{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:EKPLQWI3KDX22BLH3N7IPM4JPC","short_pith_number":"pith:EKPLQWI3","schema_version":"1.0","canonical_sha256":"229eb8591b50efad0567db7e87b38978939c81401546c9e0e59fdfa2c6609f69","source":{"kind":"arxiv","id":"0809.1079","version":1},"attestation_state":"computed","paper":{"title":"Discrete Fourier analysis on fundamental domain of $A_d$ lattice and on simplex in $d$-variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.CA","authors_text":"Huiyuan Li, Yuan Xu","submitted_at":"2008-09-05T17:10:02Z","abstract_excerpt":"A discrete Fourier analysis on the fundamental domain $\\Omega_d$ of the $d$-dimensional lattice of type $A_d$ is studied, where $\\Omega_2$ is the regular hexagon and $\\Omega_3$ is the rhombic dodecahedron, and analogous results on $d$-dimensional simplex are derived by considering invariant and anti-invariant elements. Our main results include Fourier analysis in trigonometric functions, interpolation and cubature formulas on these domains. In particular, a trigonometric Lagrange interpolation on the simplex is shown to satisfy an explicit compact formula and the Lebesgue constant of the inter"},"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":"0809.1079","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2008-09-05T17:10:02Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"17eaa1259fe95606ab669feed7953e9ef2675ea940757c8f02ecc9f50d7d1371","abstract_canon_sha256":"65898d839c025c103435780bfb876a0946b28cd50714ce35437b7cdd8e7d11c6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T22:06:09.672446Z","signature_b64":"I+hii6I5gZPHOuqqO1WeW8K8jS3BXzPwgZtEZzN53WbxfHj/LCaRUgUMPHy/YWlsxFO80O8H4ewXSqQZT7jCDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"229eb8591b50efad0567db7e87b38978939c81401546c9e0e59fdfa2c6609f69","last_reissued_at":"2026-06-03T22:06:09.671881Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T22:06:09.671881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Discrete Fourier analysis on fundamental domain of $A_d$ lattice and on simplex in $d$-variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.CA","authors_text":"Huiyuan Li, Yuan Xu","submitted_at":"2008-09-05T17:10:02Z","abstract_excerpt":"A discrete Fourier analysis on the fundamental domain $\\Omega_d$ of the $d$-dimensional lattice of type $A_d$ is studied, where $\\Omega_2$ is the regular hexagon and $\\Omega_3$ is the rhombic dodecahedron, and analogous results on $d$-dimensional simplex are derived by considering invariant and anti-invariant elements. Our main results include Fourier analysis in trigonometric functions, interpolation and cubature formulas on these domains. In particular, a trigonometric Lagrange interpolation on the simplex is shown to satisfy an explicit compact formula and the Lebesgue constant of the inter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.1079","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/0809.1079/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":"0809.1079","created_at":"2026-06-03T22:06:09.671964+00:00"},{"alias_kind":"arxiv_version","alias_value":"0809.1079v1","created_at":"2026-06-03T22:06:09.671964+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.1079","created_at":"2026-06-03T22:06:09.671964+00:00"},{"alias_kind":"pith_short_12","alias_value":"EKPLQWI3KDX2","created_at":"2026-06-03T22:06:09.671964+00:00"},{"alias_kind":"pith_short_16","alias_value":"EKPLQWI3KDX22BLH","created_at":"2026-06-03T22:06:09.671964+00:00"},{"alias_kind":"pith_short_8","alias_value":"EKPLQWI3","created_at":"2026-06-03T22:06:09.671964+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/EKPLQWI3KDX22BLH3N7IPM4JPC","json":"https://pith.science/pith/EKPLQWI3KDX22BLH3N7IPM4JPC.json","graph_json":"https://pith.science/api/pith-number/EKPLQWI3KDX22BLH3N7IPM4JPC/graph.json","events_json":"https://pith.science/api/pith-number/EKPLQWI3KDX22BLH3N7IPM4JPC/events.json","paper":"https://pith.science/paper/EKPLQWI3"},"agent_actions":{"view_html":"https://pith.science/pith/EKPLQWI3KDX22BLH3N7IPM4JPC","download_json":"https://pith.science/pith/EKPLQWI3KDX22BLH3N7IPM4JPC.json","view_paper":"https://pith.science/paper/EKPLQWI3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0809.1079&json=true","fetch_graph":"https://pith.science/api/pith-number/EKPLQWI3KDX22BLH3N7IPM4JPC/graph.json","fetch_events":"https://pith.science/api/pith-number/EKPLQWI3KDX22BLH3N7IPM4JPC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EKPLQWI3KDX22BLH3N7IPM4JPC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EKPLQWI3KDX22BLH3N7IPM4JPC/action/storage_attestation","attest_author":"https://pith.science/pith/EKPLQWI3KDX22BLH3N7IPM4JPC/action/author_attestation","sign_citation":"https://pith.science/pith/EKPLQWI3KDX22BLH3N7IPM4JPC/action/citation_signature","submit_replication":"https://pith.science/pith/EKPLQWI3KDX22BLH3N7IPM4JPC/action/replication_record"}},"created_at":"2026-06-03T22:06:09.671964+00:00","updated_at":"2026-06-03T22:06:09.671964+00:00"}