{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2003:OKGHTVQ54344AMEGPRJF4NNHFK","short_pith_number":"pith:OKGHTVQ5","schema_version":"1.0","canonical_sha256":"728c79d61de6f9c030867c525e35a72aaa6f170793671f1f3dee87a60f2c6555","source":{"kind":"arxiv","id":"cond-mat/0303241","version":1},"attestation_state":"computed","paper":{"title":"Computing the ground state solution of Bose-Einstein condensates by a normalized gradient flow","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat","authors_text":"Qiang Du, Weizhu Bao","submitted_at":"2003-03-13T04:08:20Z","abstract_excerpt":"In this paper, we prove the energy diminishing of a normalized gradient flow which provides a mathematical justification of the imaginary time method used in physical literatures to compute the ground state solution of Bose-Einstein condensates (BEC). We also investigate the energy diminishing property for the discretization of the normalized gradient flow. Two numerical methods are proposed for such discretizations: one is the backward Euler centered finite difference (BEFD), the other one is an explicit time-splitting sine-spectral (TSSP) method. Energy diminishing for BEFD and TSSP for line"},"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":"cond-mat/0303241","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat","submitted_at":"2003-03-13T04:08:20Z","cross_cats_sorted":[],"title_canon_sha256":"87715b4d608f99768d85f0df64be8db8cfbe8765fe9fff50c3dd349a4f97443f","abstract_canon_sha256":"1792d341a11963c62e581ae752d43f90a97c29e4aec8311f10db5124115c78e5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:12.833265Z","signature_b64":"PRrVPSqJqs3QFsTtGV/dri5ZcMW6faxLSH7FVVysdRuz8GiCKG1wnMLxMub68jknmaOA7n9Lkq4BPbGJofxeDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"728c79d61de6f9c030867c525e35a72aaa6f170793671f1f3dee87a60f2c6555","last_reissued_at":"2026-05-18T00:53:12.832740Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:12.832740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Computing the ground state solution of Bose-Einstein condensates by a normalized gradient flow","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat","authors_text":"Qiang Du, Weizhu Bao","submitted_at":"2003-03-13T04:08:20Z","abstract_excerpt":"In this paper, we prove the energy diminishing of a normalized gradient flow which provides a mathematical justification of the imaginary time method used in physical literatures to compute the ground state solution of Bose-Einstein condensates (BEC). We also investigate the energy diminishing property for the discretization of the normalized gradient flow. Two numerical methods are proposed for such discretizations: one is the backward Euler centered finite difference (BEFD), the other one is an explicit time-splitting sine-spectral (TSSP) method. Energy diminishing for BEFD and TSSP for line"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0303241","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":"cond-mat/0303241","created_at":"2026-05-18T00:53:12.832822+00:00"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0303241v1","created_at":"2026-05-18T00:53:12.832822+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0303241","created_at":"2026-05-18T00:53:12.832822+00:00"},{"alias_kind":"pith_short_12","alias_value":"OKGHTVQ54344","created_at":"2026-05-18T12:25:52.051335+00:00"},{"alias_kind":"pith_short_16","alias_value":"OKGHTVQ54344AMEG","created_at":"2026-05-18T12:25:52.051335+00:00"},{"alias_kind":"pith_short_8","alias_value":"OKGHTVQ5","created_at":"2026-05-18T12:25:52.051335+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/OKGHTVQ54344AMEGPRJF4NNHFK","json":"https://pith.science/pith/OKGHTVQ54344AMEGPRJF4NNHFK.json","graph_json":"https://pith.science/api/pith-number/OKGHTVQ54344AMEGPRJF4NNHFK/graph.json","events_json":"https://pith.science/api/pith-number/OKGHTVQ54344AMEGPRJF4NNHFK/events.json","paper":"https://pith.science/paper/OKGHTVQ5"},"agent_actions":{"view_html":"https://pith.science/pith/OKGHTVQ54344AMEGPRJF4NNHFK","download_json":"https://pith.science/pith/OKGHTVQ54344AMEGPRJF4NNHFK.json","view_paper":"https://pith.science/paper/OKGHTVQ5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=cond-mat/0303241&json=true","fetch_graph":"https://pith.science/api/pith-number/OKGHTVQ54344AMEGPRJF4NNHFK/graph.json","fetch_events":"https://pith.science/api/pith-number/OKGHTVQ54344AMEGPRJF4NNHFK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OKGHTVQ54344AMEGPRJF4NNHFK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OKGHTVQ54344AMEGPRJF4NNHFK/action/storage_attestation","attest_author":"https://pith.science/pith/OKGHTVQ54344AMEGPRJF4NNHFK/action/author_attestation","sign_citation":"https://pith.science/pith/OKGHTVQ54344AMEGPRJF4NNHFK/action/citation_signature","submit_replication":"https://pith.science/pith/OKGHTVQ54344AMEGPRJF4NNHFK/action/replication_record"}},"created_at":"2026-05-18T00:53:12.832822+00:00","updated_at":"2026-05-18T00:53:12.832822+00:00"}