{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:UL2Q2Q5T26VYUNEJJLC2GR34CJ","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":"9eaf35b99e26f09fba7c73a9ea3cda2d60e2e417f7d25eae9d2009c81ee90616","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-07-02T20:53:41Z","title_canon_sha256":"c6ae3facb8915a46a66d1247c7bcc96863dc636470fa3a3ad937c4cbe259c916"},"schema_version":"1.0","source":{"id":"1907.01630","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.01630","created_at":"2026-05-17T23:41:35Z"},{"alias_kind":"arxiv_version","alias_value":"1907.01630v1","created_at":"2026-05-17T23:41:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.01630","created_at":"2026-05-17T23:41:35Z"},{"alias_kind":"pith_short_12","alias_value":"UL2Q2Q5T26VY","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"UL2Q2Q5T26VYUNEJ","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"UL2Q2Q5T","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:a9df988984994b839f955af5244f7a14f912d4995f002e24eccadd56c4ae247d","target":"graph","created_at":"2026-05-17T23:41:35Z","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":"Given a planar digraph $G$ and a positive even integer $k$, an embedding of $G$ in the plane is k-modal, if every vertex of $G$ is incident to at most $k$ pairs of consecutive edges with opposite orientations, i.e., the incoming and the outgoing edges at each vertex are grouped by the embedding into at most k sets of consecutive edges with the same orientation. In this paper, we study the $k$-Modality problem, which asks for the existence of a $k$-modal embedding of a planar digraph. This combinatorial problem is at the very core of a variety of constrained embedding questions for planar digra","authors_text":"Giordano Da Lozzo, Juan Jose Besa, Michael T. Goodrich","cross_cats":["cs.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-07-02T20:53:41Z","title":"Computing k-Modal Embeddings of Planar Digraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.01630","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:d8f12b81d886529a3391175f7ca75de705ce54d32683721c4dc3d407186010d4","target":"record","created_at":"2026-05-17T23:41:35Z","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":"9eaf35b99e26f09fba7c73a9ea3cda2d60e2e417f7d25eae9d2009c81ee90616","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-07-02T20:53:41Z","title_canon_sha256":"c6ae3facb8915a46a66d1247c7bcc96863dc636470fa3a3ad937c4cbe259c916"},"schema_version":"1.0","source":{"id":"1907.01630","kind":"arxiv","version":1}},"canonical_sha256":"a2f50d43b3d7ab8a34894ac5a3477c127487d6e3ff29f0d0eca25f2ac08b84de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2f50d43b3d7ab8a34894ac5a3477c127487d6e3ff29f0d0eca25f2ac08b84de","first_computed_at":"2026-05-17T23:41:35.713880Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:35.713880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RK/hgZeZQ4FNg6HFMgcTyIsgXsBR58/dN6MogADJeKxGbx3Y6Mg90YRmV8yfr4VG/7H9UxGgk3Bf0MVx8DSFAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:35.714654Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.01630","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8f12b81d886529a3391175f7ca75de705ce54d32683721c4dc3d407186010d4","sha256:a9df988984994b839f955af5244f7a14f912d4995f002e24eccadd56c4ae247d"],"state_sha256":"99c01842f4f703720da249a56ead6838a366afa349ee340f700a3dccab0922f6"}