{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:KW6GOV3227R5FY7NBGBPLT7DA5","short_pith_number":"pith:KW6GOV32","schema_version":"1.0","canonical_sha256":"55bc67577ad7e3d2e3ed0982f5cfe3077c437e07965e0444d87cdf7fc266cc18","source":{"kind":"arxiv","id":"2510.20124","version":2},"attestation_state":"computed","paper":{"title":"Memory-Dependent FPK Equations for Nonlinear SDOF Oscillators Under Fractional Gaussian Noise Excitation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bin Pei, Lifang Feng, Yong Xu","submitted_at":"2025-10-23T01:59:31Z","abstract_excerpt":"This paper investigates the transient probabilistic responses of nonlinear single-degree-of-freedom oscillators subjected to external fractional Gaussian noise (FGN) excitation. Owing to the inherent long-range correlations and memory characteristics of FGN, the resulting response process exhibits non-Markovian properties, rendering the classical Fokker-Planck-Kolmogorov (FPK) equation method inapplicable in its direct form. To overcome this critical challenge, a memory-dependent FPK (memFPK) equation is formulated for two-dimensional nonlinear stochastic systems within the fractional Wick-It\\"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2510.20124","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-10-23T01:59:31Z","cross_cats_sorted":[],"title_canon_sha256":"34e9229c064bdae6923d5ea4c216c62871dfa996df58dce1b8e4e2a8cf10c382","abstract_canon_sha256":"89ff5d5bc7f757625632e03534f3a0e04631fdb42c6ee7ae555f93601c6ee510"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-28T01:04:31.975103Z","signature_b64":"9hbGkKjgwWsouLIyAMr3YpN6UQ1Dg4iJMMpRkdt/3r3x5JOX6nDVoXYMohDt582k8L+SIEzWfghtjbE53a1/AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55bc67577ad7e3d2e3ed0982f5cfe3077c437e07965e0444d87cdf7fc266cc18","last_reissued_at":"2026-05-28T01:04:31.974570Z","signature_status":"signed_v1","first_computed_at":"2026-05-28T01:04:31.974570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Memory-Dependent FPK Equations for Nonlinear SDOF Oscillators Under Fractional Gaussian Noise Excitation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bin Pei, Lifang Feng, Yong Xu","submitted_at":"2025-10-23T01:59:31Z","abstract_excerpt":"This paper investigates the transient probabilistic responses of nonlinear single-degree-of-freedom oscillators subjected to external fractional Gaussian noise (FGN) excitation. Owing to the inherent long-range correlations and memory characteristics of FGN, the resulting response process exhibits non-Markovian properties, rendering the classical Fokker-Planck-Kolmogorov (FPK) equation method inapplicable in its direct form. To overcome this critical challenge, a memory-dependent FPK (memFPK) equation is formulated for two-dimensional nonlinear stochastic systems within the fractional Wick-It\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.20124","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2510.20124/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2510.20124","created_at":"2026-05-28T01:04:31.974629+00:00"},{"alias_kind":"arxiv_version","alias_value":"2510.20124v2","created_at":"2026-05-28T01:04:31.974629+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.20124","created_at":"2026-05-28T01:04:31.974629+00:00"},{"alias_kind":"pith_short_12","alias_value":"KW6GOV3227R5","created_at":"2026-05-28T01:04:31.974629+00:00"},{"alias_kind":"pith_short_16","alias_value":"KW6GOV3227R5FY7N","created_at":"2026-05-28T01:04:31.974629+00:00"},{"alias_kind":"pith_short_8","alias_value":"KW6GOV32","created_at":"2026-05-28T01:04:31.974629+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KW6GOV3227R5FY7NBGBPLT7DA5","json":"https://pith.science/pith/KW6GOV3227R5FY7NBGBPLT7DA5.json","graph_json":"https://pith.science/api/pith-number/KW6GOV3227R5FY7NBGBPLT7DA5/graph.json","events_json":"https://pith.science/api/pith-number/KW6GOV3227R5FY7NBGBPLT7DA5/events.json","paper":"https://pith.science/paper/KW6GOV32"},"agent_actions":{"view_html":"https://pith.science/pith/KW6GOV3227R5FY7NBGBPLT7DA5","download_json":"https://pith.science/pith/KW6GOV3227R5FY7NBGBPLT7DA5.json","view_paper":"https://pith.science/paper/KW6GOV32","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2510.20124&json=true","fetch_graph":"https://pith.science/api/pith-number/KW6GOV3227R5FY7NBGBPLT7DA5/graph.json","fetch_events":"https://pith.science/api/pith-number/KW6GOV3227R5FY7NBGBPLT7DA5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KW6GOV3227R5FY7NBGBPLT7DA5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KW6GOV3227R5FY7NBGBPLT7DA5/action/storage_attestation","attest_author":"https://pith.science/pith/KW6GOV3227R5FY7NBGBPLT7DA5/action/author_attestation","sign_citation":"https://pith.science/pith/KW6GOV3227R5FY7NBGBPLT7DA5/action/citation_signature","submit_replication":"https://pith.science/pith/KW6GOV3227R5FY7NBGBPLT7DA5/action/replication_record"}},"created_at":"2026-05-28T01:04:31.974629+00:00","updated_at":"2026-05-28T01:04:31.974629+00:00"}