{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:32UVQ5OFYYY3ORN2D3PZ5BA4ZI","short_pith_number":"pith:32UVQ5OF","schema_version":"1.0","canonical_sha256":"dea95875c5c631b745ba1edf9e841cca2e480f418b744101e4590e59d088e7f5","source":{"kind":"arxiv","id":"1010.0133","version":1},"attestation_state":"computed","paper":{"title":"Local chromatic number of quadrangulations of surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CO","authors_text":"Bojan Mohar, G\\'abor Simonyi, G\\'abor Tardos","submitted_at":"2010-10-01T12:02:23Z","abstract_excerpt":"The local chromatic number of a graph was introduced by Erd\\H{o}s et al. [4]. In [17] a connection to topological properties of (a box complex of) the graph was established and in [18] it was shown that if a graph is strongly topologically 4-chromatic then its local chromatic number is at least four. As a consequence one obtains a generalization of the following theorem of Youngs: If a quadrangulation of the projective plane is not bipartite it has chromatic number four. The generalization states that in this case the local chromatic number is also four. Both papers [1] and [13] generalize You"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1010.0133","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-10-01T12:02:23Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"cb407106ad10c1faac5fc89d33be5f02524972ec12b596938cba09bd10da2192","abstract_canon_sha256":"79cc900962ed67efebec9133448b0810512eeaf07a6fd29375f111ae902bd223"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:00.226172Z","signature_b64":"/USeAZFo5aOBI1EK05XGyuFhFOrHJ80HpCpE5RPd0dGILh1AjMl0+k4gRj56ka9HocjMwGyO5wtC9zWRCQp+Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dea95875c5c631b745ba1edf9e841cca2e480f418b744101e4590e59d088e7f5","last_reissued_at":"2026-05-18T04:40:00.225768Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:00.225768Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local chromatic number of quadrangulations of surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CO","authors_text":"Bojan Mohar, G\\'abor Simonyi, G\\'abor Tardos","submitted_at":"2010-10-01T12:02:23Z","abstract_excerpt":"The local chromatic number of a graph was introduced by Erd\\H{o}s et al. [4]. In [17] a connection to topological properties of (a box complex of) the graph was established and in [18] it was shown that if a graph is strongly topologically 4-chromatic then its local chromatic number is at least four. As a consequence one obtains a generalization of the following theorem of Youngs: If a quadrangulation of the projective plane is not bipartite it has chromatic number four. The generalization states that in this case the local chromatic number is also four. Both papers [1] and [13] generalize You"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0133","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1010.0133","created_at":"2026-05-18T04:40:00.225829+00:00"},{"alias_kind":"arxiv_version","alias_value":"1010.0133v1","created_at":"2026-05-18T04:40:00.225829+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.0133","created_at":"2026-05-18T04:40:00.225829+00:00"},{"alias_kind":"pith_short_12","alias_value":"32UVQ5OFYYY3","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_16","alias_value":"32UVQ5OFYYY3ORN2","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_8","alias_value":"32UVQ5OF","created_at":"2026-05-18T12:26:03.138858+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/32UVQ5OFYYY3ORN2D3PZ5BA4ZI","json":"https://pith.science/pith/32UVQ5OFYYY3ORN2D3PZ5BA4ZI.json","graph_json":"https://pith.science/api/pith-number/32UVQ5OFYYY3ORN2D3PZ5BA4ZI/graph.json","events_json":"https://pith.science/api/pith-number/32UVQ5OFYYY3ORN2D3PZ5BA4ZI/events.json","paper":"https://pith.science/paper/32UVQ5OF"},"agent_actions":{"view_html":"https://pith.science/pith/32UVQ5OFYYY3ORN2D3PZ5BA4ZI","download_json":"https://pith.science/pith/32UVQ5OFYYY3ORN2D3PZ5BA4ZI.json","view_paper":"https://pith.science/paper/32UVQ5OF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1010.0133&json=true","fetch_graph":"https://pith.science/api/pith-number/32UVQ5OFYYY3ORN2D3PZ5BA4ZI/graph.json","fetch_events":"https://pith.science/api/pith-number/32UVQ5OFYYY3ORN2D3PZ5BA4ZI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/32UVQ5OFYYY3ORN2D3PZ5BA4ZI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/32UVQ5OFYYY3ORN2D3PZ5BA4ZI/action/storage_attestation","attest_author":"https://pith.science/pith/32UVQ5OFYYY3ORN2D3PZ5BA4ZI/action/author_attestation","sign_citation":"https://pith.science/pith/32UVQ5OFYYY3ORN2D3PZ5BA4ZI/action/citation_signature","submit_replication":"https://pith.science/pith/32UVQ5OFYYY3ORN2D3PZ5BA4ZI/action/replication_record"}},"created_at":"2026-05-18T04:40:00.225829+00:00","updated_at":"2026-05-18T04:40:00.225829+00:00"}