{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:UT4QPNDA3UESXNRO52AHAJ42FS","short_pith_number":"pith:UT4QPNDA","schema_version":"1.0","canonical_sha256":"a4f907b460dd092bb62eee8070279a2c9621e9fd7cc893b0151f31ef9635d418","source":{"kind":"arxiv","id":"1810.13297","version":1},"attestation_state":"computed","paper":{"title":"Multilevel Planarity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.DS","authors_text":"Guido Br\\\"uckner, Lukas Barth, Marcel Radermacher, Paul Jungeblut","submitted_at":"2018-10-31T14:18:11Z","abstract_excerpt":"In this paper, we introduce and study the multilevel-planarity testing problem, which is a generalization of upward planarity and level planarity. Let $G = (V, E)$ be a directed graph and let $\\ell: V \\to \\mathcal P(\\mathbb Z)$ be a function that assigns a finite set of integers to each vertex. A multilevel-planar drawing of $G$ is a planar drawing of $G$ such that the $y$-coordinate of each vertex $v \\in V$ is $y(v) \\in \\ell(v)$, and each edge is drawn as a strictly $y$-monotone curve. We present linear-time algorithms for testing multilevel planarity of embedded graphs with a single source a"},"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":"1810.13297","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-10-31T14:18:11Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"391dd3fcbaf5e9b8c67069b8be53a9232411d7aae1ac68081feaaf9394cd3fb1","abstract_canon_sha256":"293c37aecb4d04e2bcbcf478c3117dcf8ae95d34b73c7b08d76f4f49c95125e5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:49.750990Z","signature_b64":"z/GYqJUazwJudruEhDCWZYLXurDO5JzsJ4SkxTXxrJ64S5NfpkYB+AEzG6xm3OZSlNeLh8FMppZy0aen0SYWBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4f907b460dd092bb62eee8070279a2c9621e9fd7cc893b0151f31ef9635d418","last_reissued_at":"2026-05-18T00:01:49.750334Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:49.750334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multilevel Planarity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.DS","authors_text":"Guido Br\\\"uckner, Lukas Barth, Marcel Radermacher, Paul Jungeblut","submitted_at":"2018-10-31T14:18:11Z","abstract_excerpt":"In this paper, we introduce and study the multilevel-planarity testing problem, which is a generalization of upward planarity and level planarity. Let $G = (V, E)$ be a directed graph and let $\\ell: V \\to \\mathcal P(\\mathbb Z)$ be a function that assigns a finite set of integers to each vertex. A multilevel-planar drawing of $G$ is a planar drawing of $G$ such that the $y$-coordinate of each vertex $v \\in V$ is $y(v) \\in \\ell(v)$, and each edge is drawn as a strictly $y$-monotone curve. We present linear-time algorithms for testing multilevel planarity of embedded graphs with a single source a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.13297","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":"1810.13297","created_at":"2026-05-18T00:01:49.750441+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.13297v1","created_at":"2026-05-18T00:01:49.750441+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.13297","created_at":"2026-05-18T00:01:49.750441+00:00"},{"alias_kind":"pith_short_12","alias_value":"UT4QPNDA3UES","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_16","alias_value":"UT4QPNDA3UESXNRO","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_8","alias_value":"UT4QPNDA","created_at":"2026-05-18T12:32:56.356000+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/UT4QPNDA3UESXNRO52AHAJ42FS","json":"https://pith.science/pith/UT4QPNDA3UESXNRO52AHAJ42FS.json","graph_json":"https://pith.science/api/pith-number/UT4QPNDA3UESXNRO52AHAJ42FS/graph.json","events_json":"https://pith.science/api/pith-number/UT4QPNDA3UESXNRO52AHAJ42FS/events.json","paper":"https://pith.science/paper/UT4QPNDA"},"agent_actions":{"view_html":"https://pith.science/pith/UT4QPNDA3UESXNRO52AHAJ42FS","download_json":"https://pith.science/pith/UT4QPNDA3UESXNRO52AHAJ42FS.json","view_paper":"https://pith.science/paper/UT4QPNDA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.13297&json=true","fetch_graph":"https://pith.science/api/pith-number/UT4QPNDA3UESXNRO52AHAJ42FS/graph.json","fetch_events":"https://pith.science/api/pith-number/UT4QPNDA3UESXNRO52AHAJ42FS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UT4QPNDA3UESXNRO52AHAJ42FS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UT4QPNDA3UESXNRO52AHAJ42FS/action/storage_attestation","attest_author":"https://pith.science/pith/UT4QPNDA3UESXNRO52AHAJ42FS/action/author_attestation","sign_citation":"https://pith.science/pith/UT4QPNDA3UESXNRO52AHAJ42FS/action/citation_signature","submit_replication":"https://pith.science/pith/UT4QPNDA3UESXNRO52AHAJ42FS/action/replication_record"}},"created_at":"2026-05-18T00:01:49.750441+00:00","updated_at":"2026-05-18T00:01:49.750441+00:00"}