{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:DVYKOITOXJJ2TI2ALO7LEOHJPD","short_pith_number":"pith:DVYKOITO","canonical_record":{"source":{"id":"1809.10786","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-27T22:26:37Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"d82a6d1a38f6eeed2cf6a038de314b51bfcb50dc95becc71cc85df90f6d47c83","abstract_canon_sha256":"489aa5f881d61eba2218ae5ce9e5a907111fe4052c67e74cbf61aa0eacd374ea"},"schema_version":"1.0"},"canonical_sha256":"1d70a7226eba53a9a3405bbeb238e978e9d48097b726c63be5f36a9486047700","source":{"kind":"arxiv","id":"1809.10786","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.10786","created_at":"2026-05-17T23:41:17Z"},{"alias_kind":"arxiv_version","alias_value":"1809.10786v2","created_at":"2026-05-17T23:41:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.10786","created_at":"2026-05-17T23:41:17Z"},{"alias_kind":"pith_short_12","alias_value":"DVYKOITOXJJ2","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DVYKOITOXJJ2TI2A","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DVYKOITO","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:DVYKOITOXJJ2TI2ALO7LEOHJPD","target":"record","payload":{"canonical_record":{"source":{"id":"1809.10786","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-27T22:26:37Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"d82a6d1a38f6eeed2cf6a038de314b51bfcb50dc95becc71cc85df90f6d47c83","abstract_canon_sha256":"489aa5f881d61eba2218ae5ce9e5a907111fe4052c67e74cbf61aa0eacd374ea"},"schema_version":"1.0"},"canonical_sha256":"1d70a7226eba53a9a3405bbeb238e978e9d48097b726c63be5f36a9486047700","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:17.840644Z","signature_b64":"ttHTtRnu2QmxsZ8wjPiVrYVP8Wqtk88jD7Aptj87jyVoF2bs/oOGk8jjzMkqYDIGB2v8+vTkfBQss/OSfSnIAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d70a7226eba53a9a3405bbeb238e978e9d48097b726c63be5f36a9486047700","last_reissued_at":"2026-05-17T23:41:17.840073Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:17.840073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.10786","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:41:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QkpwK3r/LJHuFQUjkikEGjM33WkHcm9kNECUswJZl8EEAKdeuKfJq0kXnOQAsRN0y0eOrXlJtUk++aGF9YMjAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T04:22:35.700128Z"},"content_sha256":"002a321ed94a272a7eae14691add2a16d2e4b9c496e898d16303dda013b27984","schema_version":"1.0","event_id":"sha256:002a321ed94a272a7eae14691add2a16d2e4b9c496e898d16303dda013b27984"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:DVYKOITOXJJ2TI2ALO7LEOHJPD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fast SGL Fourier transforms for scattered data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Christian W\\\"ulker","submitted_at":"2018-09-27T22:26:37Z","abstract_excerpt":"Spherical Gauss-Laguerre (SGL) basis functions, i. e., normalized functions of the type $L_{n-l-1}^{(l + 1/2)}(r^2) r^l Y_{lm}(\\vartheta,\\varphi)$, $|m| \\leq l < n \\in \\mathbb{N}$, $L_{n-l-1}^{(l + 1/2)}$ being a generalized Laguerre polynomial, $Y_{lm}$ a spherical harmonic, constitute an orthonormal polynomial basis of the space $L^2$ on $\\mathbb{R}^3$ with radial Gaussian (multivariate Hermite) weight $\\exp(-r^2)$. We have recently described fast Fourier transforms for the SGL basis functions based on an exact quadrature formula with certain grid points in $\\mathbb{R}^3$. In this paper, we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10786","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:41:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wVjQDTmRlmDIY0lkGwzFJpZWn9hSdJS9oo9USeZJ5a1GUwMc5+v4p8vTh2796lGPUNw5qN3l4ufiTSarJUv+CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T04:22:35.700785Z"},"content_sha256":"a92ad62672990cce559bacae77da72bf7e168619547b98063af30e1df2ae6850","schema_version":"1.0","event_id":"sha256:a92ad62672990cce559bacae77da72bf7e168619547b98063af30e1df2ae6850"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DVYKOITOXJJ2TI2ALO7LEOHJPD/bundle.json","state_url":"https://pith.science/pith/DVYKOITOXJJ2TI2ALO7LEOHJPD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DVYKOITOXJJ2TI2ALO7LEOHJPD/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T04:22:35Z","links":{"resolver":"https://pith.science/pith/DVYKOITOXJJ2TI2ALO7LEOHJPD","bundle":"https://pith.science/pith/DVYKOITOXJJ2TI2ALO7LEOHJPD/bundle.json","state":"https://pith.science/pith/DVYKOITOXJJ2TI2ALO7LEOHJPD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DVYKOITOXJJ2TI2ALO7LEOHJPD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DVYKOITOXJJ2TI2ALO7LEOHJPD","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"489aa5f881d61eba2218ae5ce9e5a907111fe4052c67e74cbf61aa0eacd374ea","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-27T22:26:37Z","title_canon_sha256":"d82a6d1a38f6eeed2cf6a038de314b51bfcb50dc95becc71cc85df90f6d47c83"},"schema_version":"1.0","source":{"id":"1809.10786","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.10786","created_at":"2026-05-17T23:41:17Z"},{"alias_kind":"arxiv_version","alias_value":"1809.10786v2","created_at":"2026-05-17T23:41:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.10786","created_at":"2026-05-17T23:41:17Z"},{"alias_kind":"pith_short_12","alias_value":"DVYKOITOXJJ2","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DVYKOITOXJJ2TI2A","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DVYKOITO","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:a92ad62672990cce559bacae77da72bf7e168619547b98063af30e1df2ae6850","target":"graph","created_at":"2026-05-17T23:41:17Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Spherical Gauss-Laguerre (SGL) basis functions, i. e., normalized functions of the type $L_{n-l-1}^{(l + 1/2)}(r^2) r^l Y_{lm}(\\vartheta,\\varphi)$, $|m| \\leq l < n \\in \\mathbb{N}$, $L_{n-l-1}^{(l + 1/2)}$ being a generalized Laguerre polynomial, $Y_{lm}$ a spherical harmonic, constitute an orthonormal polynomial basis of the space $L^2$ on $\\mathbb{R}^3$ with radial Gaussian (multivariate Hermite) weight $\\exp(-r^2)$. We have recently described fast Fourier transforms for the SGL basis functions based on an exact quadrature formula with certain grid points in $\\mathbb{R}^3$. In this paper, we ","authors_text":"Christian W\\\"ulker","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-27T22:26:37Z","title":"Fast SGL Fourier transforms for scattered data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.10786","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:002a321ed94a272a7eae14691add2a16d2e4b9c496e898d16303dda013b27984","target":"record","created_at":"2026-05-17T23:41:17Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"489aa5f881d61eba2218ae5ce9e5a907111fe4052c67e74cbf61aa0eacd374ea","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-27T22:26:37Z","title_canon_sha256":"d82a6d1a38f6eeed2cf6a038de314b51bfcb50dc95becc71cc85df90f6d47c83"},"schema_version":"1.0","source":{"id":"1809.10786","kind":"arxiv","version":2}},"canonical_sha256":"1d70a7226eba53a9a3405bbeb238e978e9d48097b726c63be5f36a9486047700","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d70a7226eba53a9a3405bbeb238e978e9d48097b726c63be5f36a9486047700","first_computed_at":"2026-05-17T23:41:17.840073Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:17.840073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ttHTtRnu2QmxsZ8wjPiVrYVP8Wqtk88jD7Aptj87jyVoF2bs/oOGk8jjzMkqYDIGB2v8+vTkfBQss/OSfSnIAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:17.840644Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.10786","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:002a321ed94a272a7eae14691add2a16d2e4b9c496e898d16303dda013b27984","sha256:a92ad62672990cce559bacae77da72bf7e168619547b98063af30e1df2ae6850"],"state_sha256":"adabca4849079bc6bf7f2e6f776469412c7ab0e3086eb35cb60319068ad29dc1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A0Em7eqXqIRvJRvk8MtxKyP05aetNE8+wLG5sfA/YG9rk6sceWrS81Jf67XQE3wvrUJpnQiuTb3P+5STC+/LDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T04:22:35.703839Z","bundle_sha256":"b19cd6c08a427ebafd5a01dd55c6c44b10c364c0da92b59c6edccf978b2678da"}}