{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:HCKFPCXRQPN7GY2A3YJVWTDWML","short_pith_number":"pith:HCKFPCXR","canonical_record":{"source":{"id":"1709.01456","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-09-05T15:32:32Z","cross_cats_sorted":[],"title_canon_sha256":"722bd1761446da294571d3397066b467b9ea83e62dda1b4b76a0bf3ea35334ac","abstract_canon_sha256":"7551c24d32bb38f010c079499c0e4104d3d3f5aa62307780677cdeda9319dfb4"},"schema_version":"1.0"},"canonical_sha256":"3894578af183dbf36340de135b4c7662d9902e99330201affca6a761c0d9037f","source":{"kind":"arxiv","id":"1709.01456","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:HCKFPCXRQPN7GY2A3YJVWTDWML","target":"record","payload":{"canonical_record":{"source":{"id":"1709.01456","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2017-09-05T15:32:32Z","cross_cats_sorted":[],"title_canon_sha256":"722bd1761446da294571d3397066b467b9ea83e62dda1b4b76a0bf3ea35334ac","abstract_canon_sha256":"7551c24d32bb38f010c079499c0e4104d3d3f5aa62307780677cdeda9319dfb4"},"schema_version":"1.0"},"canonical_sha256":"3894578af183dbf36340de135b4c7662d9902e99330201affca6a761c0d9037f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:00.042493Z","signature_b64":"JJ1UnQxNtPCnbK8TaXf+zcP+G0LVNo4K+P8wD3w2yAGrfxo7QDnW2MIY4NXT50PxkCdDkT7gVo1LndfsP0h9Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3894578af183dbf36340de135b4c7662d9902e99330201affca6a761c0d9037f","last_reissued_at":"2026-05-18T00:36:00.041992Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:00.041992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.01456","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:36:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cockwGHTXREhm5GK1mjZOl9eU/3Jgs5gVy+/ss/oeCZRuwvmLdGISqc/aNVWH+dbyCRuKAcQBOrFAU2NMlNIDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:57:50.671449Z"},"content_sha256":"a37a788538b6f64469d3844761649f24a4e9bc14861216b405464b8da83e1745","schema_version":"1.0","event_id":"sha256:a37a788538b6f64469d3844761649f24a4e9bc14861216b405464b8da83e1745"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:HCKFPCXRQPN7GY2A3YJVWTDWML","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Improved Bounds for Drawing Trees on Fixed Points with L-shaped Edges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Anna Lubiw, Kshitij Jain, Martin Derka, Therese Biedl, Timothy M. Chan","submitted_at":"2017-09-05T15:32:32Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01456","kind":"arxiv","version":1},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:36:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bWxyuyYD9IUYxDuPNjf2ivzxCoxXcQEzWcWu74R5lJ3Ao60SQuf2TqjBHdcJKj3g7eSqaCODiwycQNF5LLx4CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:57:50.671799Z"},"content_sha256":"55a9bf148168c1746c68a08a9979e077c3e5c1adbf00847ca108048888b7ade5","schema_version":"1.0","event_id":"sha256:55a9bf148168c1746c68a08a9979e077c3e5c1adbf00847ca108048888b7ade5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HCKFPCXRQPN7GY2A3YJVWTDWML/bundle.json","state_url":"https://pith.science/pith/HCKFPCXRQPN7GY2A3YJVWTDWML/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HCKFPCXRQPN7GY2A3YJVWTDWML/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-31T02:57:50Z","links":{"resolver":"https://pith.science/pith/HCKFPCXRQPN7GY2A3YJVWTDWML","bundle":"https://pith.science/pith/HCKFPCXRQPN7GY2A3YJVWTDWML/bundle.json","state":"https://pith.science/pith/HCKFPCXRQPN7GY2A3YJVWTDWML/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HCKFPCXRQPN7GY2A3YJVWTDWML/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RNMTGE1Zsq6MbrLsqRQ8gdywL/LAAm0/BoT1o+xHQALhPAZhx/bGVYQKfxbloAdja56Q+IbDMtVi1D+hYZFqBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T02:57:50.673741Z","bundle_sha256":"2f7913b17cf79b3fbd460e09ec3219abd411e978bd867a4f1f6642d77a77e328"}}