{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:GCPOFKYLSGPUJVZ2CNZKVIRVPY","short_pith_number":"pith:GCPOFKYL","schema_version":"1.0","canonical_sha256":"309ee2ab0b919f44d73a1372aaa2357e335a4aa193f20a6c8120b3c73a33e9f4","source":{"kind":"arxiv","id":"2504.06842","version":4},"attestation_state":"computed","paper":{"title":"Optimality of Gradient-MUSIC for spectral estimation","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Albert Fannjiang, Weilin Li, Wenjing Liao","submitted_at":"2025-04-09T13:00:49Z","abstract_excerpt":"We introduce the Gradient-MUSIC algorithm for estimating the unknown frequencies and amplitudes of a nonharmonic signal from noisy time samples. While the classical MUSIC algorithm performs a computationally expensive search over a fine grid, Gradient-MUSIC is significantly more efficient and eliminates the need for discretization over a fine grid by using optimization techniques. It coarsely scans the 1D landscape to find initialization simultaneously for all frequencies followed by parallelizable local refinement via gradient descent. We also analyze its performance when the noise level is s"},"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":"2504.06842","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.IT","submitted_at":"2025-04-09T13:00:49Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"fa2a0b83ed96a8d2609f24ba32def6183b023c975255f67bb7f7f583d2d76ad5","abstract_canon_sha256":"5bd0f2b39c4b0c8e28c6070861ad182d5467a34d8d0b83100cd2b5f04a5a1180"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-07T03:18:46.560599Z","signature_b64":"qhEjSkiGqlk52QAEdTAQH+kugxTxIaxoHsnaGZDz1W7n5t+52lA+gkMhPErM9ocYiKTwbNJIIKxKWaqML3PWDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"309ee2ab0b919f44d73a1372aaa2357e335a4aa193f20a6c8120b3c73a33e9f4","last_reissued_at":"2026-07-07T03:18:46.560034Z","signature_status":"signed_v1","first_computed_at":"2026-07-07T03:18:46.560034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimality of Gradient-MUSIC for spectral estimation","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Albert Fannjiang, Weilin Li, Wenjing Liao","submitted_at":"2025-04-09T13:00:49Z","abstract_excerpt":"We introduce the Gradient-MUSIC algorithm for estimating the unknown frequencies and amplitudes of a nonharmonic signal from noisy time samples. While the classical MUSIC algorithm performs a computationally expensive search over a fine grid, Gradient-MUSIC is significantly more efficient and eliminates the need for discretization over a fine grid by using optimization techniques. It coarsely scans the 1D landscape to find initialization simultaneously for all frequencies followed by parallelizable local refinement via gradient descent. We also analyze its performance when the noise level is s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.06842","kind":"arxiv","version":4},"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/2504.06842/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":"2504.06842","created_at":"2026-07-07T03:18:46.560096+00:00"},{"alias_kind":"arxiv_version","alias_value":"2504.06842v4","created_at":"2026-07-07T03:18:46.560096+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.06842","created_at":"2026-07-07T03:18:46.560096+00:00"},{"alias_kind":"pith_short_12","alias_value":"GCPOFKYLSGPU","created_at":"2026-07-07T03:18:46.560096+00:00"},{"alias_kind":"pith_short_16","alias_value":"GCPOFKYLSGPUJVZ2","created_at":"2026-07-07T03:18:46.560096+00:00"},{"alias_kind":"pith_short_8","alias_value":"GCPOFKYL","created_at":"2026-07-07T03:18:46.560096+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2607.08108","citing_title":"Low-Complexity Gridless Single-Snapshot DoA Estimation via Truncated Hankel Newton-MUSIC","ref_index":13,"is_internal_anchor":true},{"citing_arxiv_id":"2606.04003","citing_title":"A sharp analysis of Root-MUSIC: locations of correct and extraneous roots","ref_index":10,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GCPOFKYLSGPUJVZ2CNZKVIRVPY","json":"https://pith.science/pith/GCPOFKYLSGPUJVZ2CNZKVIRVPY.json","graph_json":"https://pith.science/api/pith-number/GCPOFKYLSGPUJVZ2CNZKVIRVPY/graph.json","events_json":"https://pith.science/api/pith-number/GCPOFKYLSGPUJVZ2CNZKVIRVPY/events.json","paper":"https://pith.science/paper/GCPOFKYL"},"agent_actions":{"view_html":"https://pith.science/pith/GCPOFKYLSGPUJVZ2CNZKVIRVPY","download_json":"https://pith.science/pith/GCPOFKYLSGPUJVZ2CNZKVIRVPY.json","view_paper":"https://pith.science/paper/GCPOFKYL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2504.06842&json=true","fetch_graph":"https://pith.science/api/pith-number/GCPOFKYLSGPUJVZ2CNZKVIRVPY/graph.json","fetch_events":"https://pith.science/api/pith-number/GCPOFKYLSGPUJVZ2CNZKVIRVPY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GCPOFKYLSGPUJVZ2CNZKVIRVPY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GCPOFKYLSGPUJVZ2CNZKVIRVPY/action/storage_attestation","attest_author":"https://pith.science/pith/GCPOFKYLSGPUJVZ2CNZKVIRVPY/action/author_attestation","sign_citation":"https://pith.science/pith/GCPOFKYLSGPUJVZ2CNZKVIRVPY/action/citation_signature","submit_replication":"https://pith.science/pith/GCPOFKYLSGPUJVZ2CNZKVIRVPY/action/replication_record"}},"created_at":"2026-07-07T03:18:46.560096+00:00","updated_at":"2026-07-07T03:18:46.560096+00:00"}