{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:T7KCYHAUNKOQR7BRIDM2A4CTDY","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":"30c5e014c1a83a7e7657d5b4c26837085d834f4d618b9cbe44d97796e88408b2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-31T10:39:48Z","title_canon_sha256":"1cb8498161d5103862e1479ee2dd894c2189cac2e66ea6a45152a88927f00299"},"schema_version":"1.0","source":{"id":"1305.7348","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.7348","created_at":"2026-05-18T00:13:14Z"},{"alias_kind":"arxiv_version","alias_value":"1305.7348v1","created_at":"2026-05-18T00:13:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.7348","created_at":"2026-05-18T00:13:14Z"},{"alias_kind":"pith_short_12","alias_value":"T7KCYHAUNKOQ","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"T7KCYHAUNKOQR7BR","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"T7KCYHAU","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:595227a4dd4ee9f7ddc151ce3bfc842c0981a69849e312df3309be164036465f","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":"We prove a new uniqueness result for solutions to Fokker-Planck-Kolmogorov (FPK) equations for probability measures on infinite-dimensional spaces. We consider infinite-dimensional drifts that admit certain finite-dimensional approximations. In contrast to most of the previous work on FPK-equations in infinite dimensions, we include cases with non-constant coefficients in the second order part and also include degenerate cases where these coefficients can even be zero. Also a new existence result is proved. Some applications to Fokker-Planck-Kolmogorov equations associated with SPDEs are prese","authors_text":"Giuseppe Da Prato, Michael R\\\"ockner, Stanislav V. Shaposhnikov, Vladimir I. Bogachev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-31T10:39:48Z","title":"An analytic approach to infinite-dimensional continuity and Fokker-Planck-Kolmogorov equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.7348","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:b78def2589d6f44510627b825862e10c24d2607ec3798a07ced7aaccbbb8aba9","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":"30c5e014c1a83a7e7657d5b4c26837085d834f4d618b9cbe44d97796e88408b2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-31T10:39:48Z","title_canon_sha256":"1cb8498161d5103862e1479ee2dd894c2189cac2e66ea6a45152a88927f00299"},"schema_version":"1.0","source":{"id":"1305.7348","kind":"arxiv","version":1}},"canonical_sha256":"9fd42c1c146a9d08fc3140d9a070531e096883d64c2ab01e4746157cf5d67b05","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9fd42c1c146a9d08fc3140d9a070531e096883d64c2ab01e4746157cf5d67b05","first_computed_at":"2026-05-18T00:13:14.077115Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:14.077115Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xWwq2een8e+2nzRrQ3GgZ8F81zs513B191egRB9mn7amfbtkIWY50SvSJjsHAHJTyigFniSUEZUY7yO/RytVAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:14.077791Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.7348","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b78def2589d6f44510627b825862e10c24d2607ec3798a07ced7aaccbbb8aba9","sha256:595227a4dd4ee9f7ddc151ce3bfc842c0981a69849e312df3309be164036465f"],"state_sha256":"7e0a44281331040482d3f4bc6a983089d51f33404f6c063164995b2c468c165d"}