{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:KQEVCKQ6RDXH4BOY6BBFT4ZOGH","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":"ccbaa9d86a4b3a337a399b42b981edd9b7aa652e9a6b7b1ddb203ea2342d1f34","cross_cats_sorted":["physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2010-02-23T12:25:59Z","title_canon_sha256":"f3ce3c62f7d4df6ba5f104470e7b15193b634da213f2be83851358a1d9995b56"},"schema_version":"1.0","source":{"id":"1002.4316","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.4316","created_at":"2026-05-18T02:08:57Z"},{"alias_kind":"arxiv_version","alias_value":"1002.4316v1","created_at":"2026-05-18T02:08:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.4316","created_at":"2026-05-18T02:08:57Z"},{"alias_kind":"pith_short_12","alias_value":"KQEVCKQ6RDXH","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KQEVCKQ6RDXH4BOY","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KQEVCKQ6","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:0468a82842c0e782f5c61d628ce28b3ea60bc7911631ba95652ad5b4971581b3","target":"graph","created_at":"2026-05-18T02:08:57Z","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":"We consider a class of nonlinear stochastic differential equations, giving the power-law behavior of the power spectral density in any desirably wide range of frequency. Such equations were obtained starting from the point process models of 1/f^b noise. In this article the power-law behavior of spectrum is derived directly from the stochastic differential equations, without using the point process models. The analysis reveals that the power spectrum may be represented as a sum of the Lorentzian spectra. Such a derivation provides additional justification of equations, expands the class of equa","authors_text":"B. Kaulakys, J. Ruseckas","cross_cats":["physics.data-an"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2010-02-23T12:25:59Z","title":"1/f noise from nonlinear stochastic differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.4316","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:ee06f906850def0a6d45a1608189d608c762c40b40177386e4dd4509c5c7ede8","target":"record","created_at":"2026-05-18T02:08:57Z","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":"ccbaa9d86a4b3a337a399b42b981edd9b7aa652e9a6b7b1ddb203ea2342d1f34","cross_cats_sorted":["physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.AO","submitted_at":"2010-02-23T12:25:59Z","title_canon_sha256":"f3ce3c62f7d4df6ba5f104470e7b15193b634da213f2be83851358a1d9995b56"},"schema_version":"1.0","source":{"id":"1002.4316","kind":"arxiv","version":1}},"canonical_sha256":"5409512a1e88ee7e05d8f04259f32e31f55fb69066e40cb3e5f33ad7ea8d3cd2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5409512a1e88ee7e05d8f04259f32e31f55fb69066e40cb3e5f33ad7ea8d3cd2","first_computed_at":"2026-05-18T02:08:57.796189Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:08:57.796189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k7RW2XXe6tJ5hYnMq3B5BjSdBPK5POKzyKi7k3N3PnsTD/4Fe5AhkGj48eC6yxF9VZK4a16yG22s9cK4NhQVAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:08:57.796878Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.4316","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee06f906850def0a6d45a1608189d608c762c40b40177386e4dd4509c5c7ede8","sha256:0468a82842c0e782f5c61d628ce28b3ea60bc7911631ba95652ad5b4971581b3"],"state_sha256":"8c90acf8f2375447e149281aa58ff0023c300f961baa3a1034b41d53ce88c5a0"}