{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YY6MTPPRBHDNXDYRSOKVOWQ4YM","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":"902c091422bc410364577fa5e8aa107a11a7d444f64e68fe39f172cd77fb10f5","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-02-02T21:02:51Z","title_canon_sha256":"a04b2156c669fd8161e6a303896f3e6b2c33643b61ad5a3130962897c697b582"},"schema_version":"1.0","source":{"id":"1702.00827","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.00827","created_at":"2026-05-18T00:35:23Z"},{"alias_kind":"arxiv_version","alias_value":"1702.00827v2","created_at":"2026-05-18T00:35:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.00827","created_at":"2026-05-18T00:35:23Z"},{"alias_kind":"pith_short_12","alias_value":"YY6MTPPRBHDN","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"YY6MTPPRBHDNXDYR","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"YY6MTPPR","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:49da63b43e8566039b91926705072f6f25d0f1b3d94429b57c28a4a3fafb0322","target":"graph","created_at":"2026-05-18T00:35:23Z","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"},"paper":{"abstract_excerpt":"We consider mixtures of Bose gases of different species. We prove that in the mean field limit and under suitable conditions on the initial condition a system composed of two Bose species can be effectively described by a system of coupled Hartree equations. Moreover, we derive quantitative bounds on the rates of convergence of the reduced density matrices in Sobolev trace norms. We treat both the non-relativistic case in the presence of an external magnetic field $A\\in L^2_{\\text{loc}}(\\R^3;\\R^3)$ and the semi-relativistic case.","authors_text":"Dirk Hundertmark, Ioannis Anapolitanos, Michael Hott","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-02-02T21:02:51Z","title":"Derivation of the Hartree equation for compound Bose gases in the mean field limit"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00827","kind":"arxiv","version":2},"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":"sha256:3cf6a013b04256c3aa145e21bbf36a46f9c125c1c146fe51aae54cf3b07dc739","target":"record","created_at":"2026-05-18T00:35:23Z","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":"902c091422bc410364577fa5e8aa107a11a7d444f64e68fe39f172cd77fb10f5","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-02-02T21:02:51Z","title_canon_sha256":"a04b2156c669fd8161e6a303896f3e6b2c33643b61ad5a3130962897c697b582"},"schema_version":"1.0","source":{"id":"1702.00827","kind":"arxiv","version":2}},"canonical_sha256":"c63cc9bdf109c6db8f119395575a1cc3285d05b71a193273d2cb9844d4da6629","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c63cc9bdf109c6db8f119395575a1cc3285d05b71a193273d2cb9844d4da6629","first_computed_at":"2026-05-18T00:35:23.742478Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:23.742478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7sukjyOqVu1A7OYBZ2oxzh8u47wKlsMeXjAaED2buVOIairS6bd5geEbMyL826G3vftuS9jvaGdaRK73nlmFDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:23.743016Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.00827","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3cf6a013b04256c3aa145e21bbf36a46f9c125c1c146fe51aae54cf3b07dc739","sha256:49da63b43e8566039b91926705072f6f25d0f1b3d94429b57c28a4a3fafb0322"],"state_sha256":"6e4e01fba407a1598afcffb3a311508f00d14923eecb3e6869e1815035a376c0"}