{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:IVEYMR4ZZEU2CUHDVGLDLOZTI4","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":"ddee20785a9a43877419b5115ab5a3f2bc1ee0713c9458b5029526d6a9df7055","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-09-14T13:34:09Z","title_canon_sha256":"07bfbd3d74e9ebb64cfd53fb2e08abf8616319cdada12e6e4bc481d7c4c66a45"},"schema_version":"1.0","source":{"id":"1409.4054","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.4054","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"arxiv_version","alias_value":"1409.4054v2","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.4054","created_at":"2026-05-18T02:41:52Z"},{"alias_kind":"pith_short_12","alias_value":"IVEYMR4ZZEU2","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IVEYMR4ZZEU2CUHD","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IVEYMR4Z","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:e6393418b770d38c19eaf3a838114aa430e579bac3a354ca7ca1996ea50ac133","target":"graph","created_at":"2026-05-18T02:41:52Z","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 $(c_1,c_2,...,c_k)$-coloring of $G$ is a mapping $\\varphi:V(G)\\mapsto\\{1,2,...,k\\}$ such that for every $i,1 \\leq i \\leq k$, $G[V_i]$ has maximum degree at most $c_i$, where $G[V_i]$ denotes the subgraph induced by the vertices colored $i$. Borodin and Raspaud conjecture that every planar graph without $5$-cycles and intersecting triangles is $(0,0,0)$-colorable. We prove in this paper that such graphs are $(1,1,0)$-colorable.","authors_text":"Gexin Yu, Runrun Liu, Xiangwen Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-09-14T13:34:09Z","title":"Planar graphs without 5-cycles and intersecting triangles are $(1,1,0)$-colorable"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4054","kind":"arxiv","version":2},"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":"sha256:984c180c4a214da75408806a862888e5317b6f13463992bd5b195795b4bc237e","target":"record","created_at":"2026-05-18T02:41:52Z","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":"ddee20785a9a43877419b5115ab5a3f2bc1ee0713c9458b5029526d6a9df7055","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-09-14T13:34:09Z","title_canon_sha256":"07bfbd3d74e9ebb64cfd53fb2e08abf8616319cdada12e6e4bc481d7c4c66a45"},"schema_version":"1.0","source":{"id":"1409.4054","kind":"arxiv","version":2}},"canonical_sha256":"4549864799c929a150e3a99635bb33473cc1da181ec72dea0834fa20c7cb1243","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4549864799c929a150e3a99635bb33473cc1da181ec72dea0834fa20c7cb1243","first_computed_at":"2026-05-18T02:41:52.858132Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:52.858132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LFCTbPvbgJnZQspOCRhLmr2stv/HjMq+YjYAZZDqaFFfwF/+p/FGufDs68It9tZLE0F/cMyoC8G7e5aIKDekCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:52.858800Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.4054","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:984c180c4a214da75408806a862888e5317b6f13463992bd5b195795b4bc237e","sha256:e6393418b770d38c19eaf3a838114aa430e579bac3a354ca7ca1996ea50ac133"],"state_sha256":"fe7f22d1719ae81088cefee01433db68ed6bfacfadfb9bbc81bf9dbf75d92907"}