{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:NW6F5X6FP52G6OSDMWJOOHRSKV","short_pith_number":"pith:NW6F5X6F","schema_version":"1.0","canonical_sha256":"6dbc5edfc57f746f3a436592e71e32556ce571593049598147ba8579210480d3","source":{"kind":"arxiv","id":"1206.0514","version":1},"attestation_state":"computed","paper":{"title":"Simultaneous Embeddings with Vertices Mapping to Pre-Specified Points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.CG","authors_text":"Taylor Gordon","submitted_at":"2012-06-04T04:06:13Z","abstract_excerpt":"We discuss the problem of embedding graphs in the plane with restrictions on the vertex mapping. In particular, we introduce a technique for drawing planar graphs with a fixed vertex mapping that bounds the number of times edges bend. An immediate consequence of this technique is that any planar graph can be drawn with a fixed vertex mapping so that edges map to piecewise linear curves with at most $3n + O(1)$ bends each. By considering uniformly random planar graphs, we show that $2n + O(1)$ bends per edge is sufficient on average.\n  To further utilize our technique, we consider simultaneous "},"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":"1206.0514","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2012-06-04T04:06:13Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"02c7d19349a8a4d11f1791160a77f967eea5d72af1c352aa81135014447c7b7b","abstract_canon_sha256":"1fc66c94ba5de4ac102c7f9a7d90fdf5c9c24051f22988121a1423f498a608dc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:17.459096Z","signature_b64":"t1ZgKWUtxqGep5o2wPQXbQyb2QubXtBGjdAVoqxAUaaLJFNwT4OnbjWgA5MJvlSIJOulT9vGU8xFF9QK651KBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6dbc5edfc57f746f3a436592e71e32556ce571593049598147ba8579210480d3","last_reissued_at":"2026-05-18T03:54:17.458036Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:17.458036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Simultaneous Embeddings with Vertices Mapping to Pre-Specified Points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.CG","authors_text":"Taylor Gordon","submitted_at":"2012-06-04T04:06:13Z","abstract_excerpt":"We discuss the problem of embedding graphs in the plane with restrictions on the vertex mapping. In particular, we introduce a technique for drawing planar graphs with a fixed vertex mapping that bounds the number of times edges bend. An immediate consequence of this technique is that any planar graph can be drawn with a fixed vertex mapping so that edges map to piecewise linear curves with at most $3n + O(1)$ bends each. By considering uniformly random planar graphs, we show that $2n + O(1)$ bends per edge is sufficient on average.\n  To further utilize our technique, we consider simultaneous "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.0514","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":"1206.0514","created_at":"2026-05-18T03:54:17.458368+00:00"},{"alias_kind":"arxiv_version","alias_value":"1206.0514v1","created_at":"2026-05-18T03:54:17.458368+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.0514","created_at":"2026-05-18T03:54:17.458368+00:00"},{"alias_kind":"pith_short_12","alias_value":"NW6F5X6FP52G","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"NW6F5X6FP52G6OSD","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"NW6F5X6F","created_at":"2026-05-18T12:27:16.716162+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/NW6F5X6FP52G6OSDMWJOOHRSKV","json":"https://pith.science/pith/NW6F5X6FP52G6OSDMWJOOHRSKV.json","graph_json":"https://pith.science/api/pith-number/NW6F5X6FP52G6OSDMWJOOHRSKV/graph.json","events_json":"https://pith.science/api/pith-number/NW6F5X6FP52G6OSDMWJOOHRSKV/events.json","paper":"https://pith.science/paper/NW6F5X6F"},"agent_actions":{"view_html":"https://pith.science/pith/NW6F5X6FP52G6OSDMWJOOHRSKV","download_json":"https://pith.science/pith/NW6F5X6FP52G6OSDMWJOOHRSKV.json","view_paper":"https://pith.science/paper/NW6F5X6F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1206.0514&json=true","fetch_graph":"https://pith.science/api/pith-number/NW6F5X6FP52G6OSDMWJOOHRSKV/graph.json","fetch_events":"https://pith.science/api/pith-number/NW6F5X6FP52G6OSDMWJOOHRSKV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NW6F5X6FP52G6OSDMWJOOHRSKV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NW6F5X6FP52G6OSDMWJOOHRSKV/action/storage_attestation","attest_author":"https://pith.science/pith/NW6F5X6FP52G6OSDMWJOOHRSKV/action/author_attestation","sign_citation":"https://pith.science/pith/NW6F5X6FP52G6OSDMWJOOHRSKV/action/citation_signature","submit_replication":"https://pith.science/pith/NW6F5X6FP52G6OSDMWJOOHRSKV/action/replication_record"}},"created_at":"2026-05-18T03:54:17.458368+00:00","updated_at":"2026-05-18T03:54:17.458368+00:00"}