{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:HO4KFXAAFBRGJXWRJJPBOIUAJD","short_pith_number":"pith:HO4KFXAA","canonical_record":{"source":{"id":"1512.04866","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-12-15T17:23:50Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"f787e6f28e4975a6fd4c6ec82737c16d0b718e1ecf71b40a108d189093383417","abstract_canon_sha256":"eb0e15ec012a5c8bf2aff468c2e830d79b1abd34a460e14283b3a602dc7bc146"},"schema_version":"1.0"},"canonical_sha256":"3bb8a2dc00286264ded14a5e17228048e45942cbab6a68c34e6a501d64a8d5a8","source":{"kind":"arxiv","id":"1512.04866","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.04866","created_at":"2026-05-18T01:24:15Z"},{"alias_kind":"arxiv_version","alias_value":"1512.04866v1","created_at":"2026-05-18T01:24:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04866","created_at":"2026-05-18T01:24:15Z"},{"alias_kind":"pith_short_12","alias_value":"HO4KFXAAFBRG","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HO4KFXAAFBRGJXWR","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HO4KFXAA","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:HO4KFXAAFBRGJXWRJJPBOIUAJD","target":"record","payload":{"canonical_record":{"source":{"id":"1512.04866","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-12-15T17:23:50Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"f787e6f28e4975a6fd4c6ec82737c16d0b718e1ecf71b40a108d189093383417","abstract_canon_sha256":"eb0e15ec012a5c8bf2aff468c2e830d79b1abd34a460e14283b3a602dc7bc146"},"schema_version":"1.0"},"canonical_sha256":"3bb8a2dc00286264ded14a5e17228048e45942cbab6a68c34e6a501d64a8d5a8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:15.238887Z","signature_b64":"OT7Oyrxf78D9j055X8jcbWSEqARqvj8uX1sACZQ18EpITbGGKbqxLJh98u4dOBDMj+aJV8Xw+IoCc54fF85GBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3bb8a2dc00286264ded14a5e17228048e45942cbab6a68c34e6a501d64a8d5a8","last_reissued_at":"2026-05-18T01:24:15.238130Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:15.238130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.04866","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":"2026-05-18T01:24:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0zB+B4sCbkmyvWNVNfrz70k83eHdEdrTopUGzcUFd990ksLKionF+BHL9pWFvut9zQx+BHdqSPv62I0acnUpCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T00:36:28.409089Z"},"content_sha256":"59b18d20efd9114d57566e45dc1c283bcd887dc6e7879a69483581f6d4642943","schema_version":"1.0","event_id":"sha256:59b18d20efd9114d57566e45dc1c283bcd887dc6e7879a69483581f6d4642943"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:HO4KFXAAFBRGJXWRJJPBOIUAJD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Total Number of Bends for Planar Octilinear Drawings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"Michael A. Bekos, Michael Kaufmann, Robert Krug","submitted_at":"2015-12-15T17:23:50Z","abstract_excerpt":"An octilinear drawing of a planar graph is one in which each edge is drawn as a sequence of horizontal, vertical and diagonal at 45 degrees line-segments. For such drawings to be readable, special care is needed in order to keep the number of bends small. As the problem of finding planar octilinear drawings of minimum number of bends is NP-hard, in this paper we focus on upper and lower bounds. From a recent result of Keszegh et al. on the slope number of planar graphs, we can derive an upper bound of 4n-10 bends for 8-planar graphs with n vertices. We considerably improve this general bound a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04866","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":"2026-05-18T01:24:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gyj35vzA3c27oS+9pJNZlG2QGeYchSSlUCLhXb92wTzaORe9z/U3TQ0YN1MuLrg7sTnpIZNH9D2CZ11v7sdaDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T00:36:28.409456Z"},"content_sha256":"a70070463d93a7f4f27e0f2b94baa0f31edc446aeb4a16adb7610c6201a815ea","schema_version":"1.0","event_id":"sha256:a70070463d93a7f4f27e0f2b94baa0f31edc446aeb4a16adb7610c6201a815ea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HO4KFXAAFBRGJXWRJJPBOIUAJD/bundle.json","state_url":"https://pith.science/pith/HO4KFXAAFBRGJXWRJJPBOIUAJD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HO4KFXAAFBRGJXWRJJPBOIUAJD/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":"2026-05-28T00:36:28Z","links":{"resolver":"https://pith.science/pith/HO4KFXAAFBRGJXWRJJPBOIUAJD","bundle":"https://pith.science/pith/HO4KFXAAFBRGJXWRJJPBOIUAJD/bundle.json","state":"https://pith.science/pith/HO4KFXAAFBRGJXWRJJPBOIUAJD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HO4KFXAAFBRGJXWRJJPBOIUAJD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HO4KFXAAFBRGJXWRJJPBOIUAJD","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":"eb0e15ec012a5c8bf2aff468c2e830d79b1abd34a460e14283b3a602dc7bc146","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-12-15T17:23:50Z","title_canon_sha256":"f787e6f28e4975a6fd4c6ec82737c16d0b718e1ecf71b40a108d189093383417"},"schema_version":"1.0","source":{"id":"1512.04866","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.04866","created_at":"2026-05-18T01:24:15Z"},{"alias_kind":"arxiv_version","alias_value":"1512.04866v1","created_at":"2026-05-18T01:24:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04866","created_at":"2026-05-18T01:24:15Z"},{"alias_kind":"pith_short_12","alias_value":"HO4KFXAAFBRG","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HO4KFXAAFBRGJXWR","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HO4KFXAA","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:a70070463d93a7f4f27e0f2b94baa0f31edc446aeb4a16adb7610c6201a815ea","target":"graph","created_at":"2026-05-18T01:24:15Z","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":"An octilinear drawing of a planar graph is one in which each edge is drawn as a sequence of horizontal, vertical and diagonal at 45 degrees line-segments. For such drawings to be readable, special care is needed in order to keep the number of bends small. As the problem of finding planar octilinear drawings of minimum number of bends is NP-hard, in this paper we focus on upper and lower bounds. From a recent result of Keszegh et al. on the slope number of planar graphs, we can derive an upper bound of 4n-10 bends for 8-planar graphs with n vertices. We considerably improve this general bound a","authors_text":"Michael A. Bekos, Michael Kaufmann, Robert Krug","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-12-15T17:23:50Z","title":"On the Total Number of Bends for Planar Octilinear Drawings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04866","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":"sha256:59b18d20efd9114d57566e45dc1c283bcd887dc6e7879a69483581f6d4642943","target":"record","created_at":"2026-05-18T01:24:15Z","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":"eb0e15ec012a5c8bf2aff468c2e830d79b1abd34a460e14283b3a602dc7bc146","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-12-15T17:23:50Z","title_canon_sha256":"f787e6f28e4975a6fd4c6ec82737c16d0b718e1ecf71b40a108d189093383417"},"schema_version":"1.0","source":{"id":"1512.04866","kind":"arxiv","version":1}},"canonical_sha256":"3bb8a2dc00286264ded14a5e17228048e45942cbab6a68c34e6a501d64a8d5a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3bb8a2dc00286264ded14a5e17228048e45942cbab6a68c34e6a501d64a8d5a8","first_computed_at":"2026-05-18T01:24:15.238130Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:15.238130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OT7Oyrxf78D9j055X8jcbWSEqARqvj8uX1sACZQ18EpITbGGKbqxLJh98u4dOBDMj+aJV8Xw+IoCc54fF85GBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:15.238887Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.04866","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59b18d20efd9114d57566e45dc1c283bcd887dc6e7879a69483581f6d4642943","sha256:a70070463d93a7f4f27e0f2b94baa0f31edc446aeb4a16adb7610c6201a815ea"],"state_sha256":"2e0d3529e0211d70206a3d527fe6c47e9a3be5e8837a8fdfbf93d6ae8d3f52a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rLi79TVuwFZaRN0r6T4tXsndXwnuLZE5rvaXCaY82DzB/C/rDXgUvkk6V6YCWM2rhjjaC3GYvoozaLwGMc2QAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T00:36:28.411432Z","bundle_sha256":"9215053d989263c3364b7b88f0d63dfdb894d404715edb951bc6f243e20d7b7a"}}