{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:OJGECJEB4FUGSL27M5ZRN5UJAZ","short_pith_number":"pith:OJGECJEB","schema_version":"1.0","canonical_sha256":"724c412481e168692f5f677316f689065e9c7355f6bdeb6991edbd3da22558e3","source":{"kind":"arxiv","id":"2410.21690","version":3},"attestation_state":"computed","paper":{"title":"Improved Spectral Density Estimation via Explicit and Implicit Deflation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"cs.DS","authors_text":"Archan Ray, Cameron Musco, Christopher Musco, Rajarshi Bhattacharjee, Rajesh Jayaram","submitted_at":"2024-10-29T03:18:31Z","abstract_excerpt":"We study algorithms for approximating the spectral density of a symmetric matrix $A$ that is accessed through matrix-vector product queries. By combining a previously studied Chebyshev polynomial moment matching method with a deflation step that approximately projects off the largest magnitude eigendirections of $A$ before estimating the spectral density, we give an $\\epsilon\\cdot\\sigma_\\ell(A)$ error approximation to the spectral density in the Wasserstein-$1$ metric using $O(\\ell\\log n+ 1/\\epsilon)$ matrix-vector products, where $\\sigma_\\ell(A)$ is the $\\ell^{th}$ largest singular value of $"},"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":"2410.21690","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2024-10-29T03:18:31Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"c31747d5586dda289f88371d6244d07e4e42cf4438d2616ae4c797744f8b36dc","abstract_canon_sha256":"c9ab3b5869fa441a3ef1ac261d8848b6d2f9852afb5b6b573fd001444fc8b7e8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:44:16.324073Z","signature_b64":"P2QtVes0B0SKVXONGn+FDPFkVciz3KDR9RfcFMwr0PNnOKDMDVAyD/7Y/NMrSKEhfEOVBrdodjnm/+/hWQdmAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"724c412481e168692f5f677316f689065e9c7355f6bdeb6991edbd3da22558e3","last_reissued_at":"2026-07-05T09:44:16.323590Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:44:16.323590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Improved Spectral Density Estimation via Explicit and Implicit Deflation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"cs.DS","authors_text":"Archan Ray, Cameron Musco, Christopher Musco, Rajarshi Bhattacharjee, Rajesh Jayaram","submitted_at":"2024-10-29T03:18:31Z","abstract_excerpt":"We study algorithms for approximating the spectral density of a symmetric matrix $A$ that is accessed through matrix-vector product queries. By combining a previously studied Chebyshev polynomial moment matching method with a deflation step that approximately projects off the largest magnitude eigendirections of $A$ before estimating the spectral density, we give an $\\epsilon\\cdot\\sigma_\\ell(A)$ error approximation to the spectral density in the Wasserstein-$1$ metric using $O(\\ell\\log n+ 1/\\epsilon)$ matrix-vector products, where $\\sigma_\\ell(A)$ is the $\\ell^{th}$ largest singular value of $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.21690","kind":"arxiv","version":3},"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/2410.21690/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":"2410.21690","created_at":"2026-07-05T09:44:16.323647+00:00"},{"alias_kind":"arxiv_version","alias_value":"2410.21690v3","created_at":"2026-07-05T09:44:16.323647+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.21690","created_at":"2026-07-05T09:44:16.323647+00:00"},{"alias_kind":"pith_short_12","alias_value":"OJGECJEB4FUG","created_at":"2026-07-05T09:44:16.323647+00:00"},{"alias_kind":"pith_short_16","alias_value":"OJGECJEB4FUGSL27","created_at":"2026-07-05T09:44:16.323647+00:00"},{"alias_kind":"pith_short_8","alias_value":"OJGECJEB","created_at":"2026-07-05T09:44:16.323647+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/OJGECJEB4FUGSL27M5ZRN5UJAZ","json":"https://pith.science/pith/OJGECJEB4FUGSL27M5ZRN5UJAZ.json","graph_json":"https://pith.science/api/pith-number/OJGECJEB4FUGSL27M5ZRN5UJAZ/graph.json","events_json":"https://pith.science/api/pith-number/OJGECJEB4FUGSL27M5ZRN5UJAZ/events.json","paper":"https://pith.science/paper/OJGECJEB"},"agent_actions":{"view_html":"https://pith.science/pith/OJGECJEB4FUGSL27M5ZRN5UJAZ","download_json":"https://pith.science/pith/OJGECJEB4FUGSL27M5ZRN5UJAZ.json","view_paper":"https://pith.science/paper/OJGECJEB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2410.21690&json=true","fetch_graph":"https://pith.science/api/pith-number/OJGECJEB4FUGSL27M5ZRN5UJAZ/graph.json","fetch_events":"https://pith.science/api/pith-number/OJGECJEB4FUGSL27M5ZRN5UJAZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OJGECJEB4FUGSL27M5ZRN5UJAZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OJGECJEB4FUGSL27M5ZRN5UJAZ/action/storage_attestation","attest_author":"https://pith.science/pith/OJGECJEB4FUGSL27M5ZRN5UJAZ/action/author_attestation","sign_citation":"https://pith.science/pith/OJGECJEB4FUGSL27M5ZRN5UJAZ/action/citation_signature","submit_replication":"https://pith.science/pith/OJGECJEB4FUGSL27M5ZRN5UJAZ/action/replication_record"}},"created_at":"2026-07-05T09:44:16.323647+00:00","updated_at":"2026-07-05T09:44:16.323647+00:00"}