{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:2WGI3NJAMCCK3AKFPVXMXZJFLW","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"80ac5e3f64028190acbd88a3f70d56e5eea56bfb735fa487ff8e5e2f4379755f","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-08-19T13:04:42Z","title_canon_sha256":"dd9d296a7633312747dbae5f9fea9c03f0cb7b8ba3aff855aed522e7f4df7a7c"},"schema_version":"1.0","source":{"id":"2008.08413","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2008.08413","created_at":"2026-07-05T01:28:25Z"},{"alias_kind":"arxiv_version","alias_value":"2008.08413v1","created_at":"2026-07-05T01:28:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2008.08413","created_at":"2026-07-05T01:28:25Z"},{"alias_kind":"pith_short_12","alias_value":"2WGI3NJAMCCK","created_at":"2026-07-05T01:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"2WGI3NJAMCCK3AKF","created_at":"2026-07-05T01:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"2WGI3NJA","created_at":"2026-07-05T01:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:1bfe56a0ee50b2dad0c13a9d5dc760095248a6638e4c949cb21164b1b46b5ebf","target":"graph","created_at":"2026-07-05T01:28:25Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2008.08413/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study noncrossing geometric graphs and their disjoint compatible geometric matchings. Given a cycle (a polygon) P we want to draw a set of pairwise disjoint straight-line edges with endpoints on the vertices of P such that these new edges neither cross nor contain any edge of the polygon. We prove NP-completeness of deciding whether there is such a perfect matching. For any n-vertex polygon, with n > 3, we show that such a matching with less than n/7 edges is not maximal, that is, it can be extended by another compatible matching edge. We also construct polygons with maximal compatible matc","authors_text":"Alexander Pilz, Andr\\'e Schulz, Jonathan Rollin, Lena Schlipf","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-08-19T13:04:42Z","title":"Augmenting Geometric Graphs with Matchings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2008.08413","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:760d5dcfab9f382c11d1338567699c2e2e575dd7ff344d342f857e09710fdbc2","target":"record","created_at":"2026-07-05T01:28:25Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"80ac5e3f64028190acbd88a3f70d56e5eea56bfb735fa487ff8e5e2f4379755f","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2020-08-19T13:04:42Z","title_canon_sha256":"dd9d296a7633312747dbae5f9fea9c03f0cb7b8ba3aff855aed522e7f4df7a7c"},"schema_version":"1.0","source":{"id":"2008.08413","kind":"arxiv","version":1}},"canonical_sha256":"d58c8db5206084ad81457d6ecbe5255da8898c526538bf77dee404288cdd27bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d58c8db5206084ad81457d6ecbe5255da8898c526538bf77dee404288cdd27bd","first_computed_at":"2026-07-05T01:28:25.516654Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:28:25.516654Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M8lP2NkOAMUqDE0TzcbHXjIrSj1KbRzTL481fXnCIXl3rkjesytYwgNXkDjQoCx51lvkyLzURId7W0UErcsrCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:28:25.517052Z","signed_message":"canonical_sha256_bytes"},"source_id":"2008.08413","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:760d5dcfab9f382c11d1338567699c2e2e575dd7ff344d342f857e09710fdbc2","sha256:1bfe56a0ee50b2dad0c13a9d5dc760095248a6638e4c949cb21164b1b46b5ebf"],"state_sha256":"cb7212c424dc7f653ab6c8bdf9b45e84df5afad8a21a8262a9f9445671c9b908"}