{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7KWCMOYDTGVD376TGDOT72SQHA","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":"9c0efd10cbbe2af89c8554b7dc567d422a08102df0767a8a19cc17eb4b76200f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-02-24T20:00:45Z","title_canon_sha256":"de5f68fa4ddeb3c41a01216c70d39435c82908243a6dddcc5706513153c3ff55"},"schema_version":"1.0","source":{"id":"1502.06928","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.06928","created_at":"2026-05-18T01:20:36Z"},{"alias_kind":"arxiv_version","alias_value":"1502.06928v2","created_at":"2026-05-18T01:20:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06928","created_at":"2026-05-18T01:20:36Z"},{"alias_kind":"pith_short_12","alias_value":"7KWCMOYDTGVD","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7KWCMOYDTGVD376T","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7KWCMOYD","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:580dc1ccbe490846fa9f574cb20c278a2d16722e1d7201f6514fd871f53985b8","target":"graph","created_at":"2026-05-18T01:20:36Z","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":"In this paper, we study degenerate Hopf bifurcations in a class of parametrized retarded functional differential equations. Specifically, we are interested in the case where the eigenvalue crossing condition of the classical Hopf bifurcation theorem is violated. Our approach is based on center manifold reduction and Poincare-Birkhoff normal forms, and a singularity theoretical classification of this degenerate Hopf bifurcation. Our results are then applied to a recently developed SIS model incorporating a delayed behavioral response. We show that the phenomenon of endemic bubbles, which is cha","authors_text":"Victor G. LeBlanc","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-02-24T20:00:45Z","title":"A degenerate Hopf bifurcation in retarded functional differential equations, and applications to endemic bubbles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06928","kind":"arxiv","version":2},"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:ccbcc8dcadce6a1c1fc971b38190754913f73af620684bfeeb31f1478866f142","target":"record","created_at":"2026-05-18T01:20:36Z","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":"9c0efd10cbbe2af89c8554b7dc567d422a08102df0767a8a19cc17eb4b76200f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-02-24T20:00:45Z","title_canon_sha256":"de5f68fa4ddeb3c41a01216c70d39435c82908243a6dddcc5706513153c3ff55"},"schema_version":"1.0","source":{"id":"1502.06928","kind":"arxiv","version":2}},"canonical_sha256":"faac263b0399aa3dffd330dd3fea50383e20ef1a8d9b6be66f53ee102691dc9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"faac263b0399aa3dffd330dd3fea50383e20ef1a8d9b6be66f53ee102691dc9c","first_computed_at":"2026-05-18T01:20:36.810134Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:36.810134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4+rcK5K01aytBa3tg84kNRuKXfGp4rOLzzrJ98g0Vnjih7Pi5OhNPge+ISzK9DLl58AZXmBMPRxFEsaQ6+i4CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:36.810601Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.06928","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ccbcc8dcadce6a1c1fc971b38190754913f73af620684bfeeb31f1478866f142","sha256:580dc1ccbe490846fa9f574cb20c278a2d16722e1d7201f6514fd871f53985b8"],"state_sha256":"bd75ef8fd8b2e5f8229c60251ed68fdb5e98fef13433911e4a038df174a7acb5"}