{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:LD3KS2YEYXL5TYOPHL27MVBPSY","short_pith_number":"pith:LD3KS2YE","schema_version":"1.0","canonical_sha256":"58f6a96b04c5d7d9e1cf3af5f6542f963e167b476dc60d63c161e8051dfbdb2a","source":{"kind":"arxiv","id":"1311.4120","version":2},"attestation_state":"computed","paper":{"title":"Fast and Accurate Evaluation of Nonlocal Coulomb and Dipole-Dipole Interactions via the Nonuniform FFT","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Leslie Greengard, Shidong Jiang, Weizhu Bao","submitted_at":"2013-11-17T05:40:27Z","abstract_excerpt":"We present a fast and accurate algorithm for the evaluation of nonlocal (long-range) Coulomb and dipole-dipole interactions in free space. The governing potential is simply the convolution of an interaction kernel $U(\\bx)$ and a density function $\\rho(\\bx)=|\\psi(\\bx)|^2$, for some complex-valued wave function $\\psi(\\bx)$, permitting the formal use of Fourier methods. These are hampered by the fact that the Fourier transform of the interaction kernel $\\widehat{U}(\\bk)$ has a singularity at the origin $\\bk={\\bf 0}$ in Fourier (phase) space. Thus, accuracy is lost when using a uniform Cartesian g"},"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":"1311.4120","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-11-17T05:40:27Z","cross_cats_sorted":[],"title_canon_sha256":"bf420ad7ce1de23c292a718c3816bb11c31e3fad3616faa833723c7370fe56fd","abstract_canon_sha256":"33cbdc7392e56d40daef4a19c81b0b2303f8faa0a4c241264548631444c2281e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:08.846447Z","signature_b64":"XJQNisuUl1wxY72G2peWvJPff8wBMHg6fFUWcR5aSbwMfOGpPeKoJDeTQZoFz8ZGFfSavbGmCv12MFaDdpQcDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58f6a96b04c5d7d9e1cf3af5f6542f963e167b476dc60d63c161e8051dfbdb2a","last_reissued_at":"2026-05-18T02:41:08.846022Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:08.846022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fast and Accurate Evaluation of Nonlocal Coulomb and Dipole-Dipole Interactions via the Nonuniform FFT","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Leslie Greengard, Shidong Jiang, Weizhu Bao","submitted_at":"2013-11-17T05:40:27Z","abstract_excerpt":"We present a fast and accurate algorithm for the evaluation of nonlocal (long-range) Coulomb and dipole-dipole interactions in free space. The governing potential is simply the convolution of an interaction kernel $U(\\bx)$ and a density function $\\rho(\\bx)=|\\psi(\\bx)|^2$, for some complex-valued wave function $\\psi(\\bx)$, permitting the formal use of Fourier methods. These are hampered by the fact that the Fourier transform of the interaction kernel $\\widehat{U}(\\bk)$ has a singularity at the origin $\\bk={\\bf 0}$ in Fourier (phase) space. Thus, accuracy is lost when using a uniform Cartesian g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4120","kind":"arxiv","version":2},"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":"1311.4120","created_at":"2026-05-18T02:41:08.846091+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.4120v2","created_at":"2026-05-18T02:41:08.846091+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.4120","created_at":"2026-05-18T02:41:08.846091+00:00"},{"alias_kind":"pith_short_12","alias_value":"LD3KS2YEYXL5","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"LD3KS2YEYXL5TYOP","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"LD3KS2YE","created_at":"2026-05-18T12:27:51.066281+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/LD3KS2YEYXL5TYOPHL27MVBPSY","json":"https://pith.science/pith/LD3KS2YEYXL5TYOPHL27MVBPSY.json","graph_json":"https://pith.science/api/pith-number/LD3KS2YEYXL5TYOPHL27MVBPSY/graph.json","events_json":"https://pith.science/api/pith-number/LD3KS2YEYXL5TYOPHL27MVBPSY/events.json","paper":"https://pith.science/paper/LD3KS2YE"},"agent_actions":{"view_html":"https://pith.science/pith/LD3KS2YEYXL5TYOPHL27MVBPSY","download_json":"https://pith.science/pith/LD3KS2YEYXL5TYOPHL27MVBPSY.json","view_paper":"https://pith.science/paper/LD3KS2YE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.4120&json=true","fetch_graph":"https://pith.science/api/pith-number/LD3KS2YEYXL5TYOPHL27MVBPSY/graph.json","fetch_events":"https://pith.science/api/pith-number/LD3KS2YEYXL5TYOPHL27MVBPSY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LD3KS2YEYXL5TYOPHL27MVBPSY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LD3KS2YEYXL5TYOPHL27MVBPSY/action/storage_attestation","attest_author":"https://pith.science/pith/LD3KS2YEYXL5TYOPHL27MVBPSY/action/author_attestation","sign_citation":"https://pith.science/pith/LD3KS2YEYXL5TYOPHL27MVBPSY/action/citation_signature","submit_replication":"https://pith.science/pith/LD3KS2YEYXL5TYOPHL27MVBPSY/action/replication_record"}},"created_at":"2026-05-18T02:41:08.846091+00:00","updated_at":"2026-05-18T02:41:08.846091+00:00"}