{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:2DL5VIGKBH3WZX3VLME2YPJI3C","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":"d22e9d7e3496518aa6174de8ebf5896dc4711de7805ace3a32aa2a4f0733ccce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-08T04:10:29Z","title_canon_sha256":"6bd2c5bf5cc533b00fe907c30e865fe9a2daaf4ca9b60c33b16169eac26a95b1"},"schema_version":"1.0","source":{"id":"1210.2142","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.2142","created_at":"2026-05-18T01:10:39Z"},{"alias_kind":"arxiv_version","alias_value":"1210.2142v3","created_at":"2026-05-18T01:10:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.2142","created_at":"2026-05-18T01:10:39Z"},{"alias_kind":"pith_short_12","alias_value":"2DL5VIGKBH3W","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2DL5VIGKBH3WZX3V","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2DL5VIGK","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:dd24cc337a5d6d63dc82d4b716757c68e1ab4bdfb58009ec450b8a721613b9c2","target":"graph","created_at":"2026-05-18T01:10:39Z","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":"We prove that every simple connected graph with no $K_5$ minor admits a proper 4-coloring such that the neighborhood of each vertex $v$ having more than one neighbor is not monochromatic, unless the graph is isomorphic to the cycle of length 5. This generalizes the result by S.-J. Kim, S. J. Lee, and W.-J. Park on planar graphs.","authors_text":"Sang-il Oum, Sang June Lee, Younjin Kim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-08T04:10:29Z","title":"Dynamic coloring of graphs having no $K_5$ minor"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2142","kind":"arxiv","version":3},"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":"sha256:872debb40506a1f245b56e1a48743e14c20af0218d3df860c229616297b4b106","target":"record","created_at":"2026-05-18T01:10:39Z","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":"d22e9d7e3496518aa6174de8ebf5896dc4711de7805ace3a32aa2a4f0733ccce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-08T04:10:29Z","title_canon_sha256":"6bd2c5bf5cc533b00fe907c30e865fe9a2daaf4ca9b60c33b16169eac26a95b1"},"schema_version":"1.0","source":{"id":"1210.2142","kind":"arxiv","version":3}},"canonical_sha256":"d0d7daa0ca09f76cdf755b09ac3d28d8a7dc8fefa8fc87f7c98dbd60058e0a5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d0d7daa0ca09f76cdf755b09ac3d28d8a7dc8fefa8fc87f7c98dbd60058e0a5c","first_computed_at":"2026-05-18T01:10:39.020105Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:39.020105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E38qz6gk7XPda2xtk+kznpPVLYGHMbolOFE3offir+tHmrnPBXg85SERL4xkRbjDxfGbc4HiTy1IuidHYOWFAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:39.020488Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.2142","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:872debb40506a1f245b56e1a48743e14c20af0218d3df860c229616297b4b106","sha256:dd24cc337a5d6d63dc82d4b716757c68e1ab4bdfb58009ec450b8a721613b9c2"],"state_sha256":"a890edd354e15b652e5837496e2b912a51cc32df69cb005695c0b11e161defc5"}