{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:NQW4IQ5YFGNONHRM5QFCON3IQL","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":"54e6b78ec3d45f0ba29e424bbbb03e4cbb5d77a68a83dbecfaffb2cdcbbc7436","cross_cats_sorted":["cs.SY","eess.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-19T13:33:25Z","title_canon_sha256":"62e8ed2ec844f404bfc16cf99f0d3c06b51de8651fc86b3fe998e298f4785ac9"},"schema_version":"1.0","source":{"id":"1908.07996","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.07996","created_at":"2026-07-05T00:27:32Z"},{"alias_kind":"arxiv_version","alias_value":"1908.07996v3","created_at":"2026-07-05T00:27:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07996","created_at":"2026-07-05T00:27:32Z"},{"alias_kind":"pith_short_12","alias_value":"NQW4IQ5YFGNO","created_at":"2026-07-05T00:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"NQW4IQ5YFGNONHRM","created_at":"2026-07-05T00:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"NQW4IQ5Y","created_at":"2026-07-05T00:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:5f270ba6424e8ad739768b1feb1e5de47073993d9a344c9ddd64f7c1a71aea6b","target":"graph","created_at":"2026-07-05T00:27:32Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.07996/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The present paper addresses the swing equation with additional delayed damping as an example for pendulum-like systems. In this context, it is proved that recurring sub- and supercritical Hopf bifurcations occur if time delay is increased. To this end, a general formula for the first Lyapunov coefficient in second order systems with additional delayed damping and delay-free nonlinearity is given. In so far the paper extends results about stability switching of equilibria in linear time delay systems from Cooke and Grossman. In addition to the analytical results, periodic solutions are numerica","authors_text":"Lutz Gr\\\"oll, Tessina H. Scholl, Veit Hagenmeyer","cross_cats":["cs.SY","eess.SY"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-19T13:33:25Z","title":"Time Delay in the Swing Equation: A Variety of Bifurcations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07996","kind":"arxiv","version":3},"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":"sha256:3cc406352df9a36ebe4a3aea8820ddf285119d2d522ddca87656d747c3bed748","target":"record","created_at":"2026-07-05T00:27:32Z","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":"54e6b78ec3d45f0ba29e424bbbb03e4cbb5d77a68a83dbecfaffb2cdcbbc7436","cross_cats_sorted":["cs.SY","eess.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-19T13:33:25Z","title_canon_sha256":"62e8ed2ec844f404bfc16cf99f0d3c06b51de8651fc86b3fe998e298f4785ac9"},"schema_version":"1.0","source":{"id":"1908.07996","kind":"arxiv","version":3}},"canonical_sha256":"6c2dc443b8299ae69e2cec0a27376882dee1ce1f2f71f8d4f585338528300d70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c2dc443b8299ae69e2cec0a27376882dee1ce1f2f71f8d4f585338528300d70","first_computed_at":"2026-07-05T00:27:32.552813Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:27:32.552813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UjxvT6EvOgbkhJIHXL4xYLSUFd8Gcb/y60j0VMG+/eKrVYoS6+u+reQjONtDqUSx7YTsVIK+5uVXwIWlrzTDCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:27:32.553352Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.07996","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3cc406352df9a36ebe4a3aea8820ddf285119d2d522ddca87656d747c3bed748","sha256:5f270ba6424e8ad739768b1feb1e5de47073993d9a344c9ddd64f7c1a71aea6b"],"state_sha256":"ca17a3fd7006fad849c810d6593a0fd87017c111de552c9af9a5218591b08c22"}