{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:MA6CZQJTEGHHY3DE6IC7SDSGX5","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":"ba943b21b423b8029b591e3d7e29b6de5402dec99f70b5a4dd0ac3fec71ebcb3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-08-17T04:31:01Z","title_canon_sha256":"96c0a8960b02358db8a1d95e220901e63f2433894cea7991c4b237260e0c0fa4"},"schema_version":"1.0","source":{"id":"2508.12234","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.12234","created_at":"2026-07-05T11:55:02Z"},{"alias_kind":"arxiv_version","alias_value":"2508.12234v1","created_at":"2026-07-05T11:55:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.12234","created_at":"2026-07-05T11:55:02Z"},{"alias_kind":"pith_short_12","alias_value":"MA6CZQJTEGHH","created_at":"2026-07-05T11:55:02Z"},{"alias_kind":"pith_short_16","alias_value":"MA6CZQJTEGHHY3DE","created_at":"2026-07-05T11:55:02Z"},{"alias_kind":"pith_short_8","alias_value":"MA6CZQJT","created_at":"2026-07-05T11:55:02Z"}],"graph_snapshots":[{"event_id":"sha256:7049f2eda79400fc96e48491202f7ba17e3b518e8cef81f8a5340ecb006e8d1c","target":"graph","created_at":"2026-07-05T11:55:02Z","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/2508.12234/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we study the well-posedness of the kinetic stochastic differential equation (SDE) in $\\mathbb R^{2d}(d\\geq2)$ driven by Brownian motion: $$\\mathord{{\\rm d}} X_t=V_t\\mathord{{\\rm d}} t,\\ \\mathord{{\\rm d}} V_t=b(t,X_t,V_t)\\mathord{{\\rm d}} t+\\sqrt{2}\\mathord{{\\rm d}} W_t,$$ where the subcritical distribution-valued drift $b$ belongs to the weighted anisotropic H\\\"{o}lder space $\\mathbb L_T^{q_b}\\mathbf C_{\\boldsymbol{a}}^{\\alpha_b}(\\rho_\\kappa)$ with parameters $\\alpha_b\\in(-1,0)$, $q_b\\in(\\frac{2}{1+\\alpha_b},\\infty]$, $\\kappa\\in[0,1+\\alpha_b)$ and $\\div_v b$ is bounded. We establ","authors_text":"Xicheng Zhang, Zikai Chen, Zimo Hao","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-08-17T04:31:01Z","title":"Kinetic SDEs with subcritical distributional drifts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.12234","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":"sha256:578774acf4ae07b737035179aad197ec7be97fcde692d3bb80b4af2e3fdd0a63","target":"record","created_at":"2026-07-05T11:55:02Z","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":"ba943b21b423b8029b591e3d7e29b6de5402dec99f70b5a4dd0ac3fec71ebcb3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-08-17T04:31:01Z","title_canon_sha256":"96c0a8960b02358db8a1d95e220901e63f2433894cea7991c4b237260e0c0fa4"},"schema_version":"1.0","source":{"id":"2508.12234","kind":"arxiv","version":1}},"canonical_sha256":"603c2cc133218e7c6c64f205f90e46bf5f1ad6a160d27378ba1c1ee4a5895709","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"603c2cc133218e7c6c64f205f90e46bf5f1ad6a160d27378ba1c1ee4a5895709","first_computed_at":"2026-07-05T11:55:02.139443Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:55:02.139443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lQL0rSxHMPIwLsatLs/ZK5Q3hlMjRUX5SMj6JZhjrrtmfyOTY7nHBf6+OItt7J1yE2t4reg7LafjHZxKvHAvDg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:55:02.139905Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.12234","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:578774acf4ae07b737035179aad197ec7be97fcde692d3bb80b4af2e3fdd0a63","sha256:7049f2eda79400fc96e48491202f7ba17e3b518e8cef81f8a5340ecb006e8d1c"],"state_sha256":"bb637ff42a69906e282ac7f12ed375ed60f39112e788330fe77d1408413a1579"}