{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:LIT6NW6CMWZCMRB4CCEEWCHBLZ","short_pith_number":"pith:LIT6NW6C","schema_version":"1.0","canonical_sha256":"5a27e6dbc265b226443c10884b08e15e49404a21b3cfc210eefd8d79d47859c9","source":{"kind":"arxiv","id":"1808.10738","version":2},"attestation_state":"computed","paper":{"title":"Pole Dancing: 3D Morphs for Tree Drawings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.CO"],"primary_cat":"cs.CG","authors_text":"Alessandra Tappini, Anthony D'Angelo, Elena Arseneva, Fabrizio Frati, Pilar Cano, Prosenjit Bose, Stefan Langerman, Vida Dujmovic","submitted_at":"2018-08-31T13:49:44Z","abstract_excerpt":"We study the question whether a crossing-free 3D morph between two straight-line drawings of an $n$-vertex tree can be constructed consisting of a small number of linear morphing steps. We look both at the case in which the two given drawings are two-dimensional and at the one in which they are three-dimensional. In the former setting we prove that a crossing-free 3D morph always exists with $O(\\log n)$ steps, while for the latter $\\Theta(n)$ steps are always sufficient and sometimes necessary."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1808.10738","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-08-31T13:49:44Z","cross_cats_sorted":["cs.DS","math.CO"],"title_canon_sha256":"2ce4a8738ed42aa0ec38270279080254c9fd11bd6421cd50996ced8b87badc2d","abstract_canon_sha256":"cd3b201d8513666095e4b8c063a6e61ace9e900bce7b425b161b46d5b52a0e4a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:36.448891Z","signature_b64":"hkWhQ4rJOEeCQAT9ocsvM+D1qUHwmWP9WutCfZYYBsujXlWPy9qUNRvy/qKpu8SE/7Ac2k8GMQx6nbMZE5uQCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a27e6dbc265b226443c10884b08e15e49404a21b3cfc210eefd8d79d47859c9","last_reissued_at":"2026-05-18T00:06:36.448407Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:36.448407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pole Dancing: 3D Morphs for Tree Drawings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.CO"],"primary_cat":"cs.CG","authors_text":"Alessandra Tappini, Anthony D'Angelo, Elena Arseneva, Fabrizio Frati, Pilar Cano, Prosenjit Bose, Stefan Langerman, Vida Dujmovic","submitted_at":"2018-08-31T13:49:44Z","abstract_excerpt":"We study the question whether a crossing-free 3D morph between two straight-line drawings of an $n$-vertex tree can be constructed consisting of a small number of linear morphing steps. We look both at the case in which the two given drawings are two-dimensional and at the one in which they are three-dimensional. In the former setting we prove that a crossing-free 3D morph always exists with $O(\\log n)$ steps, while for the latter $\\Theta(n)$ steps are always sufficient and sometimes necessary."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.10738","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1808.10738","created_at":"2026-05-18T00:06:36.448482+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.10738v2","created_at":"2026-05-18T00:06:36.448482+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.10738","created_at":"2026-05-18T00:06:36.448482+00:00"},{"alias_kind":"pith_short_12","alias_value":"LIT6NW6CMWZC","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_16","alias_value":"LIT6NW6CMWZCMRB4","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_8","alias_value":"LIT6NW6C","created_at":"2026-05-18T12:32:37.024351+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LIT6NW6CMWZCMRB4CCEEWCHBLZ","json":"https://pith.science/pith/LIT6NW6CMWZCMRB4CCEEWCHBLZ.json","graph_json":"https://pith.science/api/pith-number/LIT6NW6CMWZCMRB4CCEEWCHBLZ/graph.json","events_json":"https://pith.science/api/pith-number/LIT6NW6CMWZCMRB4CCEEWCHBLZ/events.json","paper":"https://pith.science/paper/LIT6NW6C"},"agent_actions":{"view_html":"https://pith.science/pith/LIT6NW6CMWZCMRB4CCEEWCHBLZ","download_json":"https://pith.science/pith/LIT6NW6CMWZCMRB4CCEEWCHBLZ.json","view_paper":"https://pith.science/paper/LIT6NW6C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.10738&json=true","fetch_graph":"https://pith.science/api/pith-number/LIT6NW6CMWZCMRB4CCEEWCHBLZ/graph.json","fetch_events":"https://pith.science/api/pith-number/LIT6NW6CMWZCMRB4CCEEWCHBLZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LIT6NW6CMWZCMRB4CCEEWCHBLZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LIT6NW6CMWZCMRB4CCEEWCHBLZ/action/storage_attestation","attest_author":"https://pith.science/pith/LIT6NW6CMWZCMRB4CCEEWCHBLZ/action/author_attestation","sign_citation":"https://pith.science/pith/LIT6NW6CMWZCMRB4CCEEWCHBLZ/action/citation_signature","submit_replication":"https://pith.science/pith/LIT6NW6CMWZCMRB4CCEEWCHBLZ/action/replication_record"}},"created_at":"2026-05-18T00:06:36.448482+00:00","updated_at":"2026-05-18T00:06:36.448482+00:00"}