{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:TOMBN43WU5KCY64AQ3P2MUXWJB","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":"a17a239c5efd074fe5b6d0971c28dd16d452bdd9315b14a7a04db1e5b2c8466c","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-08-20T23:52:50Z","title_canon_sha256":"e477ddff1d6effaea90ef639c7dd083db8fae89fb5002edeae4d512ce727bf9c"},"schema_version":"1.0","source":{"id":"1908.07647","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.07647","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"arxiv_version","alias_value":"1908.07647v1","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07647","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"pith_short_12","alias_value":"TOMBN43WU5KC","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"pith_short_16","alias_value":"TOMBN43WU5KCY64A","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"pith_short_8","alias_value":"TOMBN43W","created_at":"2026-07-04T23:58:59Z"}],"graph_snapshots":[{"event_id":"sha256:0ea72bbd1c110312197f098b40bf40f0b930c89873f1c75514297a8ddfd47b42","target":"graph","created_at":"2026-07-04T23:58:59Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.07647/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A measure for the visual complexity of a straight-line crossing-free drawing of a graph is the minimum number of lines needed to cover all vertices. For a given graph $G$, the minimum such number (over all drawings in dimension $d \\in \\{2,3\\}$) is called the \\emph{$d$-dimensional weak line cover number} and denoted by $\\pi^1_d(G)$. In 3D, the minimum number of \\emph{planes} needed to cover all vertices of~$G$ is denoted by $\\pi^2_3(G)$. When edges are also required to be covered, the corresponding numbers $\\rho^1_d(G)$ and $\\rho^2_3(G)$ are called the \\emph{(strong) line cover number} and the ","authors_text":"Alexander Wolff, Henk Meijer, Stefan Felsner, Therese Biedl","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-08-20T23:52:50Z","title":"Line and Plane Cover Numbers Revisited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07647","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":"sha256:6de51dc7605839e4faec8617c1884bf47b5c9f13ec23b485724c5b7b56446e62","target":"record","created_at":"2026-07-04T23:58:59Z","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":"a17a239c5efd074fe5b6d0971c28dd16d452bdd9315b14a7a04db1e5b2c8466c","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-08-20T23:52:50Z","title_canon_sha256":"e477ddff1d6effaea90ef639c7dd083db8fae89fb5002edeae4d512ce727bf9c"},"schema_version":"1.0","source":{"id":"1908.07647","kind":"arxiv","version":1}},"canonical_sha256":"9b9816f376a7542c7b8086dfa652f6486d5bdcf085627da2c1d1274661eb0f65","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b9816f376a7542c7b8086dfa652f6486d5bdcf085627da2c1d1274661eb0f65","first_computed_at":"2026-07-04T23:58:59.918212Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:58:59.918212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W77uWs7lgbtZ1dd8kpliDXhSuvoRs/CY7Gr423k0+I/NVb9hDlC7iM5LeF1xkzmGSIN4ZwWUdjwQu8NS3cvFBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T23:58:59.918569Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.07647","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6de51dc7605839e4faec8617c1884bf47b5c9f13ec23b485724c5b7b56446e62","sha256:0ea72bbd1c110312197f098b40bf40f0b930c89873f1c75514297a8ddfd47b42"],"state_sha256":"cc1a5c5f52fc92e98d8deecea8165b421119f6f253d81d11f8350e87b338af7e"}