{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6ZSWAIJXIHIR7ZUB3TWSMTTTMK","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":"d2c5aee6109ce312c48a90711c33398a0a3a9244724dec1651b584c907a0c4cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-19T12:35:30Z","title_canon_sha256":"b86f047232d664d55ea68a92baa79fe42954b6e904a9525235798c67a7c5de8c"},"schema_version":"1.0","source":{"id":"1307.5200","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.5200","created_at":"2026-05-18T00:13:14Z"},{"alias_kind":"arxiv_version","alias_value":"1307.5200v2","created_at":"2026-05-18T00:13:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.5200","created_at":"2026-05-18T00:13:14Z"},{"alias_kind":"pith_short_12","alias_value":"6ZSWAIJXIHIR","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6ZSWAIJXIHIR7ZUB","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6ZSWAIJX","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:d95b806b3b96b85d9ab561cbbfb8dc5b639d62f5392af4f7042efea41aa3c927","target":"graph","created_at":"2026-05-18T00:13:14Z","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":"In this paper we develop a new technique to prove existence of solutions of Fokker-Planck equations on Hilbert spaces for Kolmogorov operators with non trace-class second order coefficients or equivalently with an associated stochastic partial differential equation (SPDE) with non trace-class noise. Applications include stochastic 2D and 3D-Navier-Stokes equations with non trace-class additive noise.","authors_text":"F. Flandoli, G. Da Prato, M. R\\\"ockner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-19T12:35:30Z","title":"Fokker-Planck equations for SPDE with non-trace class noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5200","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:a56fa98df43c205253278078187235ef381b5b9e311ffcf4a4ee57b51f43f239","target":"record","created_at":"2026-05-18T00:13:14Z","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":"d2c5aee6109ce312c48a90711c33398a0a3a9244724dec1651b584c907a0c4cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-19T12:35:30Z","title_canon_sha256":"b86f047232d664d55ea68a92baa79fe42954b6e904a9525235798c67a7c5de8c"},"schema_version":"1.0","source":{"id":"1307.5200","kind":"arxiv","version":2}},"canonical_sha256":"f66560213741d11fe681dced264e7362872d66e266d06a632b034a02b7983967","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f66560213741d11fe681dced264e7362872d66e266d06a632b034a02b7983967","first_computed_at":"2026-05-18T00:13:14.056350Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:14.056350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8+XjtGc5LhIWEhJ4+5gj5QGHFnWAM1m0gHycg4uvKwlXrdVNedd4/XwtTKLfIW14s178BtBu0H/iK7YU3QgPAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:14.057076Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.5200","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a56fa98df43c205253278078187235ef381b5b9e311ffcf4a4ee57b51f43f239","sha256:d95b806b3b96b85d9ab561cbbfb8dc5b639d62f5392af4f7042efea41aa3c927"],"state_sha256":"1afb63e52443bc9f0cffe79dd7c5bb629837953d50f2f951a0b420eda7660880"}