{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2004:OEBBDD3Q4ELH3LNOB7JYEJKO5F","short_pith_number":"pith:OEBBDD3Q","schema_version":"1.0","canonical_sha256":"7102118f70e1167dadae0fd382254ee9582c5aa9830cfd9d12a641a1450b452d","source":{"kind":"arxiv","id":"math/0409481","version":1},"attestation_state":"computed","paper":{"title":"Determining functionals for random partial differential equations","license":"","headline":"","cross_cats":["math.FA"],"primary_cat":"math.DS","authors_text":"Bj\\\"orn Schmalfu{\\ss}, Igor Chueshov, Jinqiao Duan","submitted_at":"2004-09-24T19:07:50Z","abstract_excerpt":"Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\\em random} dynamical systems. In these applications the convergence condition of the trajectories of an infinite dimensional random dynamical system with respect to a finite set of linear functionals is assumed to be either in mean or {\\em exponential} with respect to the convergence almost surely. In contrast to these ideas we introduce a convergence concept which is based on the convergence in probab"},"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":"math/0409481","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"2004-09-24T19:07:50Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"01a786de74ce710c10dbc797dc780a04775be9c0261675d26ad35b26feea46da","abstract_canon_sha256":"4726b3d4eccdf85b5e88b81bb1a6d559dc2630ef4fd64e59e022bb1263a5f88e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:51.548071Z","signature_b64":"yiTJ2I867JncJ57N8AeA839LRE2ierXSIfC0M5Hb0rBI+S5wYDQVSEnqGkX0Uoyd+Q7fmYzGNeAYMdmIwaICBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7102118f70e1167dadae0fd382254ee9582c5aa9830cfd9d12a641a1450b452d","last_reissued_at":"2026-05-18T01:08:51.547443Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:51.547443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Determining functionals for random partial differential equations","license":"","headline":"","cross_cats":["math.FA"],"primary_cat":"math.DS","authors_text":"Bj\\\"orn Schmalfu{\\ss}, Igor Chueshov, Jinqiao Duan","submitted_at":"2004-09-24T19:07:50Z","abstract_excerpt":"Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\\em random} dynamical systems. In these applications the convergence condition of the trajectories of an infinite dimensional random dynamical system with respect to a finite set of linear functionals is assumed to be either in mean or {\\em exponential} with respect to the convergence almost surely. In contrast to these ideas we introduce a convergence concept which is based on the convergence in probab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0409481","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"math/0409481","created_at":"2026-05-18T01:08:51.547547+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0409481v1","created_at":"2026-05-18T01:08:51.547547+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0409481","created_at":"2026-05-18T01:08:51.547547+00:00"},{"alias_kind":"pith_short_12","alias_value":"OEBBDD3Q4ELH","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_16","alias_value":"OEBBDD3Q4ELH3LNO","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_8","alias_value":"OEBBDD3Q","created_at":"2026-05-18T12:25:52.687210+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/OEBBDD3Q4ELH3LNOB7JYEJKO5F","json":"https://pith.science/pith/OEBBDD3Q4ELH3LNOB7JYEJKO5F.json","graph_json":"https://pith.science/api/pith-number/OEBBDD3Q4ELH3LNOB7JYEJKO5F/graph.json","events_json":"https://pith.science/api/pith-number/OEBBDD3Q4ELH3LNOB7JYEJKO5F/events.json","paper":"https://pith.science/paper/OEBBDD3Q"},"agent_actions":{"view_html":"https://pith.science/pith/OEBBDD3Q4ELH3LNOB7JYEJKO5F","download_json":"https://pith.science/pith/OEBBDD3Q4ELH3LNOB7JYEJKO5F.json","view_paper":"https://pith.science/paper/OEBBDD3Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0409481&json=true","fetch_graph":"https://pith.science/api/pith-number/OEBBDD3Q4ELH3LNOB7JYEJKO5F/graph.json","fetch_events":"https://pith.science/api/pith-number/OEBBDD3Q4ELH3LNOB7JYEJKO5F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OEBBDD3Q4ELH3LNOB7JYEJKO5F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OEBBDD3Q4ELH3LNOB7JYEJKO5F/action/storage_attestation","attest_author":"https://pith.science/pith/OEBBDD3Q4ELH3LNOB7JYEJKO5F/action/author_attestation","sign_citation":"https://pith.science/pith/OEBBDD3Q4ELH3LNOB7JYEJKO5F/action/citation_signature","submit_replication":"https://pith.science/pith/OEBBDD3Q4ELH3LNOB7JYEJKO5F/action/replication_record"}},"created_at":"2026-05-18T01:08:51.547547+00:00","updated_at":"2026-05-18T01:08:51.547547+00:00"}