{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:DNWQ37R2M23DVUS4NOKMSDE5G4","short_pith_number":"pith:DNWQ37R2","schema_version":"1.0","canonical_sha256":"1b6d0dfe3a66b63ad25c6b94c90c9d370cef5bcda68a2e1d49623bbf82578f55","source":{"kind":"arxiv","id":"2007.11863","version":1},"attestation_state":"computed","paper":{"title":"Plane augmentation of plane graphs to meet parity constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"A. Garc\\'ia, J.C. Catana, J. Tejel, J. Urrutia","submitted_at":"2020-07-23T08:43:33Z","abstract_excerpt":"A plane topological graph $G=(V,E)$ is a graph drawn in the plane whose vertices are points in the plane and whose edges are simple curves that do not intersect, except at their endpoints. Given a plane topological graph $G=(V,E)$ and a set $C_G$ of parity constraints, in which every vertex has assigned a parity constraint on its degree, either even or odd, we say that $G$ is \\emph{topologically augmentable} to meet $C_G$ if there exits a plane topological graph $H$ on the same set of vertices, such that $G$ and $H$ are edge-disjoint and their union is a plane topological graph that meets all "},"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":"2007.11863","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2020-07-23T08:43:33Z","cross_cats_sorted":[],"title_canon_sha256":"d1f14e7bd95b246ff1267c1461f0786b77714bd993a7b9d915716fbf27c08c25","abstract_canon_sha256":"cabd7645f925864c4432274543a1f2676cea6508ec062265db60bfec854b4c3e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:21:41.168873Z","signature_b64":"GCPzQ7YMQ/3tIY7srCugpG4TibV4CWEQZ119PYEuE9bNDhtnWF8rZVthCM/JRXhQFDvzLYpIHCScgQCo0+uOAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b6d0dfe3a66b63ad25c6b94c90c9d370cef5bcda68a2e1d49623bbf82578f55","last_reissued_at":"2026-07-05T01:21:41.168432Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:21:41.168432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Plane augmentation of plane graphs to meet parity constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"A. Garc\\'ia, J.C. Catana, J. Tejel, J. Urrutia","submitted_at":"2020-07-23T08:43:33Z","abstract_excerpt":"A plane topological graph $G=(V,E)$ is a graph drawn in the plane whose vertices are points in the plane and whose edges are simple curves that do not intersect, except at their endpoints. Given a plane topological graph $G=(V,E)$ and a set $C_G$ of parity constraints, in which every vertex has assigned a parity constraint on its degree, either even or odd, we say that $G$ is \\emph{topologically augmentable} to meet $C_G$ if there exits a plane topological graph $H$ on the same set of vertices, such that $G$ and $H$ are edge-disjoint and their union is a plane topological graph that meets all "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.11863","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2007.11863/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2007.11863","created_at":"2026-07-05T01:21:41.168483+00:00"},{"alias_kind":"arxiv_version","alias_value":"2007.11863v1","created_at":"2026-07-05T01:21:41.168483+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.11863","created_at":"2026-07-05T01:21:41.168483+00:00"},{"alias_kind":"pith_short_12","alias_value":"DNWQ37R2M23D","created_at":"2026-07-05T01:21:41.168483+00:00"},{"alias_kind":"pith_short_16","alias_value":"DNWQ37R2M23DVUS4","created_at":"2026-07-05T01:21:41.168483+00:00"},{"alias_kind":"pith_short_8","alias_value":"DNWQ37R2","created_at":"2026-07-05T01:21:41.168483+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/DNWQ37R2M23DVUS4NOKMSDE5G4","json":"https://pith.science/pith/DNWQ37R2M23DVUS4NOKMSDE5G4.json","graph_json":"https://pith.science/api/pith-number/DNWQ37R2M23DVUS4NOKMSDE5G4/graph.json","events_json":"https://pith.science/api/pith-number/DNWQ37R2M23DVUS4NOKMSDE5G4/events.json","paper":"https://pith.science/paper/DNWQ37R2"},"agent_actions":{"view_html":"https://pith.science/pith/DNWQ37R2M23DVUS4NOKMSDE5G4","download_json":"https://pith.science/pith/DNWQ37R2M23DVUS4NOKMSDE5G4.json","view_paper":"https://pith.science/paper/DNWQ37R2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2007.11863&json=true","fetch_graph":"https://pith.science/api/pith-number/DNWQ37R2M23DVUS4NOKMSDE5G4/graph.json","fetch_events":"https://pith.science/api/pith-number/DNWQ37R2M23DVUS4NOKMSDE5G4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DNWQ37R2M23DVUS4NOKMSDE5G4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DNWQ37R2M23DVUS4NOKMSDE5G4/action/storage_attestation","attest_author":"https://pith.science/pith/DNWQ37R2M23DVUS4NOKMSDE5G4/action/author_attestation","sign_citation":"https://pith.science/pith/DNWQ37R2M23DVUS4NOKMSDE5G4/action/citation_signature","submit_replication":"https://pith.science/pith/DNWQ37R2M23DVUS4NOKMSDE5G4/action/replication_record"}},"created_at":"2026-07-05T01:21:41.168483+00:00","updated_at":"2026-07-05T01:21:41.168483+00:00"}