{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XD7MVG75Y37RTF7BRFFTXPHHHP","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":"3350f1055302a1b8871dbd81725d609ad4dd5885dbf66e191358521f17d346a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-03-06T17:51:44Z","title_canon_sha256":"68a571a8ebb168b136a2052984441be9d73c38dbb3fa654c4532fc9d44f98417"},"schema_version":"1.0","source":{"id":"1403.1511","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.1511","created_at":"2026-05-18T02:56:58Z"},{"alias_kind":"arxiv_version","alias_value":"1403.1511v1","created_at":"2026-05-18T02:56:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.1511","created_at":"2026-05-18T02:56:58Z"},{"alias_kind":"pith_short_12","alias_value":"XD7MVG75Y37R","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XD7MVG75Y37RTF7B","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XD7MVG75","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:ed4dad512afb39dd8efbe14a55412365122a66c047d5bd8959076531aaa388c7","target":"graph","created_at":"2026-05-18T02:56:58Z","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":"The generalized Floquet exponent and the attractiveness portrait (or A-portrait for short) of the attractor and of the smallest invariant closed set are suggested to be used for the study of dynamical systems. Based on the A-portrait, some simple structures hidden in a complicated attractor may emerge from an attractor with complicated structure. The hidden structure plays important role in the bifurcation phenomena of the invariant sets. The examples of A-portraits for the Van der Pol limit cycle, for Lorenz attractor, for the closed limit orbits of different rotation numbers and complicated ","authors_text":"Keying Guan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-03-06T17:51:44Z","title":"Generalized Floquet Exponent, Attractiveness Portrait and Structure Hidden in an Attractor"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1511","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":"sha256:8b45816e53d2c29edf478b334d2053e6ee3cee0b1c1e5bc9ce0c9e865c683796","target":"record","created_at":"2026-05-18T02:56:58Z","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":"3350f1055302a1b8871dbd81725d609ad4dd5885dbf66e191358521f17d346a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-03-06T17:51:44Z","title_canon_sha256":"68a571a8ebb168b136a2052984441be9d73c38dbb3fa654c4532fc9d44f98417"},"schema_version":"1.0","source":{"id":"1403.1511","kind":"arxiv","version":1}},"canonical_sha256":"b8feca9bfdc6ff1997e1894b3bbce73bcd9825891b21748cdcfb217f72b917ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8feca9bfdc6ff1997e1894b3bbce73bcd9825891b21748cdcfb217f72b917ab","first_computed_at":"2026-05-18T02:56:58.884512Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:58.884512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iwtEteSHC2GDsyrGxfPfwMmrDNJF9MSClQ/iNiBq7jV9G3L0TnYxnUjNlT6iNa2TPqrdPyEsLbsb9ev2L7ouCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:58.885091Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.1511","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b45816e53d2c29edf478b334d2053e6ee3cee0b1c1e5bc9ce0c9e865c683796","sha256:ed4dad512afb39dd8efbe14a55412365122a66c047d5bd8959076531aaa388c7"],"state_sha256":"9aa1ac862cdb4d43637d2e46d084396754a40617d746cabfb927a6b20c35ef2a"}