{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:HCKFPCXRQPN7GY2A3YJVWTDWML","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":"7551c24d32bb38f010c079499c0e4104d3d3f5aa62307780677cdeda9319dfb4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-09-05T15:32:32Z","title_canon_sha256":"722bd1761446da294571d3397066b467b9ea83e62dda1b4b76a0bf3ea35334ac"},"schema_version":"1.0","source":{"id":"1709.01456","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.01456","created_at":"2026-05-18T00:36:00Z"},{"alias_kind":"arxiv_version","alias_value":"1709.01456v1","created_at":"2026-05-18T00:36:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.01456","created_at":"2026-05-18T00:36:00Z"},{"alias_kind":"pith_short_12","alias_value":"HCKFPCXRQPN7","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HCKFPCXRQPN7GY2A","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HCKFPCXR","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:55a9bf148168c1746c68a08a9979e077c3e5c1adbf00847ca108048888b7ade5","target":"graph","created_at":"2026-05-18T00:36:00Z","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 $T$ be an $n$-node tree of maximum degree 4, and let $P$ be a set of $n$ points in the plane with no two points on the same horizontal or vertical line. It is an open question whether $T$ always has a planar drawing on $P$ such that each edge is drawn as an orthogonal path with one bend (an \"L-shaped\" edge). By giving new methods for drawing trees, we improve the bounds on the size of the point set $P$ for which such drawings are possible to: $O(n^{1.55})$ for maximum degree 4 trees; $O(n^{1.22})$ for maximum degree 3 (binary) trees; and $O(n^{1.142})$ for perfect binary trees.\n  Drawing o","authors_text":"Anna Lubiw, Kshitij Jain, Martin Derka, Therese Biedl, Timothy M. Chan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-09-05T15:32:32Z","title":"Improved Bounds for Drawing Trees on Fixed Points with L-shaped Edges"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01456","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:a37a788538b6f64469d3844761649f24a4e9bc14861216b405464b8da83e1745","target":"record","created_at":"2026-05-18T00:36:00Z","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":"7551c24d32bb38f010c079499c0e4104d3d3f5aa62307780677cdeda9319dfb4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-09-05T15:32:32Z","title_canon_sha256":"722bd1761446da294571d3397066b467b9ea83e62dda1b4b76a0bf3ea35334ac"},"schema_version":"1.0","source":{"id":"1709.01456","kind":"arxiv","version":1}},"canonical_sha256":"3894578af183dbf36340de135b4c7662d9902e99330201affca6a761c0d9037f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3894578af183dbf36340de135b4c7662d9902e99330201affca6a761c0d9037f","first_computed_at":"2026-05-18T00:36:00.041992Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:00.041992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JJ1UnQxNtPCnbK8TaXf+zcP+G0LVNo4K+P8wD3w2yAGrfxo7QDnW2MIY4NXT50PxkCdDkT7gVo1LndfsP0h9Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:00.042493Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.01456","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a37a788538b6f64469d3844761649f24a4e9bc14861216b405464b8da83e1745","sha256:55a9bf148168c1746c68a08a9979e077c3e5c1adbf00847ca108048888b7ade5"],"state_sha256":"26566c13a5bd4a3e495f5853c28d9d1907d84f8897735973fbca72512e3d8ee4"}