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We justify the mean-field approximation and offer a rigorous derivation of the 3D cubic NLS with a quadratic trap. We establish the space-time bound conjectured by Klainerman and Machedon [30] for {\\beta} in (0,2/7] by adapting and simplifying an argument in Chen and Pavlovi\\'c [7] which solves the problem for {\\beta} in (0,1/4) in the absence of a trap."},"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":"1204.0125","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-03-31T19:38:11Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"cfb12a06bf52acec0c8226a23136c9dafa32fba295f263cea4cb1ec9f6929864","abstract_canon_sha256":"aabd2b904e7f47e7f149d1878214d520d1264b509b2c05f71b96070d7326b7e9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:34.274277Z","signature_b64":"oNYx/hpOyofi11svQ+DSRpSd/4orplzcXWdgMRIdkhzHJh/160TJZvumM/TVwx5V+1MRj1529nnBOZ5ekA9EBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ec5803f8ac9bab2fd0fc8d682e1d4b8a8552a0ed70efe0c0d558e971943245b","last_reissued_at":"2026-05-18T03:13:34.273744Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:34.273744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Rigorous Derivation of the 3D Cubic Nonlinear Schr\\\"odinger Equation with A Quadratic Trap","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Xuwen Chen","submitted_at":"2012-03-31T19:38:11Z","abstract_excerpt":"We consider the dynamics of the 3D N-body Schr\\\"{o}dinger equation in the presence of a quadratic trap. 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