{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KLH5M7NEQLF5OSB37HB5B7Y46C","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":"390f962f41911fdd6dc14ee9cb2cfbb3b92a0db39ea6897df71401d0a736a461","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-26T08:28:31Z","title_canon_sha256":"31a26235bf589edb1111c495870d61cacc4264f81e03f8fd20288df37b05b900"},"schema_version":"1.0","source":{"id":"1601.06920","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.06920","created_at":"2026-05-18T01:21:59Z"},{"alias_kind":"arxiv_version","alias_value":"1601.06920v1","created_at":"2026-05-18T01:21:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.06920","created_at":"2026-05-18T01:21:59Z"},{"alias_kind":"pith_short_12","alias_value":"KLH5M7NEQLF5","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KLH5M7NEQLF5OSB3","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KLH5M7NE","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:e12401791a87504f051dfb06afe095d86cc8847f581b79d9631f259f0e926cd0","target":"graph","created_at":"2026-05-18T01:21:59Z","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":"This paper investigates vertex colorings of graphs such that some rainbow subgraph~$R$ and some monochromatic subgraph $M$ are forbidden. Previous work focussed on the case that $R=M$. Here we consider the more general case, especially the case that $M=K_2$.","authors_text":"Honghai Xu, Wayne Goddard","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-26T08:28:31Z","title":"Vertex Colorings without Rainbow or Monochromatic Subgraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.06920","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":"sha256:589fc2aca22548c94f0374335efe23cb6c388a8a9d6dc647bcf9e718161864f0","target":"record","created_at":"2026-05-18T01:21:59Z","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":"390f962f41911fdd6dc14ee9cb2cfbb3b92a0db39ea6897df71401d0a736a461","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-26T08:28:31Z","title_canon_sha256":"31a26235bf589edb1111c495870d61cacc4264f81e03f8fd20288df37b05b900"},"schema_version":"1.0","source":{"id":"1601.06920","kind":"arxiv","version":1}},"canonical_sha256":"52cfd67da482cbd7483bf9c3d0ff1cf095cbdf4818dfb7081b6f382e14538f77","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"52cfd67da482cbd7483bf9c3d0ff1cf095cbdf4818dfb7081b6f382e14538f77","first_computed_at":"2026-05-18T01:21:59.525922Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:59.525922Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u3+Z5K9IXxFfFQcob34J4X4XRMJk+x7C49+bxdVZq6lrFW0gSFzTUm4tnUpgwO3Oufei5mo9jKcBGF80bB7xAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:59.526637Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.06920","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:589fc2aca22548c94f0374335efe23cb6c388a8a9d6dc647bcf9e718161864f0","sha256:e12401791a87504f051dfb06afe095d86cc8847f581b79d9631f259f0e926cd0"],"state_sha256":"82f4ad9278dc8614bb25af3df71703eca6c76794f40aba81702dfce3ed41ca91"}