{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:LVKKWFEZJCKXFPAMS7IVKRAPVP","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":"e9ab6d383d6152660968fefad366d2ef807be8a1dd83d846340e46d4bd92f1b2","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-02-28T16:31:56Z","title_canon_sha256":"debf6259a17b27ebb68567efaca3b5debf0900f04964855b295b8d674f08c965"},"schema_version":"1.0","source":{"id":"2302.14721","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.14721","created_at":"2026-07-05T05:46:48Z"},{"alias_kind":"arxiv_version","alias_value":"2302.14721v1","created_at":"2026-07-05T05:46:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.14721","created_at":"2026-07-05T05:46:48Z"},{"alias_kind":"pith_short_12","alias_value":"LVKKWFEZJCKX","created_at":"2026-07-05T05:46:48Z"},{"alias_kind":"pith_short_16","alias_value":"LVKKWFEZJCKXFPAM","created_at":"2026-07-05T05:46:48Z"},{"alias_kind":"pith_short_8","alias_value":"LVKKWFEZ","created_at":"2026-07-05T05:46:48Z"}],"graph_snapshots":[{"event_id":"sha256:84ee730e2077286b196a1f50c4acdf09bd3fd55c3094dbccfe6b5ba7668e6a9e","target":"graph","created_at":"2026-07-05T05:46:48Z","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/2302.14721/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A graph is 2-degenerate if every subgraph contains a vertex of degree at most 2. We show that every 2-degenerate graph can be drawn with straight lines such that the drawing decomposes into 4 plane forests. Therefore, the geometric arboricity, and hence the geometric thickness, of 2-degenerate graphs is at most 4. On the other hand, we show that there are 2-degenerate graphs that do not admit any straight-line drawing with a decomposition of the edge set into 2 plane graphs. That is, there are 2-degenerate graphs with geometric thickness, and hence geometric arboricity, at least 3. This answer","authors_text":"Andr\\'e Schulz, Jonathan Rollin, Marco Ricci, Rahul Jain","cross_cats":["cs.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-02-28T16:31:56Z","title":"On the geometric thickness of 2-degenerate graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.14721","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":"sha256:1951eb31c1c5d483f4b12d87b5d0557db7a95bae19b7dfb3ccdbafa801bc3f89","target":"record","created_at":"2026-07-05T05:46:48Z","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":"e9ab6d383d6152660968fefad366d2ef807be8a1dd83d846340e46d4bd92f1b2","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2023-02-28T16:31:56Z","title_canon_sha256":"debf6259a17b27ebb68567efaca3b5debf0900f04964855b295b8d674f08c965"},"schema_version":"1.0","source":{"id":"2302.14721","kind":"arxiv","version":1}},"canonical_sha256":"5d54ab1499489572bc0c97d155440fabeb05960c31345fef6e73a00ebb11adb4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d54ab1499489572bc0c97d155440fabeb05960c31345fef6e73a00ebb11adb4","first_computed_at":"2026-07-05T05:46:48.991724Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:46:48.991724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qbguwIS8jZx5pYMR9KHpj5oNedRX7dEPtBg5IFojmlBwzHU5dG0UHtNxAfaCrA1tQgujnCqODXl3TGKVWiZiAw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:46:48.992187Z","signed_message":"canonical_sha256_bytes"},"source_id":"2302.14721","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1951eb31c1c5d483f4b12d87b5d0557db7a95bae19b7dfb3ccdbafa801bc3f89","sha256:84ee730e2077286b196a1f50c4acdf09bd3fd55c3094dbccfe6b5ba7668e6a9e"],"state_sha256":"7728c2269d3e3152f9358371c830e077ef35683f19ad37505acfcb78581ea73d"}