{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:F3MROQ75IGKLHKIBMQKE55DKT4","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":"b9e9049fbe920e88ea1a0520f960565c3b676aebdb426d5c9c9e6b54ba8ac39d","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-07-30T05:03:59Z","title_canon_sha256":"0014706eff7399b3d8ec86cd87fa800e6e0c8e1e15350bec35b084c6c2cea09a"},"schema_version":"1.0","source":{"id":"1407.7942","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.7942","created_at":"2026-05-18T02:46:14Z"},{"alias_kind":"arxiv_version","alias_value":"1407.7942v1","created_at":"2026-05-18T02:46:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.7942","created_at":"2026-05-18T02:46:14Z"},{"alias_kind":"pith_short_12","alias_value":"F3MROQ75IGKL","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"F3MROQ75IGKLHKIB","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"F3MROQ75","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:650f710102181132bbae4be0d68a73d709bed3d6b6649b78f106920e141ca071","target":"graph","created_at":"2026-05-18T02:46:14Z","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 consider a class of higher dimensional differential systems in $\\mathbb R^n$ which have a two dimensional center manifold at the origin with a pair of pure imaginary eigenvalues. First we characterize the existence of either analytic or $C^\\infty$ inverse Jacobian multipliers of the systems around the origin, which is either a center or a focus on the center manifold. Later we study the cyclicity of the system at the origin through Hopf bifurcation by using the vanishing multiplicity of the inverse Jacobian multiplier.","authors_text":"Xiang Zhang","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-07-30T05:03:59Z","title":"Inverse Jacobian multipliers and Hopf bifurcation on center manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7942","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":"sha256:01bf20eba2ac758efa88180c453f9fad606a87805b5177a2b3fedc95fe55956b","target":"record","created_at":"2026-05-18T02:46:14Z","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":"b9e9049fbe920e88ea1a0520f960565c3b676aebdb426d5c9c9e6b54ba8ac39d","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-07-30T05:03:59Z","title_canon_sha256":"0014706eff7399b3d8ec86cd87fa800e6e0c8e1e15350bec35b084c6c2cea09a"},"schema_version":"1.0","source":{"id":"1407.7942","kind":"arxiv","version":1}},"canonical_sha256":"2ed91743fd4194b3a90164144ef46a9f1cf838d24a99ae8df506d0d94a0881f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ed91743fd4194b3a90164144ef46a9f1cf838d24a99ae8df506d0d94a0881f4","first_computed_at":"2026-05-18T02:46:14.052618Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:14.052618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gUCl1eumrgaGUsyZLFTt0uzDnOHKnC+DOZ3rD2GKKw5PymsgfA30AUhrxyKeEnTv57M2fqJ5ik7IuXBppWsoBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:14.053329Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.7942","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01bf20eba2ac758efa88180c453f9fad606a87805b5177a2b3fedc95fe55956b","sha256:650f710102181132bbae4be0d68a73d709bed3d6b6649b78f106920e141ca071"],"state_sha256":"99fd5fc791e533fe70e1fae5176721aad3b8b69c864dddcba3fdea5ddc0c7b3d"}