{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:AFSUBPJRZBZWPKIPRN62F4DZZD","short_pith_number":"pith:AFSUBPJR","canonical_record":{"source":{"id":"1508.04758","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-08-19T19:56:59Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"b97b8a36ef30e77f7da52824fa73b41ba6823e7592cee8668d12a292494af8b2","abstract_canon_sha256":"8a48b0a37099984c9767b11d9be25e30fd22cdaebf3abfb33dc6b4e456b7ff70"},"schema_version":"1.0"},"canonical_sha256":"016540bd31c87367a90f8b7da2f079c8c5c8e524b1ab4e0517fc01c6ecf6fc50","source":{"kind":"arxiv","id":"1508.04758","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.04758","created_at":"2026-05-18T01:18:14Z"},{"alias_kind":"arxiv_version","alias_value":"1508.04758v2","created_at":"2026-05-18T01:18:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.04758","created_at":"2026-05-18T01:18:14Z"},{"alias_kind":"pith_short_12","alias_value":"AFSUBPJRZBZW","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AFSUBPJRZBZWPKIP","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AFSUBPJR","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:AFSUBPJRZBZWPKIPRN62F4DZZD","target":"record","payload":{"canonical_record":{"source":{"id":"1508.04758","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-08-19T19:56:59Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"b97b8a36ef30e77f7da52824fa73b41ba6823e7592cee8668d12a292494af8b2","abstract_canon_sha256":"8a48b0a37099984c9767b11d9be25e30fd22cdaebf3abfb33dc6b4e456b7ff70"},"schema_version":"1.0"},"canonical_sha256":"016540bd31c87367a90f8b7da2f079c8c5c8e524b1ab4e0517fc01c6ecf6fc50","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:14.387046Z","signature_b64":"D/apV5XC80W0F2Ur1HHrHFWt1GqDpTC/JmxYmEKiTtynsYA+NC+Re3HCMRpsSMD4iMxTMITncbjc6VdTBKvqDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"016540bd31c87367a90f8b7da2f079c8c5c8e524b1ab4e0517fc01c6ecf6fc50","last_reissued_at":"2026-05-18T01:18:14.386477Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:14.386477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.04758","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":"2026-05-18T01:18:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JVlhKVL9wfZI0cGJ3qVVwuRorwHFplDjxuReShLAVcK9de7Wf5847y7tImLGkhhWYqRaQSDIFa2GvArVUMbWCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T12:50:16.493155Z"},"content_sha256":"871df83f4a10707ba33bc5b8962d309756fff5d7d8e577ad887e8bbff1276054","schema_version":"1.0","event_id":"sha256:871df83f4a10707ba33bc5b8962d309756fff5d7d8e577ad887e8bbff1276054"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:AFSUBPJRZBZWPKIPRN62F4DZZD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rapidly Computing Sparse Legendre Expansions via Sparse Fourier Transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Hyejin Kim, Mark Iwen, Xianfeng Hu","submitted_at":"2015-08-19T19:56:59Z","abstract_excerpt":"In this paper we propose a general strategy for rapidly computing sparse Legendre expansions. The resulting methods yield a new class of fast algorithms capable of approximating a given function $f:[-1,1] \\rightarrow \\mathbb{R}$ with a near-optimal linear combination of $s$ Legendre polynomials of degree $\\leq N$ in just $(s \\log N)^{\\mathcal{O}(1)}$-time. When $s \\ll N$ these algorithms exhibit sublinear runtime complexities in $N$, as opposed to traditional $\\Omega(N \\log N)$-time methods for computing all of the first $N$ Legendre coefficients of $f$. Theoretical as well as numerical result"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04758","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":"2026-05-18T01:18:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BHPrcGEaDBXQCYyiduGSskpXDBabLR+tdKDoxPU2PTZbGPGoMAoV5Kcf3wwSXtE+3lmoXBN207fabzbA6aqbAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T12:50:16.493508Z"},"content_sha256":"478efcdbabf80bf39e1eab26bfbcb71089c3f9a19b4a82ede8a0ca1fdd0a820e","schema_version":"1.0","event_id":"sha256:478efcdbabf80bf39e1eab26bfbcb71089c3f9a19b4a82ede8a0ca1fdd0a820e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AFSUBPJRZBZWPKIPRN62F4DZZD/bundle.json","state_url":"https://pith.science/pith/AFSUBPJRZBZWPKIPRN62F4DZZD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AFSUBPJRZBZWPKIPRN62F4DZZD/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":"2026-06-25T12:50:16Z","links":{"resolver":"https://pith.science/pith/AFSUBPJRZBZWPKIPRN62F4DZZD","bundle":"https://pith.science/pith/AFSUBPJRZBZWPKIPRN62F4DZZD/bundle.json","state":"https://pith.science/pith/AFSUBPJRZBZWPKIPRN62F4DZZD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AFSUBPJRZBZWPKIPRN62F4DZZD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:AFSUBPJRZBZWPKIPRN62F4DZZD","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":"8a48b0a37099984c9767b11d9be25e30fd22cdaebf3abfb33dc6b4e456b7ff70","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-08-19T19:56:59Z","title_canon_sha256":"b97b8a36ef30e77f7da52824fa73b41ba6823e7592cee8668d12a292494af8b2"},"schema_version":"1.0","source":{"id":"1508.04758","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.04758","created_at":"2026-05-18T01:18:14Z"},{"alias_kind":"arxiv_version","alias_value":"1508.04758v2","created_at":"2026-05-18T01:18:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.04758","created_at":"2026-05-18T01:18:14Z"},{"alias_kind":"pith_short_12","alias_value":"AFSUBPJRZBZW","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AFSUBPJRZBZWPKIP","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AFSUBPJR","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:478efcdbabf80bf39e1eab26bfbcb71089c3f9a19b4a82ede8a0ca1fdd0a820e","target":"graph","created_at":"2026-05-18T01:18:14Z","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":"In this paper we propose a general strategy for rapidly computing sparse Legendre expansions. The resulting methods yield a new class of fast algorithms capable of approximating a given function $f:[-1,1] \\rightarrow \\mathbb{R}$ with a near-optimal linear combination of $s$ Legendre polynomials of degree $\\leq N$ in just $(s \\log N)^{\\mathcal{O}(1)}$-time. When $s \\ll N$ these algorithms exhibit sublinear runtime complexities in $N$, as opposed to traditional $\\Omega(N \\log N)$-time methods for computing all of the first $N$ Legendre coefficients of $f$. Theoretical as well as numerical result","authors_text":"Hyejin Kim, Mark Iwen, Xianfeng Hu","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-08-19T19:56:59Z","title":"Rapidly Computing Sparse Legendre Expansions via Sparse Fourier Transforms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04758","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":"sha256:871df83f4a10707ba33bc5b8962d309756fff5d7d8e577ad887e8bbff1276054","target":"record","created_at":"2026-05-18T01:18:14Z","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":"8a48b0a37099984c9767b11d9be25e30fd22cdaebf3abfb33dc6b4e456b7ff70","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-08-19T19:56:59Z","title_canon_sha256":"b97b8a36ef30e77f7da52824fa73b41ba6823e7592cee8668d12a292494af8b2"},"schema_version":"1.0","source":{"id":"1508.04758","kind":"arxiv","version":2}},"canonical_sha256":"016540bd31c87367a90f8b7da2f079c8c5c8e524b1ab4e0517fc01c6ecf6fc50","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"016540bd31c87367a90f8b7da2f079c8c5c8e524b1ab4e0517fc01c6ecf6fc50","first_computed_at":"2026-05-18T01:18:14.386477Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:14.386477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D/apV5XC80W0F2Ur1HHrHFWt1GqDpTC/JmxYmEKiTtynsYA+NC+Re3HCMRpsSMD4iMxTMITncbjc6VdTBKvqDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:14.387046Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.04758","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:871df83f4a10707ba33bc5b8962d309756fff5d7d8e577ad887e8bbff1276054","sha256:478efcdbabf80bf39e1eab26bfbcb71089c3f9a19b4a82ede8a0ca1fdd0a820e"],"state_sha256":"0a892ab9f7fd76234ded144c50de86010e9030306e7bc08c3af300ac7a7d8c82"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YAY7BtDus8GzNcQLaC9jimFeRR0S403u/fsJ76DujCSFNcn53q0xfYywnir/hmp7n2CIft6DHNXnzS6MyKicAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T12:50:16.495376Z","bundle_sha256":"d87e86e3589888d499887ce148eaf734ff7fbe054bef25fbbf031fbe21279ce8"}}