{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:LJ6H3XPM32U4HRZAMPA7ZTNEAU","short_pith_number":"pith:LJ6H3XPM","canonical_record":{"source":{"id":"1808.10470","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-08-30T18:05:26Z","cross_cats_sorted":[],"title_canon_sha256":"738dce6e12c96ae2a9d4ba9e753feec5b954b2e38383e4ec95e0aa2f06409189","abstract_canon_sha256":"4b862f0a7a192b7be4189b637309c35813870dc7a97cb0c4dda5c5e3e5596c6d"},"schema_version":"1.0"},"canonical_sha256":"5a7c7dddecdea9c3c72063c1fccda40538adc6a988a7d9a8eeabf6a09cd2e74a","source":{"kind":"arxiv","id":"1808.10470","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.10470","created_at":"2026-05-18T00:06:45Z"},{"alias_kind":"arxiv_version","alias_value":"1808.10470v1","created_at":"2026-05-18T00:06:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.10470","created_at":"2026-05-18T00:06:45Z"},{"alias_kind":"pith_short_12","alias_value":"LJ6H3XPM32U4","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LJ6H3XPM32U4HRZA","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LJ6H3XPM","created_at":"2026-05-18T12:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:LJ6H3XPM32U4HRZAMPA7ZTNEAU","target":"record","payload":{"canonical_record":{"source":{"id":"1808.10470","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-08-30T18:05:26Z","cross_cats_sorted":[],"title_canon_sha256":"738dce6e12c96ae2a9d4ba9e753feec5b954b2e38383e4ec95e0aa2f06409189","abstract_canon_sha256":"4b862f0a7a192b7be4189b637309c35813870dc7a97cb0c4dda5c5e3e5596c6d"},"schema_version":"1.0"},"canonical_sha256":"5a7c7dddecdea9c3c72063c1fccda40538adc6a988a7d9a8eeabf6a09cd2e74a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:45.593686Z","signature_b64":"eqIBU+Ks8wLmE+ZI5bYQogAPIz5euv9ZNdINvIxNBTxP3PKg8HTgkW3dArGUgxOCNY6RVP5Qnbf7DB/nLkWVBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a7c7dddecdea9c3c72063c1fccda40538adc6a988a7d9a8eeabf6a09cd2e74a","last_reissued_at":"2026-05-18T00:06:45.593147Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:45.593147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.10470","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":"2026-05-18T00:06:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"clXCiQJpZYBkoH/PzFOuwBXd4sQnT8LkF0Yrsewu7xEXpZki+PC1eeoLmmXJ5YfwxL/k2GiHWApDXyzbQLqlCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T19:04:15.093566Z"},"content_sha256":"776c04dd272af4b7216dda22eebcd1bf5437f0e0a9d59233d8938bfe23f8c231","schema_version":"1.0","event_id":"sha256:776c04dd272af4b7216dda22eebcd1bf5437f0e0a9d59233d8938bfe23f8c231"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:LJ6H3XPM32U4HRZAMPA7ZTNEAU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On RAC Drawings of Graphs with one Bend per Edge","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Henry F\\\"orster, Michael A. Bekos, Michael Kaufmann, Patrizio Angelini","submitted_at":"2018-08-30T18:05:26Z","abstract_excerpt":"A k-bend right-angle-crossing drawing or (k-bend RAC drawing}, for short) of a graph is a polyline drawing where each edge has at most k bends and the angles formed at the crossing points of the edges are 90 degrees. Accordingly, a graph that admits a k-bend RAC drawing is referred to as k-bend right-angle-crossing graph (or k-bend RAC, for short).\n  In this paper, we continue the study of the maximum edge-density of 1-bend RAC graphs. We show that an n-vertex 1-bend RAC graph cannot have more than $5.5n-O(1)$ edges. We also demonstrate that there exist infinitely many n-vertex 1-bend RAC grap"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.10470","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":"2026-05-18T00:06:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"An59is3f/jL3PlVRg3A1W0Hx2uLPHhXE0Dcr6JGJeCQLvZ1GqrNDXzd4yVUDGYIWXfaJauR/GyTGtS9rYgDYCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T19:04:15.094024Z"},"content_sha256":"fc2e941d95175bc3e3c489dfcd9784694cb6601c38e430ee49ade9414dbe6cbf","schema_version":"1.0","event_id":"sha256:fc2e941d95175bc3e3c489dfcd9784694cb6601c38e430ee49ade9414dbe6cbf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LJ6H3XPM32U4HRZAMPA7ZTNEAU/bundle.json","state_url":"https://pith.science/pith/LJ6H3XPM32U4HRZAMPA7ZTNEAU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LJ6H3XPM32U4HRZAMPA7ZTNEAU/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":"2026-05-29T19:04:15Z","links":{"resolver":"https://pith.science/pith/LJ6H3XPM32U4HRZAMPA7ZTNEAU","bundle":"https://pith.science/pith/LJ6H3XPM32U4HRZAMPA7ZTNEAU/bundle.json","state":"https://pith.science/pith/LJ6H3XPM32U4HRZAMPA7ZTNEAU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LJ6H3XPM32U4HRZAMPA7ZTNEAU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LJ6H3XPM32U4HRZAMPA7ZTNEAU","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":"4b862f0a7a192b7be4189b637309c35813870dc7a97cb0c4dda5c5e3e5596c6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-08-30T18:05:26Z","title_canon_sha256":"738dce6e12c96ae2a9d4ba9e753feec5b954b2e38383e4ec95e0aa2f06409189"},"schema_version":"1.0","source":{"id":"1808.10470","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.10470","created_at":"2026-05-18T00:06:45Z"},{"alias_kind":"arxiv_version","alias_value":"1808.10470v1","created_at":"2026-05-18T00:06:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.10470","created_at":"2026-05-18T00:06:45Z"},{"alias_kind":"pith_short_12","alias_value":"LJ6H3XPM32U4","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LJ6H3XPM32U4HRZA","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LJ6H3XPM","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:fc2e941d95175bc3e3c489dfcd9784694cb6601c38e430ee49ade9414dbe6cbf","target":"graph","created_at":"2026-05-18T00:06:45Z","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":"A k-bend right-angle-crossing drawing or (k-bend RAC drawing}, for short) of a graph is a polyline drawing where each edge has at most k bends and the angles formed at the crossing points of the edges are 90 degrees. Accordingly, a graph that admits a k-bend RAC drawing is referred to as k-bend right-angle-crossing graph (or k-bend RAC, for short).\n  In this paper, we continue the study of the maximum edge-density of 1-bend RAC graphs. We show that an n-vertex 1-bend RAC graph cannot have more than $5.5n-O(1)$ edges. We also demonstrate that there exist infinitely many n-vertex 1-bend RAC grap","authors_text":"Henry F\\\"orster, Michael A. Bekos, Michael Kaufmann, Patrizio Angelini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-08-30T18:05:26Z","title":"On RAC Drawings of Graphs with one Bend per Edge"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.10470","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":"sha256:776c04dd272af4b7216dda22eebcd1bf5437f0e0a9d59233d8938bfe23f8c231","target":"record","created_at":"2026-05-18T00:06:45Z","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":"4b862f0a7a192b7be4189b637309c35813870dc7a97cb0c4dda5c5e3e5596c6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-08-30T18:05:26Z","title_canon_sha256":"738dce6e12c96ae2a9d4ba9e753feec5b954b2e38383e4ec95e0aa2f06409189"},"schema_version":"1.0","source":{"id":"1808.10470","kind":"arxiv","version":1}},"canonical_sha256":"5a7c7dddecdea9c3c72063c1fccda40538adc6a988a7d9a8eeabf6a09cd2e74a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a7c7dddecdea9c3c72063c1fccda40538adc6a988a7d9a8eeabf6a09cd2e74a","first_computed_at":"2026-05-18T00:06:45.593147Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:45.593147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eqIBU+Ks8wLmE+ZI5bYQogAPIz5euv9ZNdINvIxNBTxP3PKg8HTgkW3dArGUgxOCNY6RVP5Qnbf7DB/nLkWVBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:45.593686Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.10470","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:776c04dd272af4b7216dda22eebcd1bf5437f0e0a9d59233d8938bfe23f8c231","sha256:fc2e941d95175bc3e3c489dfcd9784694cb6601c38e430ee49ade9414dbe6cbf"],"state_sha256":"268baa33e2446bab8c383760fb048c9e265b023d2dfca4dd39014b82f701658e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Apq/SMvOxD2eEMK/+0DZQCJY6jT5nL+K7KT4E38ayvu5CfoSBFx+yPJLJHXcgmO39SwTVR+Mpl9NpJwy06aaAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T19:04:15.096165Z","bundle_sha256":"5c2e724109b41729a2dcf1481e1674ffbc8ad1d7e5b2af36782e0a89f40d39dc"}}