{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PJUQW36J3N2DQW25LQNUNVVYMQ","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":"e804cf89b9c60efedb18eb3244317b32947733896318be9c7fed29e384904ed4","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-06-03T13:46:52Z","title_canon_sha256":"9275d98e767bcf086036e31a91bf19547768c90dd05437cbdf5307ef417c88b0"},"schema_version":"1.0","source":{"id":"1606.01088","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.01088","created_at":"2026-05-18T00:44:37Z"},{"alias_kind":"arxiv_version","alias_value":"1606.01088v2","created_at":"2026-05-18T00:44:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.01088","created_at":"2026-05-18T00:44:37Z"},{"alias_kind":"pith_short_12","alias_value":"PJUQW36J3N2D","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PJUQW36J3N2DQW25","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PJUQW36J","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:4b004ed6354bb7bc1b9f33747d9ae5c785745605deb158361d0ed18520b4032e","target":"graph","created_at":"2026-05-18T00:44:37Z","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 consider regularity properties of stochastic kinetic equations with multiplicative noise and drift term which belongs to a space of mixed regularity ($L^p$-regularity in the velocity-variable and Sobolev regularity in the space-variable). We prove that, in contrast with the deterministic case, the SPDE admits a unique weakly differentiable solution which preserves a certain degree of Sobolev regularity of the initial condition without developing discontinuities. To prove the result we also study the related degenerate Kolmogorov equation in Bessel-Sobolev spaces and construct a suitable sto","authors_text":"Ennio Fedrizzi, Enrico Priola, Franco Flandoli, Julien Vovelle","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-06-03T13:46:52Z","title":"Regularity of Stochastic Kinetic Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01088","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":"sha256:80d8588cc87c2302b7df7c0e04e52994bbacba02159964e8b92f631c5dccc98a","target":"record","created_at":"2026-05-18T00:44:37Z","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":"e804cf89b9c60efedb18eb3244317b32947733896318be9c7fed29e384904ed4","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-06-03T13:46:52Z","title_canon_sha256":"9275d98e767bcf086036e31a91bf19547768c90dd05437cbdf5307ef417c88b0"},"schema_version":"1.0","source":{"id":"1606.01088","kind":"arxiv","version":2}},"canonical_sha256":"7a690b6fc9db74385b5d5c1b46d6b8640848058938f3716235112bac1fc281f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a690b6fc9db74385b5d5c1b46d6b8640848058938f3716235112bac1fc281f2","first_computed_at":"2026-05-18T00:44:37.116771Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:37.116771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1Dx/CVRxAD6uU/L1K7pWt4zJg0RiZY76KteXbBBcCNDMQFPmSLmvcTauDv7JcEvyZP3zSY/LPdR6LuTw4x/nDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:37.117228Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.01088","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80d8588cc87c2302b7df7c0e04e52994bbacba02159964e8b92f631c5dccc98a","sha256:4b004ed6354bb7bc1b9f33747d9ae5c785745605deb158361d0ed18520b4032e"],"state_sha256":"753da5b25f56376deb2ac1a32f49e59f09bf1000a1466c5dddd94fedf2905f14"}