{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:XDCPXNTRTQ3W3HUVHQC2FE33FR","short_pith_number":"pith:XDCPXNTR","canonical_record":{"source":{"id":"1408.5920","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"cs.DS","submitted_at":"2014-08-25T20:26:34Z","cross_cats_sorted":[],"title_canon_sha256":"21fd270eefbbc36c545a2e401e0c0bd64d2271f631632e5c65f207eb44faf954","abstract_canon_sha256":"2ac09d3728f4823f1ec7ee3176e5516f420e1ca8150bdba9229f049b21ff79b9"},"schema_version":"1.0"},"canonical_sha256":"b8c4fbb6719c376d9e953c05a2937b2c59df03a4ed2fa7802ac0d1a6e7e6da2a","source":{"kind":"arxiv","id":"1408.5920","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.5920","created_at":"2026-05-18T02:44:15Z"},{"alias_kind":"arxiv_version","alias_value":"1408.5920v1","created_at":"2026-05-18T02:44:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5920","created_at":"2026-05-18T02:44:15Z"},{"alias_kind":"pith_short_12","alias_value":"XDCPXNTRTQ3W","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XDCPXNTRTQ3W3HUV","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XDCPXNTR","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:XDCPXNTRTQ3W3HUVHQC2FE33FR","target":"record","payload":{"canonical_record":{"source":{"id":"1408.5920","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"cs.DS","submitted_at":"2014-08-25T20:26:34Z","cross_cats_sorted":[],"title_canon_sha256":"21fd270eefbbc36c545a2e401e0c0bd64d2271f631632e5c65f207eb44faf954","abstract_canon_sha256":"2ac09d3728f4823f1ec7ee3176e5516f420e1ca8150bdba9229f049b21ff79b9"},"schema_version":"1.0"},"canonical_sha256":"b8c4fbb6719c376d9e953c05a2937b2c59df03a4ed2fa7802ac0d1a6e7e6da2a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:15.866228Z","signature_b64":"tsAcHzmbCGLwNVC9MivOhQy9Wv4ioEBpzizhRv30z8ZgC/uwDJguYUyaSMXu4/3oSw+eW7axNO6jkBsaEOrgBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b8c4fbb6719c376d9e953c05a2937b2c59df03a4ed2fa7802ac0d1a6e7e6da2a","last_reissued_at":"2026-05-18T02:44:15.865630Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:15.865630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.5920","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":"2026-05-18T02:44:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+WdaxihUDH9/teteO1SXrOBSynrTDs8u7tevPcTt0OQ3iRnYNu+cchnhxqFO0WK73BYouG9JmPpdsbc0nJNgBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T07:59:11.550483Z"},"content_sha256":"2cc4774eb67bbedca3a4558c588be7764a23d399471f0afa52d5c700d02c51e5","schema_version":"1.0","event_id":"sha256:2cc4774eb67bbedca3a4558c588be7764a23d399471f0afa52d5c700d02c51e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:XDCPXNTRTQ3W3HUVHQC2FE33FR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Planar Octilinear Drawings with One Bend Per Edge","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Martin Gronemann, Michael A. Bekos, Michael Kaufmann, Robert Krug","submitted_at":"2014-08-25T20:26:34Z","abstract_excerpt":"In octilinear drawings of planar graphs, every edge is drawn as an alternating sequence of horizontal, vertical and diagonal ($45^\\circ$) line-segments. In this paper, we study octilinear drawings of low edge complexity, i.e., with few bends per edge. A $k$-planar graph is a planar graph in which each vertex has degree less or equal to $k$. In particular, we prove that every 4-planar graph admits a planar octilinear drawing with at most one bend per edge on an integer grid of size $O(n^2) \\times O(n)$. For 5-planar graphs, we prove that one bend per edge still suffices in order to construct pl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5920","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":"2026-05-18T02:44:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tDozBV2WkNhVFtPR4hC0EmCn/CWGPzWmBTbFACovJ10MR3VNW0xaDIc2iTXVGHFm7WplZJsu6EMJ4e9qQbDhAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T07:59:11.550828Z"},"content_sha256":"26c4125f1fab9e82b0036b7d6155107ba85cfdef40ffd267b6c9ba852f4f1a30","schema_version":"1.0","event_id":"sha256:26c4125f1fab9e82b0036b7d6155107ba85cfdef40ffd267b6c9ba852f4f1a30"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XDCPXNTRTQ3W3HUVHQC2FE33FR/bundle.json","state_url":"https://pith.science/pith/XDCPXNTRTQ3W3HUVHQC2FE33FR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XDCPXNTRTQ3W3HUVHQC2FE33FR/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":"2026-05-28T07:59:11Z","links":{"resolver":"https://pith.science/pith/XDCPXNTRTQ3W3HUVHQC2FE33FR","bundle":"https://pith.science/pith/XDCPXNTRTQ3W3HUVHQC2FE33FR/bundle.json","state":"https://pith.science/pith/XDCPXNTRTQ3W3HUVHQC2FE33FR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XDCPXNTRTQ3W3HUVHQC2FE33FR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XDCPXNTRTQ3W3HUVHQC2FE33FR","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":"2ac09d3728f4823f1ec7ee3176e5516f420e1ca8150bdba9229f049b21ff79b9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"cs.DS","submitted_at":"2014-08-25T20:26:34Z","title_canon_sha256":"21fd270eefbbc36c545a2e401e0c0bd64d2271f631632e5c65f207eb44faf954"},"schema_version":"1.0","source":{"id":"1408.5920","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.5920","created_at":"2026-05-18T02:44:15Z"},{"alias_kind":"arxiv_version","alias_value":"1408.5920v1","created_at":"2026-05-18T02:44:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5920","created_at":"2026-05-18T02:44:15Z"},{"alias_kind":"pith_short_12","alias_value":"XDCPXNTRTQ3W","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XDCPXNTRTQ3W3HUV","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XDCPXNTR","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:26c4125f1fab9e82b0036b7d6155107ba85cfdef40ffd267b6c9ba852f4f1a30","target":"graph","created_at":"2026-05-18T02:44:15Z","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 octilinear drawings of planar graphs, every edge is drawn as an alternating sequence of horizontal, vertical and diagonal ($45^\\circ$) line-segments. In this paper, we study octilinear drawings of low edge complexity, i.e., with few bends per edge. A $k$-planar graph is a planar graph in which each vertex has degree less or equal to $k$. In particular, we prove that every 4-planar graph admits a planar octilinear drawing with at most one bend per edge on an integer grid of size $O(n^2) \\times O(n)$. For 5-planar graphs, we prove that one bend per edge still suffices in order to construct pl","authors_text":"Martin Gronemann, Michael A. Bekos, Michael Kaufmann, Robert Krug","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"cs.DS","submitted_at":"2014-08-25T20:26:34Z","title":"Planar Octilinear Drawings with One Bend Per Edge"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5920","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":"sha256:2cc4774eb67bbedca3a4558c588be7764a23d399471f0afa52d5c700d02c51e5","target":"record","created_at":"2026-05-18T02:44:15Z","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":"2ac09d3728f4823f1ec7ee3176e5516f420e1ca8150bdba9229f049b21ff79b9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"cs.DS","submitted_at":"2014-08-25T20:26:34Z","title_canon_sha256":"21fd270eefbbc36c545a2e401e0c0bd64d2271f631632e5c65f207eb44faf954"},"schema_version":"1.0","source":{"id":"1408.5920","kind":"arxiv","version":1}},"canonical_sha256":"b8c4fbb6719c376d9e953c05a2937b2c59df03a4ed2fa7802ac0d1a6e7e6da2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8c4fbb6719c376d9e953c05a2937b2c59df03a4ed2fa7802ac0d1a6e7e6da2a","first_computed_at":"2026-05-18T02:44:15.865630Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:15.865630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tsAcHzmbCGLwNVC9MivOhQy9Wv4ioEBpzizhRv30z8ZgC/uwDJguYUyaSMXu4/3oSw+eW7axNO6jkBsaEOrgBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:15.866228Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.5920","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2cc4774eb67bbedca3a4558c588be7764a23d399471f0afa52d5c700d02c51e5","sha256:26c4125f1fab9e82b0036b7d6155107ba85cfdef40ffd267b6c9ba852f4f1a30"],"state_sha256":"2f5f3de6b2d7ce0726950713826087a1eebfac72f11c826a8260f9c4ae05d16b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VhdfURhk+vTDUQ+mYtPvIxSwf7hw4u13FNRsaHOW7m/1NFj/ut4RlDUAKkQ3mXyLOfboRrrYAZlEO+G4NSuKDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T07:59:11.552778Z","bundle_sha256":"5533d75690cde569809305c9b14ced2405ce25eff7bccfcb2c590d865d8abf98"}}