{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:LBNMPO6WPOLTKZKQDL53XCIJW4","short_pith_number":"pith:LBNMPO6W","canonical_record":{"source":{"id":"1407.8315","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-07-31T08:45:19Z","cross_cats_sorted":[],"title_canon_sha256":"5e95dc57db7fbba5d1c7c07dee6e779cf707d2a766732f351bb72fe647143016","abstract_canon_sha256":"d3f4e67e146602ddd407ba4eaabe95ae62d4b4ed5aa96f506fe0d76b7e441506"},"schema_version":"1.0"},"canonical_sha256":"585ac7bbd67b973565501afbbb8909b7073d2c2261227fa29530e1ec2b2ea435","source":{"kind":"arxiv","id":"1407.8315","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.8315","created_at":"2026-05-18T02:03:52Z"},{"alias_kind":"arxiv_version","alias_value":"1407.8315v2","created_at":"2026-05-18T02:03:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.8315","created_at":"2026-05-18T02:03:52Z"},{"alias_kind":"pith_short_12","alias_value":"LBNMPO6WPOLT","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"LBNMPO6WPOLTKZKQ","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"LBNMPO6W","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:LBNMPO6WPOLTKZKQDL53XCIJW4","target":"record","payload":{"canonical_record":{"source":{"id":"1407.8315","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-07-31T08:45:19Z","cross_cats_sorted":[],"title_canon_sha256":"5e95dc57db7fbba5d1c7c07dee6e779cf707d2a766732f351bb72fe647143016","abstract_canon_sha256":"d3f4e67e146602ddd407ba4eaabe95ae62d4b4ed5aa96f506fe0d76b7e441506"},"schema_version":"1.0"},"canonical_sha256":"585ac7bbd67b973565501afbbb8909b7073d2c2261227fa29530e1ec2b2ea435","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:52.769851Z","signature_b64":"4vFKXiAy14RD/+c+IRxud837ynp01SWrXR2O9CiiVX5gpvpg8s90taXKpxSEMwMdd8K4XDf/3STAh4gfL7lqCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"585ac7bbd67b973565501afbbb8909b7073d2c2261227fa29530e1ec2b2ea435","last_reissued_at":"2026-05-18T02:03:52.769220Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:52.769220Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.8315","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":"2026-05-18T02:03:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8dxf77GODXJEkMROlsMxSVXXJh2FYSigq6yEBoUvEq/BOlO4p3zwlPPbTDU/i2U8HG85139IWiiVuhZys5uTDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:02:21.340080Z"},"content_sha256":"e2c0c33577822258c30dd9f4b291638e748d011f290d332bf24b36c3747e31b6","schema_version":"1.0","event_id":"sha256:e2c0c33577822258c30dd9f4b291638e748d011f290d332bf24b36c3747e31b6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:LBNMPO6WPOLTKZKQDL53XCIJW4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sparse Fast Fourier Transform for Exactly and Generally K-Sparse Signals by Downsampling and Sparse Recovery","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Chun-Shien Lu, Soo-Chang Pei, Sung-Hsien Hsieh","submitted_at":"2014-07-31T08:45:19Z","abstract_excerpt":"Fast Fourier Transform (FFT) is one of the most important tools in digital signal processing. FFT costs O(N \\log N) for transforming a signal of length N. Recently, Sparse Fourier Transform (SFT) has emerged as a critical issue addressing how to compute a compressed Fourier transform of a signal with complexity being related to the sparsity of its spectrum. In this paper, a new SFT algorithm is proposed for both exactly K-sparse signals (with K non-zero frequencies) and generally K-sparse signals (with K significant frequencies), with the assumption that the distribution of the non-zero freque"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.8315","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":"2026-05-18T02:03:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y0LCv4CSflg4KZHrXk20yHsP2PEhpKEwzHO90KQfhaAAJhCBKdtCEQrRr3nf376uy1bGlsqIO1BxEeyZQ/lCDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:02:21.340435Z"},"content_sha256":"22bf0da2f5ef7979a645d819a2a2041f8210fd654fff34572e1f0b3f58d3c4fe","schema_version":"1.0","event_id":"sha256:22bf0da2f5ef7979a645d819a2a2041f8210fd654fff34572e1f0b3f58d3c4fe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LBNMPO6WPOLTKZKQDL53XCIJW4/bundle.json","state_url":"https://pith.science/pith/LBNMPO6WPOLTKZKQDL53XCIJW4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LBNMPO6WPOLTKZKQDL53XCIJW4/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":"2026-06-26T11:02:21Z","links":{"resolver":"https://pith.science/pith/LBNMPO6WPOLTKZKQDL53XCIJW4","bundle":"https://pith.science/pith/LBNMPO6WPOLTKZKQDL53XCIJW4/bundle.json","state":"https://pith.science/pith/LBNMPO6WPOLTKZKQDL53XCIJW4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LBNMPO6WPOLTKZKQDL53XCIJW4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LBNMPO6WPOLTKZKQDL53XCIJW4","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":"d3f4e67e146602ddd407ba4eaabe95ae62d4b4ed5aa96f506fe0d76b7e441506","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-07-31T08:45:19Z","title_canon_sha256":"5e95dc57db7fbba5d1c7c07dee6e779cf707d2a766732f351bb72fe647143016"},"schema_version":"1.0","source":{"id":"1407.8315","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.8315","created_at":"2026-05-18T02:03:52Z"},{"alias_kind":"arxiv_version","alias_value":"1407.8315v2","created_at":"2026-05-18T02:03:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.8315","created_at":"2026-05-18T02:03:52Z"},{"alias_kind":"pith_short_12","alias_value":"LBNMPO6WPOLT","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"LBNMPO6WPOLTKZKQ","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"LBNMPO6W","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:22bf0da2f5ef7979a645d819a2a2041f8210fd654fff34572e1f0b3f58d3c4fe","target":"graph","created_at":"2026-05-18T02:03:52Z","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":"Fast Fourier Transform (FFT) is one of the most important tools in digital signal processing. FFT costs O(N \\log N) for transforming a signal of length N. Recently, Sparse Fourier Transform (SFT) has emerged as a critical issue addressing how to compute a compressed Fourier transform of a signal with complexity being related to the sparsity of its spectrum. In this paper, a new SFT algorithm is proposed for both exactly K-sparse signals (with K non-zero frequencies) and generally K-sparse signals (with K significant frequencies), with the assumption that the distribution of the non-zero freque","authors_text":"Chun-Shien Lu, Soo-Chang Pei, Sung-Hsien Hsieh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-07-31T08:45:19Z","title":"Sparse Fast Fourier Transform for Exactly and Generally K-Sparse Signals by Downsampling and Sparse Recovery"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.8315","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:e2c0c33577822258c30dd9f4b291638e748d011f290d332bf24b36c3747e31b6","target":"record","created_at":"2026-05-18T02:03:52Z","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":"d3f4e67e146602ddd407ba4eaabe95ae62d4b4ed5aa96f506fe0d76b7e441506","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-07-31T08:45:19Z","title_canon_sha256":"5e95dc57db7fbba5d1c7c07dee6e779cf707d2a766732f351bb72fe647143016"},"schema_version":"1.0","source":{"id":"1407.8315","kind":"arxiv","version":2}},"canonical_sha256":"585ac7bbd67b973565501afbbb8909b7073d2c2261227fa29530e1ec2b2ea435","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"585ac7bbd67b973565501afbbb8909b7073d2c2261227fa29530e1ec2b2ea435","first_computed_at":"2026-05-18T02:03:52.769220Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:52.769220Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4vFKXiAy14RD/+c+IRxud837ynp01SWrXR2O9CiiVX5gpvpg8s90taXKpxSEMwMdd8K4XDf/3STAh4gfL7lqCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:52.769851Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.8315","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2c0c33577822258c30dd9f4b291638e748d011f290d332bf24b36c3747e31b6","sha256:22bf0da2f5ef7979a645d819a2a2041f8210fd654fff34572e1f0b3f58d3c4fe"],"state_sha256":"80af8c7630d754550099f35df2bd603b237ddec27c88fbd529a6aad4ab9893f7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hP95wkTMhQ1CA99qp3iKInVvCwgOw3ZCmLZg8rvtaZgWzjkm7aFatNd7/sLnGRnc6ZfgVvEbwC05ix532Qx/Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T11:02:21.342307Z","bundle_sha256":"53e8b3420ba8babe7c90837c090038cabc3c9cc3d2f0894e54302203cd81dae1"}}