{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:LLOJF5LZOX6ZVGJN4J3WHSB22W","short_pith_number":"pith:LLOJF5LZ","canonical_record":{"source":{"id":"1312.3538","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-12-12T16:34:10Z","cross_cats_sorted":[],"title_canon_sha256":"4785cf2ea4c5a23c6aebc4fd5d8da4a6ca19a4eb95d45f7a608a32f9bfe0004d","abstract_canon_sha256":"d773edfe81127afc79bab0480160ffe6359452f7cfa24729bf29c82f6c219b82"},"schema_version":"1.0"},"canonical_sha256":"5adc92f57975fd9a992de27763c83ad59be63a37f901823ceaea8783510e2487","source":{"kind":"arxiv","id":"1312.3538","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.3538","created_at":"2026-05-18T03:04:50Z"},{"alias_kind":"arxiv_version","alias_value":"1312.3538v1","created_at":"2026-05-18T03:04:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.3538","created_at":"2026-05-18T03:04:50Z"},{"alias_kind":"pith_short_12","alias_value":"LLOJF5LZOX6Z","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LLOJF5LZOX6ZVGJN","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LLOJF5LZ","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:LLOJF5LZOX6ZVGJN4J3WHSB22W","target":"record","payload":{"canonical_record":{"source":{"id":"1312.3538","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-12-12T16:34:10Z","cross_cats_sorted":[],"title_canon_sha256":"4785cf2ea4c5a23c6aebc4fd5d8da4a6ca19a4eb95d45f7a608a32f9bfe0004d","abstract_canon_sha256":"d773edfe81127afc79bab0480160ffe6359452f7cfa24729bf29c82f6c219b82"},"schema_version":"1.0"},"canonical_sha256":"5adc92f57975fd9a992de27763c83ad59be63a37f901823ceaea8783510e2487","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:50.636762Z","signature_b64":"v2SExNEyiLBF10RcjvhuryiVLoKkzeRQvQRud0rIwBE/6zJCVpX/ddvTxEqWNr1K33DOYDHpVoTS0RIZPzdlBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5adc92f57975fd9a992de27763c83ad59be63a37f901823ceaea8783510e2487","last_reissued_at":"2026-05-18T03:04:50.635981Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:50.635981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.3538","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":"2026-05-18T03:04:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vrvoW439SOjTSI0ttOZhNblq6kW9tX4g1Ond97DB9XpKdOVzcdaYgY/4PlLrDSFEyZ0BOUlWNC2w2rusnDE2Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:58:30.650628Z"},"content_sha256":"94a9fccf0d68802e9826f5afc773a20fa500fdf3fa8a5efbe0b7ea6e0af4857f","schema_version":"1.0","event_id":"sha256:94a9fccf0d68802e9826f5afc773a20fa500fdf3fa8a5efbe0b7ea6e0af4857f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:LLOJF5LZOX6ZVGJN4J3WHSB22W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Smooth Orthogonal Drawings of Planar Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Alexander Wolff, Md. Jawaherul Alam, Michael A. Bekos, Michael Kaufmann, Philipp Kindermann, Stephen G. Kobourov","submitted_at":"2013-12-12T16:34:10Z","abstract_excerpt":"In \\emph{smooth orthogonal layouts} of planar graphs, every edge is an alternating sequence of axis-aligned segments and circular arcs with common axis-aligned tangents. In this paper, we study the problem of finding smooth orthogonal layouts of low \\emph{edge complexity}, that is, with few segments per edge. We say that a graph has \\emph{smooth complexity} k---for short, an SC_k-layout---if it admits a smooth orthogonal drawing of edge complexity at most $k$.\n  Our main result is that every 4-planar graph has an SC_2-layout. While our drawings may have super-polynomial area, we show that, for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3538","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":"2026-05-18T03:04:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rN1NadbGlcfhW9cxRA2z9DsQ7sWDTCVKN/wTUHlQyxoF9+7AqoJReMf/6yIYXEhJg2xNvbNGbLuTOqIQFjAUCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:58:30.650989Z"},"content_sha256":"18a19573823c8a75bfe4ef65c325948d3b2ed1c4b241397274c662a7cab6cd72","schema_version":"1.0","event_id":"sha256:18a19573823c8a75bfe4ef65c325948d3b2ed1c4b241397274c662a7cab6cd72"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LLOJF5LZOX6ZVGJN4J3WHSB22W/bundle.json","state_url":"https://pith.science/pith/LLOJF5LZOX6ZVGJN4J3WHSB22W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LLOJF5LZOX6ZVGJN4J3WHSB22W/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":"2026-05-28T01:58:30Z","links":{"resolver":"https://pith.science/pith/LLOJF5LZOX6ZVGJN4J3WHSB22W","bundle":"https://pith.science/pith/LLOJF5LZOX6ZVGJN4J3WHSB22W/bundle.json","state":"https://pith.science/pith/LLOJF5LZOX6ZVGJN4J3WHSB22W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LLOJF5LZOX6ZVGJN4J3WHSB22W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LLOJF5LZOX6ZVGJN4J3WHSB22W","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":"d773edfe81127afc79bab0480160ffe6359452f7cfa24729bf29c82f6c219b82","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-12-12T16:34:10Z","title_canon_sha256":"4785cf2ea4c5a23c6aebc4fd5d8da4a6ca19a4eb95d45f7a608a32f9bfe0004d"},"schema_version":"1.0","source":{"id":"1312.3538","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.3538","created_at":"2026-05-18T03:04:50Z"},{"alias_kind":"arxiv_version","alias_value":"1312.3538v1","created_at":"2026-05-18T03:04:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.3538","created_at":"2026-05-18T03:04:50Z"},{"alias_kind":"pith_short_12","alias_value":"LLOJF5LZOX6Z","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LLOJF5LZOX6ZVGJN","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LLOJF5LZ","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:18a19573823c8a75bfe4ef65c325948d3b2ed1c4b241397274c662a7cab6cd72","target":"graph","created_at":"2026-05-18T03:04:50Z","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":"In \\emph{smooth orthogonal layouts} of planar graphs, every edge is an alternating sequence of axis-aligned segments and circular arcs with common axis-aligned tangents. In this paper, we study the problem of finding smooth orthogonal layouts of low \\emph{edge complexity}, that is, with few segments per edge. We say that a graph has \\emph{smooth complexity} k---for short, an SC_k-layout---if it admits a smooth orthogonal drawing of edge complexity at most $k$.\n  Our main result is that every 4-planar graph has an SC_2-layout. While our drawings may have super-polynomial area, we show that, for","authors_text":"Alexander Wolff, Md. Jawaherul Alam, Michael A. Bekos, Michael Kaufmann, Philipp Kindermann, Stephen G. Kobourov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-12-12T16:34:10Z","title":"Smooth Orthogonal Drawings of Planar Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3538","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":"sha256:94a9fccf0d68802e9826f5afc773a20fa500fdf3fa8a5efbe0b7ea6e0af4857f","target":"record","created_at":"2026-05-18T03:04:50Z","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":"d773edfe81127afc79bab0480160ffe6359452f7cfa24729bf29c82f6c219b82","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-12-12T16:34:10Z","title_canon_sha256":"4785cf2ea4c5a23c6aebc4fd5d8da4a6ca19a4eb95d45f7a608a32f9bfe0004d"},"schema_version":"1.0","source":{"id":"1312.3538","kind":"arxiv","version":1}},"canonical_sha256":"5adc92f57975fd9a992de27763c83ad59be63a37f901823ceaea8783510e2487","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5adc92f57975fd9a992de27763c83ad59be63a37f901823ceaea8783510e2487","first_computed_at":"2026-05-18T03:04:50.635981Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:04:50.635981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v2SExNEyiLBF10RcjvhuryiVLoKkzeRQvQRud0rIwBE/6zJCVpX/ddvTxEqWNr1K33DOYDHpVoTS0RIZPzdlBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:04:50.636762Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.3538","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94a9fccf0d68802e9826f5afc773a20fa500fdf3fa8a5efbe0b7ea6e0af4857f","sha256:18a19573823c8a75bfe4ef65c325948d3b2ed1c4b241397274c662a7cab6cd72"],"state_sha256":"74bdda9513a2f751cf24dc90d59cd9ce116a65b685594c69b46945be67e111fd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P9w5XiJq9604BVfihG9aZ26pHSbS3neQuk44ajCXr1ppY3wBM1tbmHjrG/WWh/Nc2qHzZ3/yxPdZFBmxIF7YDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T01:58:30.652982Z","bundle_sha256":"0d4f3f34b69e8bb9264fd1f9fcb44b277de9ef669798d36e4a48273bb42a96e8"}}