{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:XIDGE5WDBOQ4RRAVBEWEHKG6HK","short_pith_number":"pith:XIDGE5WD","schema_version":"1.0","canonical_sha256":"ba066276c30ba1c8c415092c43a8de3a83f950d606f3a0cfab8a25b388dff7de","source":{"kind":"arxiv","id":"1611.04950","version":2},"attestation_state":"computed","paper":{"title":"The Fast Slepian Transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Justin Romberg, Mark A. Davenport, Michael B. Wakin, Santhosh Karnik, Zhihui Zhu","submitted_at":"2016-11-15T17:27:49Z","abstract_excerpt":"The discrete prolate spheroidal sequences (DPSS's) provide an efficient representation for discrete signals that are perfectly timelimited and nearly bandlimited. Due to the high computational complexity of projecting onto the DPSS basis - also known as the Slepian basis - this representation is often overlooked in favor of the fast Fourier transform (FFT). We show that there exist fast constructions for computing approximate projections onto the leading Slepian basis elements. The complexity of the resulting algorithms is comparable to the FFT, and scales favorably as the quality of the desir"},"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":"1611.04950","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-11-15T17:27:49Z","cross_cats_sorted":[],"title_canon_sha256":"c5aedabe05eff2aa4f1ead5116afc50a0f22d1583b170208acba100d4baad359","abstract_canon_sha256":"25b9be0f76a490d639929797455810126a693536cd617a676bd415ad53c1419d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:13.860654Z","signature_b64":"UT0XRtEGijThek0n9f+IFGVbvcbl+JGNsojDG3LgGQQ3crz+B4sG/VAzvz9erVZ4AFlG7Vbg1uGr18dyjYDOAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba066276c30ba1c8c415092c43a8de3a83f950d606f3a0cfab8a25b388dff7de","last_reissued_at":"2026-05-18T00:38:13.860003Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:13.860003Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Fast Slepian Transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Justin Romberg, Mark A. Davenport, Michael B. Wakin, Santhosh Karnik, Zhihui Zhu","submitted_at":"2016-11-15T17:27:49Z","abstract_excerpt":"The discrete prolate spheroidal sequences (DPSS's) provide an efficient representation for discrete signals that are perfectly timelimited and nearly bandlimited. Due to the high computational complexity of projecting onto the DPSS basis - also known as the Slepian basis - this representation is often overlooked in favor of the fast Fourier transform (FFT). We show that there exist fast constructions for computing approximate projections onto the leading Slepian basis elements. The complexity of the resulting algorithms is comparable to the FFT, and scales favorably as the quality of the desir"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04950","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":"1611.04950","created_at":"2026-05-18T00:38:13.860101+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.04950v2","created_at":"2026-05-18T00:38:13.860101+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.04950","created_at":"2026-05-18T00:38:13.860101+00:00"},{"alias_kind":"pith_short_12","alias_value":"XIDGE5WDBOQ4","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"XIDGE5WDBOQ4RRAV","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"XIDGE5WD","created_at":"2026-05-18T12:30:51.357362+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/XIDGE5WDBOQ4RRAVBEWEHKG6HK","json":"https://pith.science/pith/XIDGE5WDBOQ4RRAVBEWEHKG6HK.json","graph_json":"https://pith.science/api/pith-number/XIDGE5WDBOQ4RRAVBEWEHKG6HK/graph.json","events_json":"https://pith.science/api/pith-number/XIDGE5WDBOQ4RRAVBEWEHKG6HK/events.json","paper":"https://pith.science/paper/XIDGE5WD"},"agent_actions":{"view_html":"https://pith.science/pith/XIDGE5WDBOQ4RRAVBEWEHKG6HK","download_json":"https://pith.science/pith/XIDGE5WDBOQ4RRAVBEWEHKG6HK.json","view_paper":"https://pith.science/paper/XIDGE5WD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.04950&json=true","fetch_graph":"https://pith.science/api/pith-number/XIDGE5WDBOQ4RRAVBEWEHKG6HK/graph.json","fetch_events":"https://pith.science/api/pith-number/XIDGE5WDBOQ4RRAVBEWEHKG6HK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XIDGE5WDBOQ4RRAVBEWEHKG6HK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XIDGE5WDBOQ4RRAVBEWEHKG6HK/action/storage_attestation","attest_author":"https://pith.science/pith/XIDGE5WDBOQ4RRAVBEWEHKG6HK/action/author_attestation","sign_citation":"https://pith.science/pith/XIDGE5WDBOQ4RRAVBEWEHKG6HK/action/citation_signature","submit_replication":"https://pith.science/pith/XIDGE5WDBOQ4RRAVBEWEHKG6HK/action/replication_record"}},"created_at":"2026-05-18T00:38:13.860101+00:00","updated_at":"2026-05-18T00:38:13.860101+00:00"}