{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:2RHY2EKNN66ZQF37ZA3545WALQ","short_pith_number":"pith:2RHY2EKN","schema_version":"1.0","canonical_sha256":"d44f8d114d6fbd98177fc837de76c05c16e0a8ef50078c8d612ac3f29c662589","source":{"kind":"arxiv","id":"1706.09086","version":1},"attestation_state":"computed","paper":{"title":"On Compatible Triangulations with a Minimum Number of Steiner Points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Anna Lubiw, Debajyoti Mondal","submitted_at":"2017-06-28T00:33:18Z","abstract_excerpt":"Two vertex-labelled polygons are \\emph{compatible} if they have the same clockwise cyclic ordering of vertices. The definition extends to polygonal regions (polygons with holes) and to triangulations---for every face, the clockwise cyclic order of vertices on the boundary must be the same. It is known that every pair of compatible $n$-vertex polygonal regions can be extended to compatible triangulations by adding $O(n^2)$ Steiner points. Furthermore, $\\Omega(n^2)$ Steiner points are sometimes necessary, even for a pair of polygons. Compatible triangulations provide piecewise linear homeomorphi"},"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":"1706.09086","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-06-28T00:33:18Z","cross_cats_sorted":[],"title_canon_sha256":"3885f3fb2de96645a2d39b1f44fea3017a4a4a0104d8f7ebf0ae88fcc7d8a73e","abstract_canon_sha256":"b0d48e7bc13347cbc6dd8a173bea7cfbb340b634c4514b1fd4048436c985a978"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:19.910924Z","signature_b64":"gCk+zuIHsn0pQM4vC00ObuZSffzeXgVcVQlv8nZc+GsZ1Zgvh4nr15vC/kD2dlNZcBE75pVXl0bFdf4yh2nwDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d44f8d114d6fbd98177fc837de76c05c16e0a8ef50078c8d612ac3f29c662589","last_reissued_at":"2026-05-18T00:41:19.910344Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:19.910344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Compatible Triangulations with a Minimum Number of Steiner Points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Anna Lubiw, Debajyoti Mondal","submitted_at":"2017-06-28T00:33:18Z","abstract_excerpt":"Two vertex-labelled polygons are \\emph{compatible} if they have the same clockwise cyclic ordering of vertices. The definition extends to polygonal regions (polygons with holes) and to triangulations---for every face, the clockwise cyclic order of vertices on the boundary must be the same. It is known that every pair of compatible $n$-vertex polygonal regions can be extended to compatible triangulations by adding $O(n^2)$ Steiner points. Furthermore, $\\Omega(n^2)$ Steiner points are sometimes necessary, even for a pair of polygons. Compatible triangulations provide piecewise linear homeomorphi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09086","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":"1706.09086","created_at":"2026-05-18T00:41:19.910436+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.09086v1","created_at":"2026-05-18T00:41:19.910436+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.09086","created_at":"2026-05-18T00:41:19.910436+00:00"},{"alias_kind":"pith_short_12","alias_value":"2RHY2EKNN66Z","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_16","alias_value":"2RHY2EKNN66ZQF37","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_8","alias_value":"2RHY2EKN","created_at":"2026-05-18T12:30:55.937587+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/2RHY2EKNN66ZQF37ZA3545WALQ","json":"https://pith.science/pith/2RHY2EKNN66ZQF37ZA3545WALQ.json","graph_json":"https://pith.science/api/pith-number/2RHY2EKNN66ZQF37ZA3545WALQ/graph.json","events_json":"https://pith.science/api/pith-number/2RHY2EKNN66ZQF37ZA3545WALQ/events.json","paper":"https://pith.science/paper/2RHY2EKN"},"agent_actions":{"view_html":"https://pith.science/pith/2RHY2EKNN66ZQF37ZA3545WALQ","download_json":"https://pith.science/pith/2RHY2EKNN66ZQF37ZA3545WALQ.json","view_paper":"https://pith.science/paper/2RHY2EKN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.09086&json=true","fetch_graph":"https://pith.science/api/pith-number/2RHY2EKNN66ZQF37ZA3545WALQ/graph.json","fetch_events":"https://pith.science/api/pith-number/2RHY2EKNN66ZQF37ZA3545WALQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2RHY2EKNN66ZQF37ZA3545WALQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2RHY2EKNN66ZQF37ZA3545WALQ/action/storage_attestation","attest_author":"https://pith.science/pith/2RHY2EKNN66ZQF37ZA3545WALQ/action/author_attestation","sign_citation":"https://pith.science/pith/2RHY2EKNN66ZQF37ZA3545WALQ/action/citation_signature","submit_replication":"https://pith.science/pith/2RHY2EKNN66ZQF37ZA3545WALQ/action/replication_record"}},"created_at":"2026-05-18T00:41:19.910436+00:00","updated_at":"2026-05-18T00:41:19.910436+00:00"}