{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:EYCPZTAZ62DPAFABQB7QBZSNBX","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":"3db2a99bdb4784565ecd8ee0cdebd177e0cf80f5dec5898ddd4d3aa1ff7198c0","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-11-28T10:32:32Z","title_canon_sha256":"6d1afd5bc0c49b22925b8494d6b9a152ea6f39dcd017d18a6c13cc40593b8852"},"schema_version":"1.0","source":{"id":"2511.23058","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2511.23058","created_at":"2026-05-27T01:05:40Z"},{"alias_kind":"arxiv_version","alias_value":"2511.23058v2","created_at":"2026-05-27T01:05:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2511.23058","created_at":"2026-05-27T01:05:40Z"},{"alias_kind":"pith_short_12","alias_value":"EYCPZTAZ62DP","created_at":"2026-05-27T01:05:40Z"},{"alias_kind":"pith_short_16","alias_value":"EYCPZTAZ62DPAFAB","created_at":"2026-05-27T01:05:40Z"},{"alias_kind":"pith_short_8","alias_value":"EYCPZTAZ","created_at":"2026-05-27T01:05:40Z"}],"graph_snapshots":[{"event_id":"sha256:7ac5dde1810e660c44ee912e2c2d4c739f9409fe3d6762d24aaee17b76921a65","target":"graph","created_at":"2026-05-27T01:05:40Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2511.23058/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove existence of a probability solution to the nonlinear stationary Fokker-Planck-Kolmogorov equation on an infinite dimensional space with a centered Gaussian measure $\\gamma$ with a unit diffusion operator and a drift of the form $-x+v(p,x)$, where $v$ is a bounded mapping with values in the Cameron-Martin space $H$ of $\\gamma$ and $v$ is defined on the space $E\\times X$, where is $E$ is the subset of $L^2(\\gamma)$ consisting of probability densities. The equation has the form $L_{b(p,\\bullet)} ^*(p\\cdot \\gamma)=0$ with $L_{b(p,\\bullet)}\\varphi =\\Delta_H \\varphi + (b(p,\\bullet) , D_{_H}","authors_text":"Michael R\\\"ockner, Stanislav V. Shaposhnikov, Vladimir I. Bogachev","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-11-28T10:32:32Z","title":"Infinite-dimensional nonlinear stationary Fokker-Planck-Kolmogorov equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.23058","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":"sha256:695fb76b856fc6a19e564cf71631faad0e4d57cd54c0e8cd05c44b0b919ed520","target":"record","created_at":"2026-05-27T01:05:40Z","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":"3db2a99bdb4784565ecd8ee0cdebd177e0cf80f5dec5898ddd4d3aa1ff7198c0","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-11-28T10:32:32Z","title_canon_sha256":"6d1afd5bc0c49b22925b8494d6b9a152ea6f39dcd017d18a6c13cc40593b8852"},"schema_version":"1.0","source":{"id":"2511.23058","kind":"arxiv","version":2}},"canonical_sha256":"2604fccc19f686f01401807f00e64d0dd7bf167292c7405626d23dad6e1e1be8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2604fccc19f686f01401807f00e64d0dd7bf167292c7405626d23dad6e1e1be8","first_computed_at":"2026-05-27T01:05:40.445208Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-27T01:05:40.445208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yHlS2JonfetS0zH+WGUiLisPMRSlpbySmUdweCNca9wC/effLVULJJsWUCDifdF+3Gm9KhhgScWbpFn8V8LaBw==","signature_status":"signed_v1","signed_at":"2026-05-27T01:05:40.446023Z","signed_message":"canonical_sha256_bytes"},"source_id":"2511.23058","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:695fb76b856fc6a19e564cf71631faad0e4d57cd54c0e8cd05c44b0b919ed520","sha256:7ac5dde1810e660c44ee912e2c2d4c739f9409fe3d6762d24aaee17b76921a65"],"state_sha256":"9fdd740e0bf8ff346b3e3df153f25caab705d6fd7ca842216d813216a21eafa3"}