{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:NWDDGHSHE2NQHNIBGFY3DDCTJB","short_pith_number":"pith:NWDDGHSH","schema_version":"1.0","canonical_sha256":"6d86331e47269b03b5013171b18c534866134717df847a2dd30fb5e6d902ce8b","source":{"kind":"arxiv","id":"1501.00304","version":2},"attestation_state":"computed","paper":{"title":"Contact Representations of Graphs in 3D","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.CG","authors_text":"Jackson Toeniskoetter, Md. Jawaherul Alam, Sergey Pupyrev, Stephen G. Kobourov, Torsten Ueckerdt, William Evans","submitted_at":"2015-01-01T20:16:00Z","abstract_excerpt":"We study contact representations of graphs in which vertices are represented by axis-aligned polyhedra in 3D and edges are realized by non-zero area common boundaries between corresponding polyhedra. We show that for every 3-connected planar graph, there exists a simultaneous representation of the graph and its dual with 3D boxes. We give a linear-time algorithm for constructing such a representation. This result extends the existing primal-dual contact representations of planar graphs in 2D using circles and triangles. While contact graphs in 2D directly correspond to planar graphs, we next s"},"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":"1501.00304","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-01-01T20:16:00Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"d26fdf67dd003d924792e9399b1987312829a76675ddc69a7873249f3f04a343","abstract_canon_sha256":"159e1c42c77347b12207ed30a949fa72a21d47b776e8611e3d0b9440b3900c5a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:11.425331Z","signature_b64":"jLsU6ARfPe6t63rBr0Bw6sL1WAwNJO9+0gx4+4qHWh5K42mPavgIj4c4nEhbO2pKY5gqZpuiTLjJozmCiqgWBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d86331e47269b03b5013171b18c534866134717df847a2dd30fb5e6d902ce8b","last_reissued_at":"2026-05-18T02:17:11.424540Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:11.424540Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Contact Representations of Graphs in 3D","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.CG","authors_text":"Jackson Toeniskoetter, Md. Jawaherul Alam, Sergey Pupyrev, Stephen G. Kobourov, Torsten Ueckerdt, William Evans","submitted_at":"2015-01-01T20:16:00Z","abstract_excerpt":"We study contact representations of graphs in which vertices are represented by axis-aligned polyhedra in 3D and edges are realized by non-zero area common boundaries between corresponding polyhedra. We show that for every 3-connected planar graph, there exists a simultaneous representation of the graph and its dual with 3D boxes. We give a linear-time algorithm for constructing such a representation. This result extends the existing primal-dual contact representations of planar graphs in 2D using circles and triangles. While contact graphs in 2D directly correspond to planar graphs, we next s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00304","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":"1501.00304","created_at":"2026-05-18T02:17:11.424650+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.00304v2","created_at":"2026-05-18T02:17:11.424650+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.00304","created_at":"2026-05-18T02:17:11.424650+00:00"},{"alias_kind":"pith_short_12","alias_value":"NWDDGHSHE2NQ","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"NWDDGHSHE2NQHNIB","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"NWDDGHSH","created_at":"2026-05-18T12:29:34.919912+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/NWDDGHSHE2NQHNIBGFY3DDCTJB","json":"https://pith.science/pith/NWDDGHSHE2NQHNIBGFY3DDCTJB.json","graph_json":"https://pith.science/api/pith-number/NWDDGHSHE2NQHNIBGFY3DDCTJB/graph.json","events_json":"https://pith.science/api/pith-number/NWDDGHSHE2NQHNIBGFY3DDCTJB/events.json","paper":"https://pith.science/paper/NWDDGHSH"},"agent_actions":{"view_html":"https://pith.science/pith/NWDDGHSHE2NQHNIBGFY3DDCTJB","download_json":"https://pith.science/pith/NWDDGHSHE2NQHNIBGFY3DDCTJB.json","view_paper":"https://pith.science/paper/NWDDGHSH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.00304&json=true","fetch_graph":"https://pith.science/api/pith-number/NWDDGHSHE2NQHNIBGFY3DDCTJB/graph.json","fetch_events":"https://pith.science/api/pith-number/NWDDGHSHE2NQHNIBGFY3DDCTJB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NWDDGHSHE2NQHNIBGFY3DDCTJB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NWDDGHSHE2NQHNIBGFY3DDCTJB/action/storage_attestation","attest_author":"https://pith.science/pith/NWDDGHSHE2NQHNIBGFY3DDCTJB/action/author_attestation","sign_citation":"https://pith.science/pith/NWDDGHSHE2NQHNIBGFY3DDCTJB/action/citation_signature","submit_replication":"https://pith.science/pith/NWDDGHSHE2NQHNIBGFY3DDCTJB/action/replication_record"}},"created_at":"2026-05-18T02:17:11.424650+00:00","updated_at":"2026-05-18T02:17:11.424650+00:00"}