z"},{"alias_kind":"arxiv_version","alias_value":"1905.12414v1","created_at":"2026-05-17T23:44:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.12414","created_at":"2026-05-17T23:44:44Z"},{"alias_kind":"pith_short_12","alias_value":"BFEUCWOYR3GW","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"BFEUCWOYR3GWC7DZ","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"BFEUCWOY","created_at":"2026-05-18T12:33:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:BFEUCWOYR3GWC7DZDW67ZAWNSI","target":"record","payload":{"canonical_record":{"source":{"id":"1905.12414","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2019-05-28T13:18:45Z","cross_cats_sorted":[],"title_canon_sha256":"002ce70b610e922e04eeacbef3521604ea1e4a13bb139cc3f7a685780f93eb47","abstract_canon_sha256":"6603a27b6ebc9fbac8543420edcf0bf42c87a13eac76d26d53f048ac9f1f63e1"},"schema_version":"1.0"},"canonical_sha256":"09494159d88ecd617c791dbdfc82cd920b4a0151c7ca6d32ec8c97e4f4c15860","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:44.409503Z","signature_b64":"YFsDCTpBoLz32HjVGzFNi4aaKxahwdcZeS1TcwwPw6etgvkhyJFnIMyVBTl522tZbkSVhC3cvs7pSft3LSz0AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"09494159d88ecd617c791dbdfc82cd920b4a0151c7ca6d32ec8c97e4f4c15860","last_reissued_at":"2026-05-17T23:44:44.409054Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:44.409054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.12414","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:44:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IAEznMAi2Z0pxMRvGbBafj+tMIzOX03TkTB8OxGP1nYzpAK/VFdDCfLXO2L6qI22ib1d/BlKz6+YouG6izpvCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T05:41:43.878920Z"},"content_sha256":"69b9e6a4285304b418c03ebdd82323cc593b6c4cafad9cf334ec012a03ab8f4b","schema_version":"1.0","event_id":"sha256:69b9e6a4285304b418c03ebdd82323cc593b6c4cafad9cf334ec012a03ab8f4b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:BFEUCWOYR3GWC7DZDW67ZAWNSI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ramsey and Gallai-Ramsey number for wheels","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Colton Magnant, Ingo Schiermeyer, Yaping Mao, Zhao Wang","submitted_at":"2019-05-28T13:18:45Z","abstract_excerpt":"Given a graph $G$ and a positive integer $k$, define the \\emph{Gallai-Ramsey number} to be the minimum number of vertices $n$ such that any $k$-edge coloring of $K_n$ contains either a rainbow (all different colored) triangle or a monochromatic copy of $G$. Much like graph Ramsey numbers, Gallai-Ramsey numbers have gained a reputation as being very difficult to compute in general. As yet, still only precious few sharp results are known. In this paper, we obtain bounds on the Gallai-Ramsey number for wheels and the exact value for the wheel on $5$ vertices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.12414","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:44:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I7Cgh9DBXV3K7L2xv070HWWryO4MPncKnSEhEKal9v/jNMJDkTv5bXY6NIf0guM2jXmIHbsaJYJ/oJETwdiOAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T05:41:43.879589Z"},"content_sha256":"9628334ee8c9f6bfc3fbfb6168d49031547c65c2120dd14a1be7748c848d47e7","schema_version":"1.0","event_id":"sha256:9628334ee8c9f6bfc3fbfb6168d49031547c65c2120dd14a1be7748c848d47e7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BFEUCWOYR3GWC7DZDW67ZAWNSI/bundle.json","state_url":"https://pith.science/pith/BFEUCWOYR3GWC7DZDW67ZAWNSI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BFEUCWOYR3GWC7DZDW67ZAWNSI/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T05:41:43Z","links":{"resolver":"https://pith.science/pith/BFEUCWOYR3GWC7DZDW67ZAWNSI","bundle":"https://pith.science/pith/BFEUCWOYR3GWC7DZDW67ZAWNSI/bundle.json","state":"https://pith.science/pith/BFEUCWOYR3GWC7DZDW67ZAWNSI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BFEUCWOYR3GWC7DZDW67ZAWNSI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:BFEUCWOYR3GWC7DZDW67ZAWNSI","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":"6603a27b6ebc9fbac8543420edcf0bf42c87a13eac76d26d53f048ac9f1f63e1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2019-05-28T13:18:45Z","title_canon_sha256":"002ce70b610e922e04eeacbef3521604ea1e4a13bb139cc3f7a685780f93eb47"},"schema_version":"1.0","source":{"id":"1905.12414","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.12414","created_at":"2026-05-17T23:44:44Z"},{"alias_kind":"arxiv_version","alias_value":"1905.12414v1","created_at":"2026-05-17T23:44:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.12414","created_at":"2026-05-17T23:44:44Z"},{"alias_kind":"pith_short_12","alias_value":"BFEUCWOYR3GW","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"BFEUCWOYR3GWC7DZ","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"BFEUCWOY","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:9628334ee8c9f6bfc3fbfb6168d49031547c65c2120dd14a1be7748c848d47e7","target":"graph","created_at":"2026-05-17T23:44:44Z","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":"Given a graph $G$ and a positive integer $k$, define the \\emph{Gallai-Ramsey number} to be the minimum number of vertices $n$ such that any $k$-edge coloring of $K_n$ contains either a rainbow (all different colored) triangle or a monochromatic copy of $G$. Much like graph Ramsey numbers, Gallai-Ramsey numbers have gained a reputation as being very difficult to compute in general. As yet, still only precious few sharp results are known. In this paper, we obtain bounds on the Gallai-Ramsey number for wheels and the exact value for the wheel on $5$ vertices.","authors_text":"Colton Magnant, Ingo Schiermeyer, Yaping Mao, Zhao Wang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2019-05-28T13:18:45Z","title":"Ramsey and Gallai-Ramsey number for wheels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.12414","kind":"arxiv","version":1},"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":"sha256:69b9e6a4285304b418c03ebdd82323cc593b6c4cafad9cf334ec012a03ab8f4b","target":"record","created_at":"2026-05-17T23:44:44Z","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":"6603a27b6ebc9fbac8543420edcf0bf42c87a13eac76d26d53f048ac9f1f63e1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2019-05-28T13:18:45Z","title_canon_sha256":"002ce70b610e922e04eeacbef3521604ea1e4a13bb139cc3f7a685780f93eb47"},"schema_version":"1.0","source":{"id":"1905.12414","kind":"arxiv","version":1}},"canonical_sha256":"09494159d88ecd617c791dbdfc82cd920b4a0151c7ca6d32ec8c97e4f4c15860","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"09494159d88ecd617c791dbdfc82cd920b4a0151c7ca6d32ec8c97e4f4c15860","first_computed_at":"2026-05-17T23:44:44.409054Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:44.409054Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YFsDCTpBoLz32HjVGzFNi4aaKxahwdcZeS1TcwwPw6etgvkhyJFnIMyVBTl522tZbkSVhC3cvs7pSft3LSz0AQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:44.409503Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.12414","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69b9e6a4285304b418c03ebdd82323cc593b6c4cafad9cf334ec012a03ab8f4b","sha256:9628334ee8c9f6bfc3fbfb6168d49031547c65c2120dd14a1be7748c848d47e7"],"state_sha256":"e06c33d7087b511e3e84848ec3abd24abe10891e086d8b2b4772a178af44a961"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X7P71lFzBLDkuhENNXQ3WdYULfQ/lvnIoEGa6tD4NPzwHqh6tQBLFLYCrZdVUSpTL4QnEWu+x+mICvA8HaMADQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T05:41:43.882924Z","bundle_sha256":"ee5ebf1a98b89196ad232749e4317f809801fd0ddcc4fd5715d480c8bf7ed2ca"}}