{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:2K3CCAPBMKRPJMBPU4LFQRVVSC","short_pith_number":"pith:2K3CCAPB","schema_version":"1.0","canonical_sha256":"d2b62101e162a2f4b02fa7165846b590a96a138c12f9faeb821148a905319742","source":{"kind":"arxiv","id":"1810.09374","version":3},"attestation_state":"computed","paper":{"title":"Derivation of 3D energy-critical nonlinear Schr\\\"odinger equation and Bogoliubov excitations for Bose gases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Phan Th\\`anh Nam, Robert Salzmann","submitted_at":"2018-10-22T15:43:51Z","abstract_excerpt":"We derive the 3D quintic NLS as the mean field limit of a Bose gas with three-body interactions. The quintic NLS is energy-critical, leading to several new difficulties in comparison with the cubic NLS which emerges from Bose gases with pair-interactions. Our method is based on Bogoliubov's approximation, which also provides the information on the fluctuations around the condensate in terms of a norm approximation for the N-body wave function."},"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":"1810.09374","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-10-22T15:43:51Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"ab16fc5c85b0fb71086a719398f208425661b22c5fa0ba5001b0c0cd00570ac8","abstract_canon_sha256":"448abffcf87dd6051feb1151d9c3d7141aa781646a91dc228865ba0c81d30ff1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:48.676771Z","signature_b64":"X/9bLZHFnrBcqAvV/Q4C1g40TiVTAFOo+KCqQFHeOU2p3s6+TWCoAjDrO3Q6j0IrUdd/w7zHpSwoe7r43bL5Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2b62101e162a2f4b02fa7165846b590a96a138c12f9faeb821148a905319742","last_reissued_at":"2026-05-17T23:47:48.676103Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:48.676103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Derivation of 3D energy-critical nonlinear Schr\\\"odinger equation and Bogoliubov excitations for Bose gases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Phan Th\\`anh Nam, Robert Salzmann","submitted_at":"2018-10-22T15:43:51Z","abstract_excerpt":"We derive the 3D quintic NLS as the mean field limit of a Bose gas with three-body interactions. The quintic NLS is energy-critical, leading to several new difficulties in comparison with the cubic NLS which emerges from Bose gases with pair-interactions. Our method is based on Bogoliubov's approximation, which also provides the information on the fluctuations around the condensate in terms of a norm approximation for the N-body wave function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.09374","kind":"arxiv","version":3},"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":"1810.09374","created_at":"2026-05-17T23:47:48.676191+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.09374v3","created_at":"2026-05-17T23:47:48.676191+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.09374","created_at":"2026-05-17T23:47:48.676191+00:00"},{"alias_kind":"pith_short_12","alias_value":"2K3CCAPBMKRP","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_16","alias_value":"2K3CCAPBMKRPJMBP","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_8","alias_value":"2K3CCAPB","created_at":"2026-05-18T12:32:02.567920+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/2K3CCAPBMKRPJMBPU4LFQRVVSC","json":"https://pith.science/pith/2K3CCAPBMKRPJMBPU4LFQRVVSC.json","graph_json":"https://pith.science/api/pith-number/2K3CCAPBMKRPJMBPU4LFQRVVSC/graph.json","events_json":"https://pith.science/api/pith-number/2K3CCAPBMKRPJMBPU4LFQRVVSC/events.json","paper":"https://pith.science/paper/2K3CCAPB"},"agent_actions":{"view_html":"https://pith.science/pith/2K3CCAPBMKRPJMBPU4LFQRVVSC","download_json":"https://pith.science/pith/2K3CCAPBMKRPJMBPU4LFQRVVSC.json","view_paper":"https://pith.science/paper/2K3CCAPB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.09374&json=true","fetch_graph":"https://pith.science/api/pith-number/2K3CCAPBMKRPJMBPU4LFQRVVSC/graph.json","fetch_events":"https://pith.science/api/pith-number/2K3CCAPBMKRPJMBPU4LFQRVVSC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2K3CCAPBMKRPJMBPU4LFQRVVSC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2K3CCAPBMKRPJMBPU4LFQRVVSC/action/storage_attestation","attest_author":"https://pith.science/pith/2K3CCAPBMKRPJMBPU4LFQRVVSC/action/author_attestation","sign_citation":"https://pith.science/pith/2K3CCAPBMKRPJMBPU4LFQRVVSC/action/citation_signature","submit_replication":"https://pith.science/pith/2K3CCAPBMKRPJMBPU4LFQRVVSC/action/replication_record"}},"created_at":"2026-05-17T23:47:48.676191+00:00","updated_at":"2026-05-17T23:47:48.676191+00:00"}