{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:TBP5VH5FSSDQPVO67JVXKXQMU3","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":"131209c18db7ce4ac954d2ebb7d76488b944e35048eb2a45cda48e6bfb2f547b","cross_cats_sorted":[],"license":"","primary_cat":"nlin.CD","submitted_at":"2004-06-16T04:03:39Z","title_canon_sha256":"3cc7e57f6bfc700cd56b571b847c3251357d557af50f17f1c7459bf498c1000e"},"schema_version":"1.0","source":{"id":"nlin/0406031","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nlin/0406031","created_at":"2026-05-18T01:08:49Z"},{"alias_kind":"arxiv_version","alias_value":"nlin/0406031v2","created_at":"2026-05-18T01:08:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nlin/0406031","created_at":"2026-05-18T01:08:49Z"},{"alias_kind":"pith_short_12","alias_value":"TBP5VH5FSSDQ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"TBP5VH5FSSDQPVO6","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"TBP5VH5F","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:3ef69b9f4fe761c563abe9bb11032a971b449ae0f69cf06ca2129f10f3813b4a","target":"graph","created_at":"2026-05-18T01:08:49Z","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":"This letter suggests a new way to investigate 3-D chaos in spatial and frequency domains simultaneously. After spatially decomposing the Lorenz attractor into two separate scrolls with peaked spectra and a 1-D discrete-time zero-crossing series with a wide-band spectrum, it is found that the Lorenz chaotic attractor has an inherent frequency uniquely determined by the three system parameters. This result implies that chaos in the Lorenz attractor is mainly exhibited when the trajectory crosses from one scroll to another, not within the two scrolls. This is also true for some other double-scrol","authors_text":"Gonzalo \\'Alvarez, Guanrong Chen, Jinhu L\\\"u, Shujun Li","cross_cats":[],"headline":"","license":"","primary_cat":"nlin.CD","submitted_at":"2004-06-16T04:03:39Z","title":"Inherent Frequency and Spatial Decomposition of the Lorenz Chaotic Attractor"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nlin/0406031","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:c2b05c595d5a80ae8f4d4c5024b0debafeb54468e20b51e6ede28ff342684c1f","target":"record","created_at":"2026-05-18T01:08:49Z","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":"131209c18db7ce4ac954d2ebb7d76488b944e35048eb2a45cda48e6bfb2f547b","cross_cats_sorted":[],"license":"","primary_cat":"nlin.CD","submitted_at":"2004-06-16T04:03:39Z","title_canon_sha256":"3cc7e57f6bfc700cd56b571b847c3251357d557af50f17f1c7459bf498c1000e"},"schema_version":"1.0","source":{"id":"nlin/0406031","kind":"arxiv","version":2}},"canonical_sha256":"985fda9fa5948707d5defa6b755e0ca6d3b8631174c7ad6139e9f3a26529d6f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"985fda9fa5948707d5defa6b755e0ca6d3b8631174c7ad6139e9f3a26529d6f7","first_computed_at":"2026-05-18T01:08:49.243330Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:49.243330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YXT3b1HizWTa6pk/fAWiqaoLnsPkdjVUZt3vnGr3ku6iP5UAogfPvdcx862yzGU1gQr2L2fLlpoDDAOxFnOSBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:49.244000Z","signed_message":"canonical_sha256_bytes"},"source_id":"nlin/0406031","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c2b05c595d5a80ae8f4d4c5024b0debafeb54468e20b51e6ede28ff342684c1f","sha256:3ef69b9f4fe761c563abe9bb11032a971b449ae0f69cf06ca2129f10f3813b4a"],"state_sha256":"b96d3201678e073275d28d83181351bc015323e38768b300416f526a4a1d057a"}