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The datum has finite mass, its weighted velocity supremum belongs to $L^p_x$ for some $p>d$, and it has an arbitrarily small positive H\\\"older regularity in the velocity variable, uniformly with respect to velocity and with the same spatial $L^p$ control. The main estimate is a nonlinear mixing bound \\[\n  [\\rho(t)]_{C^\\alpha_x}\\lesssim\n  t^{-d/p-\\epsilon}C(f_0),\n  \\qquad \\epsilon>0~~\\text{small}. \\] Thus the density is integrab"},"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":"2607.24400","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-07-27T13:18:24Z","cross_cats_sorted":[],"title_canon_sha256":"8b7b206006d0f02ec9b95a0151caa2bf0414a5dcc6653b9cf293548e5d59730a","abstract_canon_sha256":"5c69352794f764338a628b79eadcdc75d2c30c96309d8ef851a680235da70c47"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-28T02:24:01.365555Z","signature_b64":"5EQ81nwL8cfwcBpYlKQrs+Qy8AX+LHrjcUWBqCCH3eHflw5FjhkaUqBEetZeTw0RSbCSNnnf4+7wkmsdrTVGCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cbb097597e284bbba4e2e048dfe178a451c59acd8ba510142cf6ca50fe8eadd3","last_reissued_at":"2026-07-28T02:24:01.364636Z","signature_status":"signed_v1","first_computed_at":"2026-07-28T02:24:01.364636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local Well-Posedness for Vlasov--Poisson with $L^{d+}$ Initial Density and Fractional Velocity Regularity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Quoc-Hung Nguyen","submitted_at":"2026-07-27T13:18:24Z","abstract_excerpt":"We prove a local well-posedness criterion for the Vlasov--Poisson system on $\\R^d_x\\times\\R^d_v$, $d\\geq2$, under an anisotropic assumption on the initial distribution. The datum has finite mass, its weighted velocity supremum belongs to $L^p_x$ for some $p>d$, and it has an arbitrarily small positive H\\\"older regularity in the velocity variable, uniformly with respect to velocity and with the same spatial $L^p$ control. The main estimate is a nonlinear mixing bound \\[\n  [\\rho(t)]_{C^\\alpha_x}\\lesssim\n  t^{-d/p-\\epsilon}C(f_0),\n  \\qquad \\epsilon>0~~\\text{small}. \\] Thus the density is integrab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.24400","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/2607.24400/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":"2607.24400","created_at":"2026-07-28T02:24:01.365122+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.24400v1","created_at":"2026-07-28T02:24:01.365122+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.24400","created_at":"2026-07-28T02:24:01.365122+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZOYJOWL6FBF3","created_at":"2026-07-28T02:24:01.365122+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZOYJOWL6FBF3XJHC","created_at":"2026-07-28T02:24:01.365122+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZOYJOWL6","created_at":"2026-07-28T02:24:01.365122+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/ZOYJOWL6FBF3XJHC4BEN7YLYUR","json":"https://pith.science/pith/ZOYJOWL6FBF3XJHC4BEN7YLYUR.json","graph_json":"https://pith.science/api/pith-number/ZOYJOWL6FBF3XJHC4BEN7YLYUR/graph.json","events_json":"https://pith.science/api/pith-number/ZOYJOWL6FBF3XJHC4BEN7YLYUR/events.json","paper":"https://pith.science/paper/ZOYJOWL6"},"agent_actions":{"view_html":"https://pith.science/pith/ZOYJOWL6FBF3XJHC4BEN7YLYUR","download_json":"https://pith.science/pith/ZOYJOWL6FBF3XJHC4BEN7YLYUR.json","view_paper":"https://pith.science/paper/ZOYJOWL6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.24400&json=true","fetch_graph":"https://pith.science/api/pith-number/ZOYJOWL6FBF3XJHC4BEN7YLYUR/graph.json","fetch_events":"https://pith.science/api/pith-number/ZOYJOWL6FBF3XJHC4BEN7YLYUR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZOYJOWL6FBF3XJHC4BEN7YLYUR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZOYJOWL6FBF3XJHC4BEN7YLYUR/action/storage_attestation","attest_author":"https://pith.science/pith/ZOYJOWL6FBF3XJHC4BEN7YLYUR/action/author_attestation","sign_citation":"https://pith.science/pith/ZOYJOWL6FBF3XJHC4BEN7YLYUR/action/citation_signature","submit_replication":"https://pith.science/pith/ZOYJOWL6FBF3XJHC4BEN7YLYUR/action/replication_record"}},"created_at":"2026-07-28T02:24:01.365122+00:00","updated_at":"2026-07-28T02:24:01.365122+00:00"}