{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MBBQ5OIJIRCZ3MISVIHE76T4AF","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":"ca2a529da205fc93122aa9dbef959630532de22d92ae9af5acc8701e1bcc93b6","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-05-07T16:45:35Z","title_canon_sha256":"21a3fd372b5a9185ab1c01a70842927ac5a7404f2f3ddd08a70c1689162e42bd"},"schema_version":"1.0","source":{"id":"1305.1579","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.1579","created_at":"2026-05-18T03:26:21Z"},{"alias_kind":"arxiv_version","alias_value":"1305.1579v1","created_at":"2026-05-18T03:26:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1579","created_at":"2026-05-18T03:26:21Z"},{"alias_kind":"pith_short_12","alias_value":"MBBQ5OIJIRCZ","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"MBBQ5OIJIRCZ3MIS","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"MBBQ5OIJ","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:c0b4e3e0c58b26b0ba7f81f7cc50f3353c689805000f1a475dc79b83784b75ed","target":"graph","created_at":"2026-05-18T03:26:21Z","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":"Inspired by an example of Grebogi et al [1], we study a class of model systems which exhibit the full two-step scenario for the nonautonomous Hopf bifurcation, as proposed by Arnold [2]. The specific structure of these models allows a rigorous and thorough analysis of the bifurcation pattern. In particular, we show the existence of an invariant 'generalised torus' splitting off a previously stable central manifold after the second bifurcation point.\n  The scenario is described in two different settings. First, we consider deterministically forced models, which can be treated as continuous skew","authors_text":"Gerhard Keller, Tobias J\\\"ager, Vasso Anagnostopoulou","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-05-07T16:45:35Z","title":"A model for the nonautonomous Hopf bifurcation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1579","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:e02ce2cd7a96dd6c3c30d6e38d8b04583f6096e3f1b49f2835c01e7cd366e500","target":"record","created_at":"2026-05-18T03:26:21Z","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":"ca2a529da205fc93122aa9dbef959630532de22d92ae9af5acc8701e1bcc93b6","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-05-07T16:45:35Z","title_canon_sha256":"21a3fd372b5a9185ab1c01a70842927ac5a7404f2f3ddd08a70c1689162e42bd"},"schema_version":"1.0","source":{"id":"1305.1579","kind":"arxiv","version":1}},"canonical_sha256":"60430eb90944459db112aa0e4ffa7c0161bed3ca14118b8fb921b61932092653","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60430eb90944459db112aa0e4ffa7c0161bed3ca14118b8fb921b61932092653","first_computed_at":"2026-05-18T03:26:21.305411Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:21.305411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kZDd2cFryUYwUd3D37q83YPQCLutnXDYs9GuIzyFjk0Ztim5sfsP+h/rDZtSseYdVgqQiW6wkh8mGdoVBJOxCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:21.306252Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.1579","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e02ce2cd7a96dd6c3c30d6e38d8b04583f6096e3f1b49f2835c01e7cd366e500","sha256:c0b4e3e0c58b26b0ba7f81f7cc50f3353c689805000f1a475dc79b83784b75ed"],"state_sha256":"b04ee3d478d7ea07c7733cd56dc1a8019848e597938a6b9f8d9d7aad8d8c6784"}