{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:SCFVWKKGZA6HZMLK5J2WN5RLAW","short_pith_number":"pith:SCFVWKKG","schema_version":"1.0","canonical_sha256":"908b5b2946c83c7cb16aea7566f62b05992f8c668d3794fddad5391adc722add","source":{"kind":"arxiv","id":"1911.02040","version":2},"attestation_state":"computed","paper":{"title":"Angle Covers: Algorithms and Complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.CG","authors_text":"Alexander Wolff, Ellen Gethner, Jack Spalding-Jamieson, William Evans","submitted_at":"2019-11-05T19:05:04Z","abstract_excerpt":"Consider a graph with a rotation system, namely, for every vertex, a circular ordering of the incident edges. Given such a graph, an angle cover maps every vertex to a pair of consecutive edges in the ordering -- an angle -- such that each edge participates in at least one such pair. We show that any graph of maximum degree 4 admits an angle cover, give a poly-time algorithm for deciding if a graph with no degree-3 vertices has an angle-cover, and prove that, given a graph of maximum degree 5, it is NP-hard to decide whether it admits an angle cover. We also consider extensions of the angle co"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1911.02040","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2019-11-05T19:05:04Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"f9d7dc219d6daa6f192206c2856623a4ac0d20f0fee3a0f51e29ead122dc4779","abstract_canon_sha256":"866ec2c540d399e71379dcd1888b2584b70935447ef60846b370e2641ee818ab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:59:56.135100Z","signature_b64":"qD5yJm264MTZCNbkx/d+ky4V/azuU0HAog3wDyo4N94WL0l9D6XAq/FDY7powSbxmZFKpzTqZMOT8AlTNmrWBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"908b5b2946c83c7cb16aea7566f62b05992f8c668d3794fddad5391adc722add","last_reissued_at":"2026-07-05T04:59:56.134751Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:59:56.134751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Angle Covers: Algorithms and Complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.CG","authors_text":"Alexander Wolff, Ellen Gethner, Jack Spalding-Jamieson, William Evans","submitted_at":"2019-11-05T19:05:04Z","abstract_excerpt":"Consider a graph with a rotation system, namely, for every vertex, a circular ordering of the incident edges. Given such a graph, an angle cover maps every vertex to a pair of consecutive edges in the ordering -- an angle -- such that each edge participates in at least one such pair. We show that any graph of maximum degree 4 admits an angle cover, give a poly-time algorithm for deciding if a graph with no degree-3 vertices has an angle-cover, and prove that, given a graph of maximum degree 5, it is NP-hard to decide whether it admits an angle cover. We also consider extensions of the angle co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.02040","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1911.02040/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1911.02040","created_at":"2026-07-05T04:59:56.134807+00:00"},{"alias_kind":"arxiv_version","alias_value":"1911.02040v2","created_at":"2026-07-05T04:59:56.134807+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.02040","created_at":"2026-07-05T04:59:56.134807+00:00"},{"alias_kind":"pith_short_12","alias_value":"SCFVWKKGZA6H","created_at":"2026-07-05T04:59:56.134807+00:00"},{"alias_kind":"pith_short_16","alias_value":"SCFVWKKGZA6HZMLK","created_at":"2026-07-05T04:59:56.134807+00:00"},{"alias_kind":"pith_short_8","alias_value":"SCFVWKKG","created_at":"2026-07-05T04:59:56.134807+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SCFVWKKGZA6HZMLK5J2WN5RLAW","json":"https://pith.science/pith/SCFVWKKGZA6HZMLK5J2WN5RLAW.json","graph_json":"https://pith.science/api/pith-number/SCFVWKKGZA6HZMLK5J2WN5RLAW/graph.json","events_json":"https://pith.science/api/pith-number/SCFVWKKGZA6HZMLK5J2WN5RLAW/events.json","paper":"https://pith.science/paper/SCFVWKKG"},"agent_actions":{"view_html":"https://pith.science/pith/SCFVWKKGZA6HZMLK5J2WN5RLAW","download_json":"https://pith.science/pith/SCFVWKKGZA6HZMLK5J2WN5RLAW.json","view_paper":"https://pith.science/paper/SCFVWKKG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1911.02040&json=true","fetch_graph":"https://pith.science/api/pith-number/SCFVWKKGZA6HZMLK5J2WN5RLAW/graph.json","fetch_events":"https://pith.science/api/pith-number/SCFVWKKGZA6HZMLK5J2WN5RLAW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SCFVWKKGZA6HZMLK5J2WN5RLAW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SCFVWKKGZA6HZMLK5J2WN5RLAW/action/storage_attestation","attest_author":"https://pith.science/pith/SCFVWKKGZA6HZMLK5J2WN5RLAW/action/author_attestation","sign_citation":"https://pith.science/pith/SCFVWKKGZA6HZMLK5J2WN5RLAW/action/citation_signature","submit_replication":"https://pith.science/pith/SCFVWKKGZA6HZMLK5J2WN5RLAW/action/replication_record"}},"created_at":"2026-07-05T04:59:56.134807+00:00","updated_at":"2026-07-05T04:59:56.134807+00:00"}