{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:22RFW7MBAXAEDXW4XLATRCWAHL","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":"ce41a6b1538f2a8779f66d4cf5b5e4215b4c3001f2b26acb11c10950ad3257cc","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-02-18T14:55:41Z","title_canon_sha256":"75b289ec6216cb995cb129f8ccfbd3fc1d9181d0d1ce60c1e0e83b775f11280c"},"schema_version":"1.0","source":{"id":"1402.4364","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.4364","created_at":"2026-05-18T02:58:34Z"},{"alias_kind":"arxiv_version","alias_value":"1402.4364v2","created_at":"2026-05-18T02:58:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.4364","created_at":"2026-05-18T02:58:34Z"},{"alias_kind":"pith_short_12","alias_value":"22RFW7MBAXAE","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"22RFW7MBAXAEDXW4","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"22RFW7MB","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:61195b43e2f91faf870e42f9574d464639d0eb5e633b2461d61a24d4bb713b6a","target":"graph","created_at":"2026-05-18T02:58:34Z","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 provide an algorithm for computing a planar morph between any two planar straight-line drawings of any $n$-vertex plane graph in $O(n)$ morphing steps, thus improving upon the previously best known $O(n^2)$ upper bound. Further, we prove that our algorithm is optimal, that is, we show that there exist two planar straight-line drawings $\\Gamma_s$ and $\\Gamma_t$ of an $n$-vertex plane graph $G$ such that any planar morph between $\\Gamma_s$ and $\\Gamma_t$ requires $\\Omega(n)$ morphing steps.","authors_text":"Fabrizio Frati, Giordano Da Lozzo, Giuseppe Di Battista, Maurizio Patrignani, Patrizio Angelini, Vincenzo Roselli","cross_cats":["cs.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-02-18T14:55:41Z","title":"Morphing Planar Graph Drawings Optimally"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4364","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":"sha256:9a760f70f8d66d930c6b1d307f56c48b826c4ab3fee02e8096636af14f39b310","target":"record","created_at":"2026-05-18T02:58:34Z","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":"ce41a6b1538f2a8779f66d4cf5b5e4215b4c3001f2b26acb11c10950ad3257cc","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-02-18T14:55:41Z","title_canon_sha256":"75b289ec6216cb995cb129f8ccfbd3fc1d9181d0d1ce60c1e0e83b775f11280c"},"schema_version":"1.0","source":{"id":"1402.4364","kind":"arxiv","version":2}},"canonical_sha256":"d6a25b7d8105c041dedcbac1388ac03af53d40ef2919685d46d59ebbd2236088","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6a25b7d8105c041dedcbac1388ac03af53d40ef2919685d46d59ebbd2236088","first_computed_at":"2026-05-18T02:58:34.094118Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:34.094118Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8PWFPKqUJLI4PGozAWDj0e6fItkakQVDf+SJR2DrKHzVk9a2MMIYefCrYslu4xpEygagpQz2rYGrveFbtHdGAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:34.094816Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.4364","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9a760f70f8d66d930c6b1d307f56c48b826c4ab3fee02e8096636af14f39b310","sha256:61195b43e2f91faf870e42f9574d464639d0eb5e633b2461d61a24d4bb713b6a"],"state_sha256":"1c4d8d848b5b84681c51049433d9348bba6b96da53fef2643f2b5830d76f2df1"}