{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:H6FHNOTVDUWSVO4DFF6CY7L7NS","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":"93334d06b4ef72245ec301ce0ea218ee0a437741c222edb0868c4fbe654ca78f","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-10-08T09:54:41Z","title_canon_sha256":"8b4ed3e71e38fdf6de4091a27b5c4959ca78c9368d19d594a50495bcd15fb869"},"schema_version":"1.0","source":{"id":"1410.2041","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.2041","created_at":"2026-05-18T01:41:50Z"},{"alias_kind":"arxiv_version","alias_value":"1410.2041v1","created_at":"2026-05-18T01:41:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.2041","created_at":"2026-05-18T01:41:50Z"},{"alias_kind":"pith_short_12","alias_value":"H6FHNOTVDUWS","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"H6FHNOTVDUWSVO4D","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"H6FHNOTV","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:53c5e5ae5ea46681801172bb8e89c5a5d87aaba07157b20c349253bb6e55a2e1","target":"graph","created_at":"2026-05-18T01:41:50Z","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 present a detailed analysis of the eigenfunctions of the Fokker-Planck operator for the L\\'evy-Ornstein-Uhlenbeck process, their asymptotic behavior and recurrence relations, explicit expressions in coordinate space for the special cases of the Ornstein-Uhlenbeck process with Gaussian and with Cauchy white noise and for the transformation kernel, which maps the fractional Fokker-Planck operator of the Cauchy-Ornstein-Uhlenbeck process to the non-fractional Fokker-Planck operator of the usual Gaussian Ornstein-Uhlenbeck process. We also describe how non-spectral relaxation can be observed in","authors_text":"Eugene B. Postnikov, Igor M. Sokolov, Ralf Toenjes","cross_cats":["cond-mat.stat-mech","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-10-08T09:54:41Z","title":"Spectral properties of fractional Fokker-Plank operator for the L\\'evy flight in a harmonic potential"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2041","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":"sha256:29ff3bacd36a63129ade597815f71c969795203d93592ce0a7341da69f4ec13e","target":"record","created_at":"2026-05-18T01:41:50Z","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":"93334d06b4ef72245ec301ce0ea218ee0a437741c222edb0868c4fbe654ca78f","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-10-08T09:54:41Z","title_canon_sha256":"8b4ed3e71e38fdf6de4091a27b5c4959ca78c9368d19d594a50495bcd15fb869"},"schema_version":"1.0","source":{"id":"1410.2041","kind":"arxiv","version":1}},"canonical_sha256":"3f8a76ba751d2d2abb83297c2c7d7f6c9c8d8613c522c48c55cfddb9f9973701","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f8a76ba751d2d2abb83297c2c7d7f6c9c8d8613c522c48c55cfddb9f9973701","first_computed_at":"2026-05-18T01:41:50.050673Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:41:50.050673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bydE5wXg9zR+nyn9Dvq6PYaPEWtnnHSfl2uvNafK1L6KZoH7S9j3nmy061q82rBgik5I7on3s+xrYaDVgHXZBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:41:50.051110Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.2041","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:29ff3bacd36a63129ade597815f71c969795203d93592ce0a7341da69f4ec13e","sha256:53c5e5ae5ea46681801172bb8e89c5a5d87aaba07157b20c349253bb6e55a2e1"],"state_sha256":"a76d69b100438f47ff8a6d2fcc901a465674e56c03429998884bd955e657d478"}