{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:23WPNROYXAUB4E22IOBDYY2Z3D","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":"6f681585ebb3e82b838316fd8b70786e4e2d2ee5dca8315a0b487f69af2817f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-09-26T09:02:35Z","title_canon_sha256":"fe38264d27976acbbfe254b7de786560f6dd717008a50ad9e226b2f6a07e652b"},"schema_version":"1.0","source":{"id":"1509.07952","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.07952","created_at":"2026-05-18T01:31:55Z"},{"alias_kind":"arxiv_version","alias_value":"1509.07952v1","created_at":"2026-05-18T01:31:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07952","created_at":"2026-05-18T01:31:55Z"},{"alias_kind":"pith_short_12","alias_value":"23WPNROYXAUB","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"23WPNROYXAUB4E22","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"23WPNROY","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:3454aad13e368ed3233c1ba3b605306d6f7fd13b1804f2a72e432ad70e704460","target":"graph","created_at":"2026-05-18T01:31:55Z","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":"Let $G$ be a connected planar (but not yet embedded) graph and $F$ a set of additional edges not yet in $G$. The {multiple edge insertion} problem (MEI) asks for a drawing of $G+F$ with the minimum number of pairwise edge crossings, such that the subdrawing of $G$ is plane. An optimal solution to this problem approximates the crossing number of the graph $G+F$.\n  Finding an exact solution to MEI is NP-hard for general $F$, but linear time solvable for the special case of $|F|=1$ (SODA01, Algorithmica) or when all of $F$ are incident to a new vertex (SODA09).\n  The complexity for general $F$ bu","authors_text":"Markus Chimani, Petr Hlin\\v{e}n\\'y","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-09-26T09:02:35Z","title":"Inserting Multiple Edges into a Planar Graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07952","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":"sha256:4d9e3dd38c4d26d3ad0e479af0b5d4a206b4befd667927b5563c2b56c842a70c","target":"record","created_at":"2026-05-18T01:31:55Z","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":"6f681585ebb3e82b838316fd8b70786e4e2d2ee5dca8315a0b487f69af2817f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-09-26T09:02:35Z","title_canon_sha256":"fe38264d27976acbbfe254b7de786560f6dd717008a50ad9e226b2f6a07e652b"},"schema_version":"1.0","source":{"id":"1509.07952","kind":"arxiv","version":1}},"canonical_sha256":"d6ecf6c5d8b8281e135a43823c6359d8e7a42fbe395a0537acbdbf2635e0be26","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6ecf6c5d8b8281e135a43823c6359d8e7a42fbe395a0537acbdbf2635e0be26","first_computed_at":"2026-05-18T01:31:55.047104Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:55.047104Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zY/odQvWNGofWITJxdiGzGm1ddu68FZ5LNGVU/EumMYGwJ6RBi1UeO+GtU79Y8kq1Qd9pfyFJi3xe6yqdYOwCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:55.047520Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.07952","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d9e3dd38c4d26d3ad0e479af0b5d4a206b4befd667927b5563c2b56c842a70c","sha256:3454aad13e368ed3233c1ba3b605306d6f7fd13b1804f2a72e432ad70e704460"],"state_sha256":"c98b23089173b315ecfb276eadc6e4f16287730a9788cb9557cd5b0296bb788c"}