{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:KDYTQ4XXWSBVHBCQT7U2T5D5PX","short_pith_number":"pith:KDYTQ4XX","schema_version":"1.0","canonical_sha256":"50f13872f7b4835384509fe9a9f47d7ddf9e42db578ff252993e1a4ca8aa476e","source":{"kind":"arxiv","id":"1502.04561","version":2},"attestation_state":"computed","paper":{"title":"Choosability in signed planar graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Eckhard Steffen, Ligang Jin, Yingli Kang","submitted_at":"2015-02-16T14:54:19Z","abstract_excerpt":"This paper studies the choosability of signed planar graphs. We prove that every signed planar graph is 5-choosable and that there is a signed planar graph which is not 4-choosable while the unsigned graph is 4-choosable. For each $k \\in \\{3,4,5,6\\}$, every signed planar graph without circuits of length $k$ is 4-choosable. Furthermore, every signed planar graph without circuits of length 3 and of length 4 is 3-choosable. We construct a signed planar graph with girth 4 which is not 3-choosable but the unsigned graph is 3-choosable."},"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":"1502.04561","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-02-16T14:54:19Z","cross_cats_sorted":[],"title_canon_sha256":"0960660d40d38c89539598e95978992f7597f372ad5511644d1f1e550f134690","abstract_canon_sha256":"cc3a4582f3f08d1b37581a87aec2cfd471b54e8a53583da71d3dc227606d0126"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:07.160410Z","signature_b64":"64mtO731G3l4wQsKPwCoh9PnYMeB2ZiVsfaOVYZXjJhXm/pSCvSHzQma8zId3ZMb3Cj6CC4YH/RkzAtYRcIQCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50f13872f7b4835384509fe9a9f47d7ddf9e42db578ff252993e1a4ca8aa476e","last_reissued_at":"2026-05-18T00:50:07.159719Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:07.159719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Choosability in signed planar graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Eckhard Steffen, Ligang Jin, Yingli Kang","submitted_at":"2015-02-16T14:54:19Z","abstract_excerpt":"This paper studies the choosability of signed planar graphs. We prove that every signed planar graph is 5-choosable and that there is a signed planar graph which is not 4-choosable while the unsigned graph is 4-choosable. For each $k \\in \\{3,4,5,6\\}$, every signed planar graph without circuits of length $k$ is 4-choosable. Furthermore, every signed planar graph without circuits of length 3 and of length 4 is 3-choosable. We construct a signed planar graph with girth 4 which is not 3-choosable but the unsigned graph is 3-choosable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04561","kind":"arxiv","version":2},"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":"1502.04561","created_at":"2026-05-18T00:50:07.159830+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.04561v2","created_at":"2026-05-18T00:50:07.159830+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04561","created_at":"2026-05-18T00:50:07.159830+00:00"},{"alias_kind":"pith_short_12","alias_value":"KDYTQ4XXWSBV","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_16","alias_value":"KDYTQ4XXWSBVHBCQ","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_8","alias_value":"KDYTQ4XX","created_at":"2026-05-18T12:29:27.538025+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/KDYTQ4XXWSBVHBCQT7U2T5D5PX","json":"https://pith.science/pith/KDYTQ4XXWSBVHBCQT7U2T5D5PX.json","graph_json":"https://pith.science/api/pith-number/KDYTQ4XXWSBVHBCQT7U2T5D5PX/graph.json","events_json":"https://pith.science/api/pith-number/KDYTQ4XXWSBVHBCQT7U2T5D5PX/events.json","paper":"https://pith.science/paper/KDYTQ4XX"},"agent_actions":{"view_html":"https://pith.science/pith/KDYTQ4XXWSBVHBCQT7U2T5D5PX","download_json":"https://pith.science/pith/KDYTQ4XXWSBVHBCQT7U2T5D5PX.json","view_paper":"https://pith.science/paper/KDYTQ4XX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.04561&json=true","fetch_graph":"https://pith.science/api/pith-number/KDYTQ4XXWSBVHBCQT7U2T5D5PX/graph.json","fetch_events":"https://pith.science/api/pith-number/KDYTQ4XXWSBVHBCQT7U2T5D5PX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KDYTQ4XXWSBVHBCQT7U2T5D5PX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KDYTQ4XXWSBVHBCQT7U2T5D5PX/action/storage_attestation","attest_author":"https://pith.science/pith/KDYTQ4XXWSBVHBCQT7U2T5D5PX/action/author_attestation","sign_citation":"https://pith.science/pith/KDYTQ4XXWSBVHBCQT7U2T5D5PX/action/citation_signature","submit_replication":"https://pith.science/pith/KDYTQ4XXWSBVHBCQT7U2T5D5PX/action/replication_record"}},"created_at":"2026-05-18T00:50:07.159830+00:00","updated_at":"2026-05-18T00:50:07.159830+00:00"}