{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:QRYT3DJK75L4AXHBMWILTQMAEH","short_pith_number":"pith:QRYT3DJK","schema_version":"1.0","canonical_sha256":"84713d8d2aff57c05ce16590b9c18021e6b6d38eec5e48d82a5ce509cc3a5410","source":{"kind":"arxiv","id":"2506.08308","version":1},"attestation_state":"computed","paper":{"title":"An efficient Fourier spectral algorithm for the Bogoliubov-de Gennes excitation eigenvalue problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Manting Xie, Yong Zhang, Yu Li, Zhixuan Li","submitted_at":"2025-06-10T00:35:34Z","abstract_excerpt":"In this paper, we propose an efficient Fourier spectral algorithm for an eigenvalue problem, that is, the Bogoliubov-de Gennes (BdG) equation arsing from spin-1 Bose-Einstein condensates (BEC) to describe the elementary/collective excitations around the mean-field ground state. The BdG equation is essentially a constrained eigenvalue/eigenfunction system. Firstly, we investigate its analytical properties, including exact eigenpairs, generalized nullspace, and bi-orthogonality of eigenspaces. Secondly, by combining the standard Fourier spectral method for spatial discretization and a stable Gra"},"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":"2506.08308","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-06-10T00:35:34Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"681fc24b1260539603bb10b34e64761b64da3a98c262b2c05199a7efac712763","abstract_canon_sha256":"23abbc17456128bdb608cc1400898162ad88246a0e00bbc07754cb4b53adeb4c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:18:47.876482Z","signature_b64":"WwrLnmcNkwAxw8ZeR2puECi93gezdvl/KT2wvkVmM+9YHj2+CwrFA2YWbdY67IOm6J2hxB1U19fdcUmtBhYeCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84713d8d2aff57c05ce16590b9c18021e6b6d38eec5e48d82a5ce509cc3a5410","last_reissued_at":"2026-07-05T11:18:47.876043Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:18:47.876043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An efficient Fourier spectral algorithm for the Bogoliubov-de Gennes excitation eigenvalue problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Manting Xie, Yong Zhang, Yu Li, Zhixuan Li","submitted_at":"2025-06-10T00:35:34Z","abstract_excerpt":"In this paper, we propose an efficient Fourier spectral algorithm for an eigenvalue problem, that is, the Bogoliubov-de Gennes (BdG) equation arsing from spin-1 Bose-Einstein condensates (BEC) to describe the elementary/collective excitations around the mean-field ground state. The BdG equation is essentially a constrained eigenvalue/eigenfunction system. Firstly, we investigate its analytical properties, including exact eigenpairs, generalized nullspace, and bi-orthogonality of eigenspaces. Secondly, by combining the standard Fourier spectral method for spatial discretization and a stable Gra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.08308","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.08308/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2506.08308","created_at":"2026-07-05T11:18:47.876100+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.08308v1","created_at":"2026-07-05T11:18:47.876100+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.08308","created_at":"2026-07-05T11:18:47.876100+00:00"},{"alias_kind":"pith_short_12","alias_value":"QRYT3DJK75L4","created_at":"2026-07-05T11:18:47.876100+00:00"},{"alias_kind":"pith_short_16","alias_value":"QRYT3DJK75L4AXHB","created_at":"2026-07-05T11:18:47.876100+00:00"},{"alias_kind":"pith_short_8","alias_value":"QRYT3DJK","created_at":"2026-07-05T11:18:47.876100+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/QRYT3DJK75L4AXHBMWILTQMAEH","json":"https://pith.science/pith/QRYT3DJK75L4AXHBMWILTQMAEH.json","graph_json":"https://pith.science/api/pith-number/QRYT3DJK75L4AXHBMWILTQMAEH/graph.json","events_json":"https://pith.science/api/pith-number/QRYT3DJK75L4AXHBMWILTQMAEH/events.json","paper":"https://pith.science/paper/QRYT3DJK"},"agent_actions":{"view_html":"https://pith.science/pith/QRYT3DJK75L4AXHBMWILTQMAEH","download_json":"https://pith.science/pith/QRYT3DJK75L4AXHBMWILTQMAEH.json","view_paper":"https://pith.science/paper/QRYT3DJK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.08308&json=true","fetch_graph":"https://pith.science/api/pith-number/QRYT3DJK75L4AXHBMWILTQMAEH/graph.json","fetch_events":"https://pith.science/api/pith-number/QRYT3DJK75L4AXHBMWILTQMAEH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QRYT3DJK75L4AXHBMWILTQMAEH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QRYT3DJK75L4AXHBMWILTQMAEH/action/storage_attestation","attest_author":"https://pith.science/pith/QRYT3DJK75L4AXHBMWILTQMAEH/action/author_attestation","sign_citation":"https://pith.science/pith/QRYT3DJK75L4AXHBMWILTQMAEH/action/citation_signature","submit_replication":"https://pith.science/pith/QRYT3DJK75L4AXHBMWILTQMAEH/action/replication_record"}},"created_at":"2026-07-05T11:18:47.876100+00:00","updated_at":"2026-07-05T11:18:47.876100+00:00"}