{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:RXPJ6G5MBHPCBYLXDX76Z3LH6Z","short_pith_number":"pith:RXPJ6G5M","schema_version":"1.0","canonical_sha256":"8dde9f1bac09de20e1771dffeced67f67c268fcc50283c02aaba18ced4136283","source":{"kind":"arxiv","id":"2507.10144","version":2},"attestation_state":"computed","paper":{"title":"A structural bound for cluster robustness of randomized small-block Lanczos","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Nian Shao","submitted_at":"2025-07-14T10:43:21Z","abstract_excerpt":"The Lanczos method is a fast and memory-efficient algorithm for solving large-scale symmetric eigenvalue problems. However, its rapid convergence can deteriorate significantly when computing clustered eigenvalues due to a lack of cluster robustness. A promising strategy to enhance cluster robustness -- without substantially compromising convergence speed or memory efficiency -- is to use a random small-block initial, where the block size is greater than one but still much smaller than the cluster size. This leads to the Randomized Small-Block Lanczos (RSBL) method. Despite its empirical effect"},"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":"2507.10144","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-07-14T10:43:21Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"a200e1a6dc0a91e2e298359725bd15fe0324e845bfb1d1e302fba4e45394ff7d","abstract_canon_sha256":"4fa27d2371f2b5b12847889ab269d970d25e050496d9084ceaf6511b5004272d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T01:03:32.667581Z","signature_b64":"qiutPQU74QcwfSzC/jM0waWVGPbN8l9c2grQvr2Bo1bkfQ2HkLTbuWocwb0ruj0JYRs+0bIUZF0jdCwVUlusCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8dde9f1bac09de20e1771dffeced67f67c268fcc50283c02aaba18ced4136283","last_reissued_at":"2026-06-02T01:03:32.667168Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T01:03:32.667168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A structural bound for cluster robustness of randomized small-block Lanczos","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Nian Shao","submitted_at":"2025-07-14T10:43:21Z","abstract_excerpt":"The Lanczos method is a fast and memory-efficient algorithm for solving large-scale symmetric eigenvalue problems. However, its rapid convergence can deteriorate significantly when computing clustered eigenvalues due to a lack of cluster robustness. A promising strategy to enhance cluster robustness -- without substantially compromising convergence speed or memory efficiency -- is to use a random small-block initial, where the block size is greater than one but still much smaller than the cluster size. This leads to the Randomized Small-Block Lanczos (RSBL) method. Despite its empirical effect"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.10144","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.10144/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":"2507.10144","created_at":"2026-06-02T01:03:32.667227+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.10144v2","created_at":"2026-06-02T01:03:32.667227+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.10144","created_at":"2026-06-02T01:03:32.667227+00:00"},{"alias_kind":"pith_short_12","alias_value":"RXPJ6G5MBHPC","created_at":"2026-06-02T01:03:32.667227+00:00"},{"alias_kind":"pith_short_16","alias_value":"RXPJ6G5MBHPCBYLX","created_at":"2026-06-02T01:03:32.667227+00:00"},{"alias_kind":"pith_short_8","alias_value":"RXPJ6G5M","created_at":"2026-06-02T01:03:32.667227+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/RXPJ6G5MBHPCBYLXDX76Z3LH6Z","json":"https://pith.science/pith/RXPJ6G5MBHPCBYLXDX76Z3LH6Z.json","graph_json":"https://pith.science/api/pith-number/RXPJ6G5MBHPCBYLXDX76Z3LH6Z/graph.json","events_json":"https://pith.science/api/pith-number/RXPJ6G5MBHPCBYLXDX76Z3LH6Z/events.json","paper":"https://pith.science/paper/RXPJ6G5M"},"agent_actions":{"view_html":"https://pith.science/pith/RXPJ6G5MBHPCBYLXDX76Z3LH6Z","download_json":"https://pith.science/pith/RXPJ6G5MBHPCBYLXDX76Z3LH6Z.json","view_paper":"https://pith.science/paper/RXPJ6G5M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.10144&json=true","fetch_graph":"https://pith.science/api/pith-number/RXPJ6G5MBHPCBYLXDX76Z3LH6Z/graph.json","fetch_events":"https://pith.science/api/pith-number/RXPJ6G5MBHPCBYLXDX76Z3LH6Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RXPJ6G5MBHPCBYLXDX76Z3LH6Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RXPJ6G5MBHPCBYLXDX76Z3LH6Z/action/storage_attestation","attest_author":"https://pith.science/pith/RXPJ6G5MBHPCBYLXDX76Z3LH6Z/action/author_attestation","sign_citation":"https://pith.science/pith/RXPJ6G5MBHPCBYLXDX76Z3LH6Z/action/citation_signature","submit_replication":"https://pith.science/pith/RXPJ6G5MBHPCBYLXDX76Z3LH6Z/action/replication_record"}},"created_at":"2026-06-02T01:03:32.667227+00:00","updated_at":"2026-06-02T01:03:32.667227+00:00"}