{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:YKEQVWW2UM6TDYHUGR6AWWYVGR","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":"32f31eff1cdb913db63e4ec32d7f1afbe91305bef28f52af9137496b386a8461","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-09-23T04:24:51Z","title_canon_sha256":"72403406a3bf3255533691ee60038fc6870405dcb9a8de75712ebcc4f1ef9ee4"},"schema_version":"1.0","source":{"id":"1009.4517","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.4517","created_at":"2026-05-18T04:06:45Z"},{"alias_kind":"arxiv_version","alias_value":"1009.4517v2","created_at":"2026-05-18T04:06:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.4517","created_at":"2026-05-18T04:06:45Z"},{"alias_kind":"pith_short_12","alias_value":"YKEQVWW2UM6T","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"YKEQVWW2UM6TDYHU","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"YKEQVWW2","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:d3eea7058cd9b8d929716d5b68cad76e61d671d753d7759014f385a450417e98","target":"graph","created_at":"2026-05-18T04:06:45Z","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":"Two planar graphs G1 and G2 sharing some vertices and edges are `simultaneously planar' if they have planar drawings such that a shared vertex [edge] is represented by the same point [curve] in both drawings. It is an open problem whether simultaneous planarity can be tested efficiently. We give a linear-time algorithm to test simultaneous planarity when the two graphs share a 2-connected subgraph. Our algorithm extends to the case of k planar graphs where each vertex [edge] is either common to all graphs or belongs to exactly one of them.","authors_text":"Anna Lubiw, Bernhard Haeupler, Krishnam Raju Jampani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-09-23T04:24:51Z","title":"Testing Simultaneous Planarity when the Common Graph is 2-Connected"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4517","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:c196a910477ccda7e27f8b33e7a646c143520d75f2f9ff0499260c323fc79231","target":"record","created_at":"2026-05-18T04:06:45Z","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":"32f31eff1cdb913db63e4ec32d7f1afbe91305bef28f52af9137496b386a8461","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-09-23T04:24:51Z","title_canon_sha256":"72403406a3bf3255533691ee60038fc6870405dcb9a8de75712ebcc4f1ef9ee4"},"schema_version":"1.0","source":{"id":"1009.4517","kind":"arxiv","version":2}},"canonical_sha256":"c2890adadaa33d31e0f4347c0b5b15345c68b23e57b06f77b1167ae96c6a56ec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2890adadaa33d31e0f4347c0b5b15345c68b23e57b06f77b1167ae96c6a56ec","first_computed_at":"2026-05-18T04:06:45.130201Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:45.130201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xtT6082CV8O6dEhvwsJGVzfeoRiwltLzCCFbIPIcAZ9/ORYeWt9JeJKWKkdrsfo93m4aqVW29fgLn6m28tkOAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:45.130868Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.4517","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c196a910477ccda7e27f8b33e7a646c143520d75f2f9ff0499260c323fc79231","sha256:d3eea7058cd9b8d929716d5b68cad76e61d671d753d7759014f385a450417e98"],"state_sha256":"25a22282c80d1b13a762747b957434fdd5e4b137d8347e6381be682a107378dc"}