{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:M4I6IB5CS57R4IVKJU7WFJ3EAK","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":"246400e7202b924a2d750cf069c1a0086ac6cf8529c41bb83214f3177268baec","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-12-02T22:13:16Z","title_canon_sha256":"0c075c2857fb192987c01e023afef39ad7f67a2e1a56ffa2027281e4e0f130a9"},"schema_version":"1.0","source":{"id":"1012.0591","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.0591","created_at":"2026-05-18T02:23:16Z"},{"alias_kind":"arxiv_version","alias_value":"1012.0591v2","created_at":"2026-05-18T02:23:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.0591","created_at":"2026-05-18T02:23:16Z"},{"alias_kind":"pith_short_12","alias_value":"M4I6IB5CS57R","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"M4I6IB5CS57R4IVK","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"M4I6IB5C","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:20d2aed849f5c5da463be0290699651693833d66aac8949d932eff1492f6a46b","target":"graph","created_at":"2026-05-18T02:23:16Z","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"},"paper":{"abstract_excerpt":"We generalize the notions of flippable and simultaneously flippable edges in a triangulation of a set S of points in the plane to so-called \\emph{pseudo-simultaneously flippable edges}. Such edges are related to the notion of convex decompositions spanned by S.\n  We prove a worst-case tight lower bound for the number of pseudo-simultaneously flippable edges in a triangulation in terms of the number of vertices. We use this bound for deriving new upper bounds for the maximal number of crossing-free straight-edge graphs that can be embedded on any fixed set of N points in the plane. We obtain ne","authors_text":"Adam Sheffer, Csaba D. T\\'oth, Emo Welzl, Michael Hoffmann, Micha Sharir","cross_cats":["cs.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-12-02T22:13:16Z","title":"Counting Plane Graphs: Flippability and its Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0591","kind":"arxiv","version":2},"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:a6a51852fd72dd98ae6a747087fc30c6899faadfc20f74c29985526d9c05d604","target":"record","created_at":"2026-05-18T02:23:16Z","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":"246400e7202b924a2d750cf069c1a0086ac6cf8529c41bb83214f3177268baec","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-12-02T22:13:16Z","title_canon_sha256":"0c075c2857fb192987c01e023afef39ad7f67a2e1a56ffa2027281e4e0f130a9"},"schema_version":"1.0","source":{"id":"1012.0591","kind":"arxiv","version":2}},"canonical_sha256":"6711e407a2977f1e22aa4d3f62a76402a381e45b064512536b1be3e5aa22f3f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6711e407a2977f1e22aa4d3f62a76402a381e45b064512536b1be3e5aa22f3f0","first_computed_at":"2026-05-18T02:23:16.439112Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:23:16.439112Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UFBTnADJEhGFuTZ1j/heqqwGtL5x0K/CBk8jcbpH525kxBJzCRF/ZMpY5GgaDkaWOgHC4nsENNVKoc14Vrd9DA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:23:16.439710Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.0591","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a6a51852fd72dd98ae6a747087fc30c6899faadfc20f74c29985526d9c05d604","sha256:20d2aed849f5c5da463be0290699651693833d66aac8949d932eff1492f6a46b"],"state_sha256":"c4b6daddbd8ba956989497b9f51c1791713e50310edfb5a4f0f3c8a889a51849"}