{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:HJSMFTJAUZSKQ2XTWTMS73KBL3","short_pith_number":"pith:HJSMFTJA","schema_version":"1.0","canonical_sha256":"3a64c2cd20a664a86af3b4d92fed415efa0110f87a78b56b927e142747de9201","source":{"kind":"arxiv","id":"1904.04756","version":1},"attestation_state":"computed","paper":{"title":"Existence of flows for linear Fokker-Planck-Kolmogorov equations and its connection to well-posedness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Marco Rehmeier","submitted_at":"2019-04-09T16:09:03Z","abstract_excerpt":"Let the coefficients $a_{ij}$ and $b_i$, $i,j \\leq d$, of the linear Fokker-Planck-Kolmogorov equation (FPK-eq.)\n  $$\\partial_t\\mu_t = \\partial_i\\partial_j(a_{ij}\\mu_t)-\\partial_i(b_i\\mu_t)$$ be Borel measurable, bounded and continuous in space. Assume that for every $s \\in [0,T]$ and every Borel probability measure $\\nu$ on $\\mathbb{R}^d$ there is at least one solution $\\mu = (\\mu_t)_{t \\in [s,T]}$ to the FPK-eq. such that $\\mu_s = \\nu$ and $t \\mapsto \\mu_t$ is continuous w.r.t. the topology of weak convergence of measures. We prove that in this situation, one can always select one solution $"},"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":"1904.04756","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-04-09T16:09:03Z","cross_cats_sorted":[],"title_canon_sha256":"643da88f679aa46e2ff56f7977c7f7f9a65aec18c89e8135363edba0e9aceafa","abstract_canon_sha256":"cc2c6d3470a8b6bd5009d190a318a43ab7f6182b0dc6be51756e01fc44eafaf6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:58.225267Z","signature_b64":"U2QHUeD+a0VzSP6U4lcv801agdExDAHXVUbARsuyhhpq0IWQnGX4xKy1y48MbQt+dtsMF/idlxrZxvHo+EtRBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a64c2cd20a664a86af3b4d92fed415efa0110f87a78b56b927e142747de9201","last_reissued_at":"2026-05-17T23:48:58.224752Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:58.224752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence of flows for linear Fokker-Planck-Kolmogorov equations and its connection to well-posedness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Marco Rehmeier","submitted_at":"2019-04-09T16:09:03Z","abstract_excerpt":"Let the coefficients $a_{ij}$ and $b_i$, $i,j \\leq d$, of the linear Fokker-Planck-Kolmogorov equation (FPK-eq.)\n  $$\\partial_t\\mu_t = \\partial_i\\partial_j(a_{ij}\\mu_t)-\\partial_i(b_i\\mu_t)$$ be Borel measurable, bounded and continuous in space. Assume that for every $s \\in [0,T]$ and every Borel probability measure $\\nu$ on $\\mathbb{R}^d$ there is at least one solution $\\mu = (\\mu_t)_{t \\in [s,T]}$ to the FPK-eq. such that $\\mu_s = \\nu$ and $t \\mapsto \\mu_t$ is continuous w.r.t. the topology of weak convergence of measures. We prove that in this situation, one can always select one solution $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.04756","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":""},"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":"1904.04756","created_at":"2026-05-17T23:48:58.224831+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.04756v1","created_at":"2026-05-17T23:48:58.224831+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.04756","created_at":"2026-05-17T23:48:58.224831+00:00"},{"alias_kind":"pith_short_12","alias_value":"HJSMFTJAUZSK","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_16","alias_value":"HJSMFTJAUZSKQ2XT","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_8","alias_value":"HJSMFTJA","created_at":"2026-05-18T12:33:18.533446+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HJSMFTJAUZSKQ2XTWTMS73KBL3","json":"https://pith.science/pith/HJSMFTJAUZSKQ2XTWTMS73KBL3.json","graph_json":"https://pith.science/api/pith-number/HJSMFTJAUZSKQ2XTWTMS73KBL3/graph.json","events_json":"https://pith.science/api/pith-number/HJSMFTJAUZSKQ2XTWTMS73KBL3/events.json","paper":"https://pith.science/paper/HJSMFTJA"},"agent_actions":{"view_html":"https://pith.science/pith/HJSMFTJAUZSKQ2XTWTMS73KBL3","download_json":"https://pith.science/pith/HJSMFTJAUZSKQ2XTWTMS73KBL3.json","view_paper":"https://pith.science/paper/HJSMFTJA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.04756&json=true","fetch_graph":"https://pith.science/api/pith-number/HJSMFTJAUZSKQ2XTWTMS73KBL3/graph.json","fetch_events":"https://pith.science/api/pith-number/HJSMFTJAUZSKQ2XTWTMS73KBL3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HJSMFTJAUZSKQ2XTWTMS73KBL3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HJSMFTJAUZSKQ2XTWTMS73KBL3/action/storage_attestation","attest_author":"https://pith.science/pith/HJSMFTJAUZSKQ2XTWTMS73KBL3/action/author_attestation","sign_citation":"https://pith.science/pith/HJSMFTJAUZSKQ2XTWTMS73KBL3/action/citation_signature","submit_replication":"https://pith.science/pith/HJSMFTJAUZSKQ2XTWTMS73KBL3/action/replication_record"}},"created_at":"2026-05-17T23:48:58.224831+00:00","updated_at":"2026-05-17T23:48:58.224831+00:00"}