{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:FV4CINGCXAY3RZKVUH3WNQOHQV","short_pith_number":"pith:FV4CINGC","schema_version":"1.0","canonical_sha256":"2d782434c2b831b8e555a1f766c1c7854b4959f581040967729ccf6d4696aac9","source":{"kind":"arxiv","id":"1903.06001","version":1},"attestation_state":"computed","paper":{"title":"Semiclassical limit to the Vlasov equation with inverse power law potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Chiara Saffirio","submitted_at":"2019-03-14T13:57:38Z","abstract_excerpt":"We consider mixed quasi-free states describing $N$ fermions in the mean-field limit. In this regime, the time evolution is governed by the nonlinear Hartree equation. In the large $N$ limit, we study the convergence towards the classical Vlasov equation. Under integrability and regularity assumptions on the initial state, we prove strong convergence in trace and Hilbert-Schmidt norm and provide explicit bounds on the convergence rate for a class of singular potentials of the form $V(x)=|x|^{-\\alpha}$, for $\\alpha\\in(0,1/2)$."},"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":"1903.06001","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-03-14T13:57:38Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"8997129c65b0dffb2fe38d8c43d2f6249ebbfe1975e51bcc0ba8dd7362a79d0e","abstract_canon_sha256":"6751fc9feac747e505efab283f861ad717079c500e13f4ebb74d8c8e8d74c694"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:18.887003Z","signature_b64":"rv6gPIfEcJ4R0zsnJp/bP5eC4mLg//MDFlE6p1En52skF7gblWX2Zx8mzKS73s3HofAEOWCvA5seeA/dYYvFBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d782434c2b831b8e555a1f766c1c7854b4959f581040967729ccf6d4696aac9","last_reissued_at":"2026-05-17T23:50:18.886375Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:18.886375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Semiclassical limit to the Vlasov equation with inverse power law potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Chiara Saffirio","submitted_at":"2019-03-14T13:57:38Z","abstract_excerpt":"We consider mixed quasi-free states describing $N$ fermions in the mean-field limit. In this regime, the time evolution is governed by the nonlinear Hartree equation. In the large $N$ limit, we study the convergence towards the classical Vlasov equation. Under integrability and regularity assumptions on the initial state, we prove strong convergence in trace and Hilbert-Schmidt norm and provide explicit bounds on the convergence rate for a class of singular potentials of the form $V(x)=|x|^{-\\alpha}$, for $\\alpha\\in(0,1/2)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.06001","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":"1903.06001","created_at":"2026-05-17T23:50:18.886466+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.06001v1","created_at":"2026-05-17T23:50:18.886466+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.06001","created_at":"2026-05-17T23:50:18.886466+00:00"},{"alias_kind":"pith_short_12","alias_value":"FV4CINGCXAY3","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_16","alias_value":"FV4CINGCXAY3RZKV","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_8","alias_value":"FV4CINGC","created_at":"2026-05-18T12:33:15.570797+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/FV4CINGCXAY3RZKVUH3WNQOHQV","json":"https://pith.science/pith/FV4CINGCXAY3RZKVUH3WNQOHQV.json","graph_json":"https://pith.science/api/pith-number/FV4CINGCXAY3RZKVUH3WNQOHQV/graph.json","events_json":"https://pith.science/api/pith-number/FV4CINGCXAY3RZKVUH3WNQOHQV/events.json","paper":"https://pith.science/paper/FV4CINGC"},"agent_actions":{"view_html":"https://pith.science/pith/FV4CINGCXAY3RZKVUH3WNQOHQV","download_json":"https://pith.science/pith/FV4CINGCXAY3RZKVUH3WNQOHQV.json","view_paper":"https://pith.science/paper/FV4CINGC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.06001&json=true","fetch_graph":"https://pith.science/api/pith-number/FV4CINGCXAY3RZKVUH3WNQOHQV/graph.json","fetch_events":"https://pith.science/api/pith-number/FV4CINGCXAY3RZKVUH3WNQOHQV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FV4CINGCXAY3RZKVUH3WNQOHQV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FV4CINGCXAY3RZKVUH3WNQOHQV/action/storage_attestation","attest_author":"https://pith.science/pith/FV4CINGCXAY3RZKVUH3WNQOHQV/action/author_attestation","sign_citation":"https://pith.science/pith/FV4CINGCXAY3RZKVUH3WNQOHQV/action/citation_signature","submit_replication":"https://pith.science/pith/FV4CINGCXAY3RZKVUH3WNQOHQV/action/replication_record"}},"created_at":"2026-05-17T23:50:18.886466+00:00","updated_at":"2026-05-17T23:50:18.886466+00:00"}