{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YYAG5LHENZFBASABCHLJZWFKKK","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":"17d32847ec599ae2822c75922853c501fe8da6266c9755e08e983eda73288ebf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-21T23:38:25Z","title_canon_sha256":"0ff467e34a8a092e21449f9b7bff6ceff50780c386b8507a24f16a48ba2d53ff"},"schema_version":"1.0","source":{"id":"1609.06778","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.06778","created_at":"2026-05-18T01:04:05Z"},{"alias_kind":"arxiv_version","alias_value":"1609.06778v1","created_at":"2026-05-18T01:04:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.06778","created_at":"2026-05-18T01:04:05Z"},{"alias_kind":"pith_short_12","alias_value":"YYAG5LHENZFB","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YYAG5LHENZFBASAB","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YYAG5LHE","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:ed6cb8d2940ccab56040b1942dac56e0f97d88d5aff4adf19c99b2104c99474d","target":"graph","created_at":"2026-05-18T01:04:05Z","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":"An orientation of a graph $G$ is proper if any two adjacent vertices have different indegrees. The proper orientation number $\\overrightarrow{\\chi}(G)$ of a graph $G$ is the minimum of the maximum indegree, taken over all proper orientations of $G$. In this paper, we show that a connected bipartite graph may be properly oriented even if we are only allowed to control the orientation of a specific set of edges, namely, the edges of a spanning tree and all the edges incident to one of its leaves. As a consequence of this result, we prove that 3-connected planar bipartite graphs have proper orien","authors_text":"Bojan Mohar, Cl\\'audia Linhares Sales, Fiachra Knox, Sebasti\\'an Gonz\\'alez Hermosillo de la Maza","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-21T23:38:25Z","title":"Proper Orientations of Planar Bipartite Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06778","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":"sha256:15d2dcef514d8f33667892561949f6551cb846fc9f6d957514bc62209480c240","target":"record","created_at":"2026-05-18T01:04:05Z","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":"17d32847ec599ae2822c75922853c501fe8da6266c9755e08e983eda73288ebf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-21T23:38:25Z","title_canon_sha256":"0ff467e34a8a092e21449f9b7bff6ceff50780c386b8507a24f16a48ba2d53ff"},"schema_version":"1.0","source":{"id":"1609.06778","kind":"arxiv","version":1}},"canonical_sha256":"c6006eace46e4a10480111d69cd8aa5285024330967efbd0aa2ee3aa30f8baeb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6006eace46e4a10480111d69cd8aa5285024330967efbd0aa2ee3aa30f8baeb","first_computed_at":"2026-05-18T01:04:05.117431Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:05.117431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6PI0VBFE7m1NqrikhmJYjLk2dS2msDzP6DeT2w3F2AY8jD2+9bNUQXo4IQCfW8/LWYA9zacAXNFTD5wZYd/DDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:05.117873Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.06778","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15d2dcef514d8f33667892561949f6551cb846fc9f6d957514bc62209480c240","sha256:ed6cb8d2940ccab56040b1942dac56e0f97d88d5aff4adf19c99b2104c99474d"],"state_sha256":"b878bca643c696c3c3fc3159fc28401b322f0de0c2ac7b2eca0555d5bec27f60"}