{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:HBSVN4UT7HXVTYSJTUNKMSAF73","short_pith_number":"pith:HBSVN4UT","schema_version":"1.0","canonical_sha256":"386556f293f9ef59e2499d1aa64805feed4e898f0c7bf269a6fc4f6fe3e4b0a0","source":{"kind":"arxiv","id":"2211.03336","version":1},"attestation_state":"computed","paper":{"title":"The Vlasov-Poisson and Vlasov-Poisson-Fokker-Planck systems in stochastic electromagnetic fields: local well-posedness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jacob Bedrossian, Stavros Papathanasiou","submitted_at":"2022-11-07T06:49:59Z","abstract_excerpt":"In this paper, we construct unique, local-in-time strong solutions to the Vlasov-Poisson (VP) and Vlasov-Poisson-Fokker-Planck (VPFP) systems subjected to external, spatially regular, white-in-time electromagnetic fields in $\\mathbb T^d \\times \\mathbb R^d$. Initial conditions are taken $H^\\sigma$ with $\\sigma > d/2 + 1$ (in addition to polynomial velocity weights). We additionally show that solutions to the VPFP are instantly $C^\\infty_{x,v}$ due to hypoelliptic regularization if the external force fields are smooth. The external forcing arises in the kinetic equation as a stochastic transport"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2211.03336","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-11-07T06:49:59Z","cross_cats_sorted":[],"title_canon_sha256":"b617b142e24d0cce760f53b48daf552c414b2b0e97d0fcf989d359b0480845c3","abstract_canon_sha256":"e52ba70218fe87888cb280e1aaf235117b728e80f362b5c1850e95597cd7f4f4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:13:47.548613Z","signature_b64":"sO37W1CtOlUPG8zy3CDlj0A1noc2LlLq6PY7oAq8agutp+Vh00fmAb4YthUif5mfjsiZcJjoqbdswGjNp7uAAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"386556f293f9ef59e2499d1aa64805feed4e898f0c7bf269a6fc4f6fe3e4b0a0","last_reissued_at":"2026-07-05T05:13:47.548168Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:13:47.548168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Vlasov-Poisson and Vlasov-Poisson-Fokker-Planck systems in stochastic electromagnetic fields: local well-posedness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jacob Bedrossian, Stavros Papathanasiou","submitted_at":"2022-11-07T06:49:59Z","abstract_excerpt":"In this paper, we construct unique, local-in-time strong solutions to the Vlasov-Poisson (VP) and Vlasov-Poisson-Fokker-Planck (VPFP) systems subjected to external, spatially regular, white-in-time electromagnetic fields in $\\mathbb T^d \\times \\mathbb R^d$. Initial conditions are taken $H^\\sigma$ with $\\sigma > d/2 + 1$ (in addition to polynomial velocity weights). We additionally show that solutions to the VPFP are instantly $C^\\infty_{x,v}$ due to hypoelliptic regularization if the external force fields are smooth. The external forcing arises in the kinetic equation as a stochastic transport"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.03336","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2211.03336/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2211.03336","created_at":"2026-07-05T05:13:47.548231+00:00"},{"alias_kind":"arxiv_version","alias_value":"2211.03336v1","created_at":"2026-07-05T05:13:47.548231+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.03336","created_at":"2026-07-05T05:13:47.548231+00:00"},{"alias_kind":"pith_short_12","alias_value":"HBSVN4UT7HXV","created_at":"2026-07-05T05:13:47.548231+00:00"},{"alias_kind":"pith_short_16","alias_value":"HBSVN4UT7HXVTYSJ","created_at":"2026-07-05T05:13:47.548231+00:00"},{"alias_kind":"pith_short_8","alias_value":"HBSVN4UT","created_at":"2026-07-05T05:13:47.548231+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.04982","citing_title":"On the well-posedness of (nonlinear) rough continuity equations","ref_index":1956,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HBSVN4UT7HXVTYSJTUNKMSAF73","json":"https://pith.science/pith/HBSVN4UT7HXVTYSJTUNKMSAF73.json","graph_json":"https://pith.science/api/pith-number/HBSVN4UT7HXVTYSJTUNKMSAF73/graph.json","events_json":"https://pith.science/api/pith-number/HBSVN4UT7HXVTYSJTUNKMSAF73/events.json","paper":"https://pith.science/paper/HBSVN4UT"},"agent_actions":{"view_html":"https://pith.science/pith/HBSVN4UT7HXVTYSJTUNKMSAF73","download_json":"https://pith.science/pith/HBSVN4UT7HXVTYSJTUNKMSAF73.json","view_paper":"https://pith.science/paper/HBSVN4UT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2211.03336&json=true","fetch_graph":"https://pith.science/api/pith-number/HBSVN4UT7HXVTYSJTUNKMSAF73/graph.json","fetch_events":"https://pith.science/api/pith-number/HBSVN4UT7HXVTYSJTUNKMSAF73/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HBSVN4UT7HXVTYSJTUNKMSAF73/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HBSVN4UT7HXVTYSJTUNKMSAF73/action/storage_attestation","attest_author":"https://pith.science/pith/HBSVN4UT7HXVTYSJTUNKMSAF73/action/author_attestation","sign_citation":"https://pith.science/pith/HBSVN4UT7HXVTYSJTUNKMSAF73/action/citation_signature","submit_replication":"https://pith.science/pith/HBSVN4UT7HXVTYSJTUNKMSAF73/action/replication_record"}},"created_at":"2026-07-05T05:13:47.548231+00:00","updated_at":"2026-07-05T05:13:47.548231+00:00"}