{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:BRJJOQTZNUL76STCTWEA6XERBM","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":"529c0f1e7cc1dd7cb6029ba48fe3c81088f18441d0ea1878131bb2b4ff411ca5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-01T04:29:37Z","title_canon_sha256":"c627f08b7594cb6a976f0b469d288c883276746e422ba05be1c62fbf8bbb0e40"},"schema_version":"1.0","source":{"id":"1412.0344","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.0344","created_at":"2026-05-18T02:32:28Z"},{"alias_kind":"arxiv_version","alias_value":"1412.0344v1","created_at":"2026-05-18T02:32:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0344","created_at":"2026-05-18T02:32:28Z"},{"alias_kind":"pith_short_12","alias_value":"BRJJOQTZNUL7","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BRJJOQTZNUL76STC","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BRJJOQTZ","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:e00e1fc58d801a666335a610496e55ad89ca6a523320d4896d9297e3af83d649","target":"graph","created_at":"2026-05-18T02:32:28Z","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":"A graph is $(d_1, ..., d_r)$-colorable if its vertex set can be partitioned into $r$ sets $V_1, ..., V_r$ so that the maximum degree of the graph induced by $V_i$ is at most $d_i$ for each $i\\in \\{1, ..., r\\}$. For a given pair $(g, d_1)$, the question of determining the minimum $d_2=d_2(g; d_1)$ such that planar graphs with girth at least $g$ are $(d_1, d_2)$-colorable has attracted much interest. The finiteness of $d_2(g; d_1)$ was known for all cases except when $(g, d_1)=(5, 1)$. Montassier and Ochem explicitly asked if $d_2(5; 1)$ is finite. We answer this question in the affirmative with","authors_text":"Geewon Suh, Hojin Choi, Ilkyoo Choi, Jisu Jeong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-01T04:29:37Z","title":"$(1, k)$-coloring of graphs with girth at least $5$ on a surface"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0344","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:d9f7c02e2b45c6f2c4af56ca3a385ca69cf8506bc80c16c9ad2de117d6f93780","target":"record","created_at":"2026-05-18T02:32:28Z","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":"529c0f1e7cc1dd7cb6029ba48fe3c81088f18441d0ea1878131bb2b4ff411ca5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-01T04:29:37Z","title_canon_sha256":"c627f08b7594cb6a976f0b469d288c883276746e422ba05be1c62fbf8bbb0e40"},"schema_version":"1.0","source":{"id":"1412.0344","kind":"arxiv","version":1}},"canonical_sha256":"0c529742796d17ff4a629d880f5c910b0b540a558333c30c8426aa9a33ae264c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c529742796d17ff4a629d880f5c910b0b540a558333c30c8426aa9a33ae264c","first_computed_at":"2026-05-18T02:32:28.042132Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:28.042132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cWmZCSSEQddHBymctB50jqjrKNSv8Ik6dhesqiLdiVu29S+pOuqXbm+T8Yo2iJgm6d/oQhSgwMdmyQwqoquJAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:28.042545Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.0344","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9f7c02e2b45c6f2c4af56ca3a385ca69cf8506bc80c16c9ad2de117d6f93780","sha256:e00e1fc58d801a666335a610496e55ad89ca6a523320d4896d9297e3af83d649"],"state_sha256":"44fbdf1067526814b1a71b9066de493ccfdc570712697e44fed6e228ce83e39e"}