{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:L3CYAP4KZG5LF7IPZDLIFYOUXC","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":"aabd2b904e7f47e7f149d1878214d520d1264b509b2c05f71b96070d7326b7e9","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-03-31T19:38:11Z","title_canon_sha256":"cfb12a06bf52acec0c8226a23136c9dafa32fba295f263cea4cb1ec9f6929864"},"schema_version":"1.0","source":{"id":"1204.0125","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.0125","created_at":"2026-05-18T03:13:34Z"},{"alias_kind":"arxiv_version","alias_value":"1204.0125v3","created_at":"2026-05-18T03:13:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.0125","created_at":"2026-05-18T03:13:34Z"},{"alias_kind":"pith_short_12","alias_value":"L3CYAP4KZG5L","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"L3CYAP4KZG5LF7IP","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"L3CYAP4K","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:87684320f4ce5e8634e6f9090654ae3c062b0d2beadbf6791ac0e6dcdfbaba81","target":"graph","created_at":"2026-05-18T03:13:34Z","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 the dynamics of the 3D N-body Schr\\\"{o}dinger equation in the presence of a quadratic trap. We assume the pair interaction potential is N^{3{\\beta}-1}V(N^{{\\beta}}x). 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.","authors_text":"Xuwen Chen","cross_cats":["math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-03-31T19:38:11Z","title":"On the Rigorous Derivation of the 3D Cubic Nonlinear Schr\\\"odinger Equation with A Quadratic Trap"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0125","kind":"arxiv","version":3},"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:e177bc0e44dfa1bdb26b3875b208a228380fea89ab921779f10c03aa8e472b9c","target":"record","created_at":"2026-05-18T03:13:34Z","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":"aabd2b904e7f47e7f149d1878214d520d1264b509b2c05f71b96070d7326b7e9","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-03-31T19:38:11Z","title_canon_sha256":"cfb12a06bf52acec0c8226a23136c9dafa32fba295f263cea4cb1ec9f6929864"},"schema_version":"1.0","source":{"id":"1204.0125","kind":"arxiv","version":3}},"canonical_sha256":"5ec5803f8ac9bab2fd0fc8d682e1d4b8a8552a0ed70efe0c0d558e971943245b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ec5803f8ac9bab2fd0fc8d682e1d4b8a8552a0ed70efe0c0d558e971943245b","first_computed_at":"2026-05-18T03:13:34.273744Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:34.273744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oNYx/hpOyofi11svQ+DSRpSd/4orplzcXWdgMRIdkhzHJh/160TJZvumM/TVwx5V+1MRj1529nnBOZ5ekA9EBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:34.274277Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.0125","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e177bc0e44dfa1bdb26b3875b208a228380fea89ab921779f10c03aa8e472b9c","sha256:87684320f4ce5e8634e6f9090654ae3c062b0d2beadbf6791ac0e6dcdfbaba81"],"state_sha256":"dce3a996f8d135b7e966fdff114348407b7516d6e83b2eca4968e6de2cb2b48c"}