{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:HREO7MB6H3JI4H2S3RBLUE6IIX","short_pith_number":"pith:HREO7MB6","schema_version":"1.0","canonical_sha256":"3c48efb03e3ed28e1f52dc42ba13c845e4846009d9e30b54398318f4083c127c","source":{"kind":"arxiv","id":"1501.00318","version":1},"attestation_state":"computed","paper":{"title":"Contact Representations of Sparse Planar Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.CG","authors_text":"Andre Schulz, David Eppstein, Md. Jawaherul Alam, Michael Kaufmann, Sergey Pupyrev, Stephen G. Kobourov, Torsten Ueckerdt","submitted_at":"2015-01-01T21:22:30Z","abstract_excerpt":"We study representations of graphs by contacts of circular arcs, CCA-representations for short, where the vertices are interior-disjoint circular arcs in the plane and each edge is realized by an endpoint of one arc touching the interior of another. A graph is (2,k)-sparse if every s-vertex subgraph has at most 2s - k edges, and (2, k)-tight if in addition it has exactly 2n - k edges, where n is the number of vertices. Every graph with a CCA- representation is planar and (2, 0)-sparse, and it follows from known results on contacts of line segments that for k >= 3 every (2, k)-sparse graph has "},"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":"1501.00318","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-01-01T21:22:30Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"ad9ed15a0f67feddecaa62e5e86c3db1c3c43fced8d07f54b0cdcdab53c9e408","abstract_canon_sha256":"d825f9781637967ac1ec45d7033d7b9209ed904ab09252da2e7220dfd3d58505"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:09.591525Z","signature_b64":"AMOLnt4st/zqGOddJRlPKvbUBmFQ8Y2roSNTmM4JB9nPpRl1u/meyRwZhHDJjhaVhIYp0I4H4yVnBEXY2Ey8Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c48efb03e3ed28e1f52dc42ba13c845e4846009d9e30b54398318f4083c127c","last_reissued_at":"2026-05-18T02:30:09.590863Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:09.590863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Contact Representations of Sparse Planar Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.CG","authors_text":"Andre Schulz, David Eppstein, Md. Jawaherul Alam, Michael Kaufmann, Sergey Pupyrev, Stephen G. Kobourov, Torsten Ueckerdt","submitted_at":"2015-01-01T21:22:30Z","abstract_excerpt":"We study representations of graphs by contacts of circular arcs, CCA-representations for short, where the vertices are interior-disjoint circular arcs in the plane and each edge is realized by an endpoint of one arc touching the interior of another. A graph is (2,k)-sparse if every s-vertex subgraph has at most 2s - k edges, and (2, k)-tight if in addition it has exactly 2n - k edges, where n is the number of vertices. Every graph with a CCA- representation is planar and (2, 0)-sparse, and it follows from known results on contacts of line segments that for k >= 3 every (2, k)-sparse graph has "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00318","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":"1501.00318","created_at":"2026-05-18T02:30:09.590959+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.00318v1","created_at":"2026-05-18T02:30:09.590959+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.00318","created_at":"2026-05-18T02:30:09.590959+00:00"},{"alias_kind":"pith_short_12","alias_value":"HREO7MB6H3JI","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_16","alias_value":"HREO7MB6H3JI4H2S","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_8","alias_value":"HREO7MB6","created_at":"2026-05-18T12:29:25.134429+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/HREO7MB6H3JI4H2S3RBLUE6IIX","json":"https://pith.science/pith/HREO7MB6H3JI4H2S3RBLUE6IIX.json","graph_json":"https://pith.science/api/pith-number/HREO7MB6H3JI4H2S3RBLUE6IIX/graph.json","events_json":"https://pith.science/api/pith-number/HREO7MB6H3JI4H2S3RBLUE6IIX/events.json","paper":"https://pith.science/paper/HREO7MB6"},"agent_actions":{"view_html":"https://pith.science/pith/HREO7MB6H3JI4H2S3RBLUE6IIX","download_json":"https://pith.science/pith/HREO7MB6H3JI4H2S3RBLUE6IIX.json","view_paper":"https://pith.science/paper/HREO7MB6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.00318&json=true","fetch_graph":"https://pith.science/api/pith-number/HREO7MB6H3JI4H2S3RBLUE6IIX/graph.json","fetch_events":"https://pith.science/api/pith-number/HREO7MB6H3JI4H2S3RBLUE6IIX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HREO7MB6H3JI4H2S3RBLUE6IIX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HREO7MB6H3JI4H2S3RBLUE6IIX/action/storage_attestation","attest_author":"https://pith.science/pith/HREO7MB6H3JI4H2S3RBLUE6IIX/action/author_attestation","sign_citation":"https://pith.science/pith/HREO7MB6H3JI4H2S3RBLUE6IIX/action/citation_signature","submit_replication":"https://pith.science/pith/HREO7MB6H3JI4H2S3RBLUE6IIX/action/replication_record"}},"created_at":"2026-05-18T02:30:09.590959+00:00","updated_at":"2026-05-18T02:30:09.590959+00:00"}