{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:USXR63QS7RVSYONKZEMMO5UNQY","short_pith_number":"pith:USXR63QS","schema_version":"1.0","canonical_sha256":"a4af1f6e12fc6b2c39aac918c7768d8615a44ae0f328e542a03569d11fee0b62","source":{"kind":"arxiv","id":"1704.01791","version":2},"attestation_state":"computed","paper":{"title":"Translation matrix elements for spherical Gauss-Laguerre basis functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Christian W\\\"ulker, J\\\"urgen Prestin","submitted_at":"2017-04-06T11:43:37Z","abstract_excerpt":"Spherical Gauss-Laguerre (SGL) basis functions, i.e., normalized functions of the type $L_{n-l-1}^{(l + 1/2)}(r^2) r^{l} Y_{lm}(\\vartheta,\\varphi)$, $|m| \\leq l < n \\in \\mathbb{N}$, constitute an orthonormal polynomial basis of the space $L^{2}$ on $\\mathbb{R}^{3}$ with radial Gaussian weight $\\exp(-r^{2})$. We have recently described reliable fast Fourier transforms for the SGL basis functions. The main application of the SGL basis functions and our fast algorithms is in solving certain three-dimensional rigid matching problems, where the center is prioritized over the periphery. For this pur"},"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":"1704.01791","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-04-06T11:43:37Z","cross_cats_sorted":[],"title_canon_sha256":"fa59c2ae62d824a6fd431b105befe5c36deb86f22289a5c6a15c43a58d6ee7d2","abstract_canon_sha256":"634fb6a1a46b12d653ed706b814878dcd90688fdc17553e00131fce91355b434"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:06.199853Z","signature_b64":"zkZ669iPTDS59pJ2lqgHU9gcP/0dpSxTKModhA8SpxurdTWruLACQwOjoVt7Siy+8/qMfNJjjzzKCwJ6ga3tAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4af1f6e12fc6b2c39aac918c7768d8615a44ae0f328e542a03569d11fee0b62","last_reissued_at":"2026-05-18T00:15:06.199040Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:06.199040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Translation matrix elements for spherical Gauss-Laguerre basis functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Christian W\\\"ulker, J\\\"urgen Prestin","submitted_at":"2017-04-06T11:43:37Z","abstract_excerpt":"Spherical Gauss-Laguerre (SGL) basis functions, i.e., normalized functions of the type $L_{n-l-1}^{(l + 1/2)}(r^2) r^{l} Y_{lm}(\\vartheta,\\varphi)$, $|m| \\leq l < n \\in \\mathbb{N}$, constitute an orthonormal polynomial basis of the space $L^{2}$ on $\\mathbb{R}^{3}$ with radial Gaussian weight $\\exp(-r^{2})$. We have recently described reliable fast Fourier transforms for the SGL basis functions. The main application of the SGL basis functions and our fast algorithms is in solving certain three-dimensional rigid matching problems, where the center is prioritized over the periphery. For this pur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01791","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":"1704.01791","created_at":"2026-05-18T00:15:06.199185+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.01791v2","created_at":"2026-05-18T00:15:06.199185+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.01791","created_at":"2026-05-18T00:15:06.199185+00:00"},{"alias_kind":"pith_short_12","alias_value":"USXR63QS7RVS","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_16","alias_value":"USXR63QS7RVSYONK","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_8","alias_value":"USXR63QS","created_at":"2026-05-18T12:31:49.984773+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/USXR63QS7RVSYONKZEMMO5UNQY","json":"https://pith.science/pith/USXR63QS7RVSYONKZEMMO5UNQY.json","graph_json":"https://pith.science/api/pith-number/USXR63QS7RVSYONKZEMMO5UNQY/graph.json","events_json":"https://pith.science/api/pith-number/USXR63QS7RVSYONKZEMMO5UNQY/events.json","paper":"https://pith.science/paper/USXR63QS"},"agent_actions":{"view_html":"https://pith.science/pith/USXR63QS7RVSYONKZEMMO5UNQY","download_json":"https://pith.science/pith/USXR63QS7RVSYONKZEMMO5UNQY.json","view_paper":"https://pith.science/paper/USXR63QS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.01791&json=true","fetch_graph":"https://pith.science/api/pith-number/USXR63QS7RVSYONKZEMMO5UNQY/graph.json","fetch_events":"https://pith.science/api/pith-number/USXR63QS7RVSYONKZEMMO5UNQY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/USXR63QS7RVSYONKZEMMO5UNQY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/USXR63QS7RVSYONKZEMMO5UNQY/action/storage_attestation","attest_author":"https://pith.science/pith/USXR63QS7RVSYONKZEMMO5UNQY/action/author_attestation","sign_citation":"https://pith.science/pith/USXR63QS7RVSYONKZEMMO5UNQY/action/citation_signature","submit_replication":"https://pith.science/pith/USXR63QS7RVSYONKZEMMO5UNQY/action/replication_record"}},"created_at":"2026-05-18T00:15:06.199185+00:00","updated_at":"2026-05-18T00:15:06.199185+00:00"}