{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SIDGTID6NECAOCBPY7OLZEWCCU","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":"101cdb5d378bf5b5d3dca30e9dfd9140064cf7a916c362dd5393fc30c802e20d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-12-26T19:43:26Z","title_canon_sha256":"8eb483ebc21b82e6cbea08d80f6f9c5aa50c1de83ae0e18e2826a234deebd880"},"schema_version":"1.0","source":{"id":"1512.08135","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08135","created_at":"2026-05-18T01:23:43Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08135v1","created_at":"2026-05-18T01:23:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08135","created_at":"2026-05-18T01:23:43Z"},{"alias_kind":"pith_short_12","alias_value":"SIDGTID6NECA","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SIDGTID6NECAOCBP","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SIDGTID6","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:2d9512b91ddfdd7fdd0317823dc94467d4e66bd7b6dfc29d7c9e39438c297411","target":"graph","created_at":"2026-05-18T01:23:43Z","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":"Polynomial filtering can provide a highly effective means of computing all eigenvalues of a real symmetric (or complex Hermitian) matrix that are located in a given interval, anywhere in the spectrum. This paper describes a technique for tackling this problem by combining a Thick-Restart version of the Lanczos algorithm with deflation (`locking') and a new type of polynomial filters obtained from a least-squares technique. The resulting algorithm can be utilized in a `spectrum-slicing' approach whereby a very large number of eigenvalues and associated eigenvectors of the matrix are computed by","authors_text":"Chao Yang, Eugene Vecharynski, Ruipeng Li, Yousef Saad, Yuanzhe Xi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-12-26T19:43:26Z","title":"A Thick-Restart Lanczos algorithm with polynomial filtering for Hermitian eigenvalue problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08135","kind":"arxiv","version":1},"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":"sha256:81fb7bc8461e365e547714284edebf5ea5667db5f67cf41d44d50b5b9640d254","target":"record","created_at":"2026-05-18T01:23:43Z","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":"101cdb5d378bf5b5d3dca30e9dfd9140064cf7a916c362dd5393fc30c802e20d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-12-26T19:43:26Z","title_canon_sha256":"8eb483ebc21b82e6cbea08d80f6f9c5aa50c1de83ae0e18e2826a234deebd880"},"schema_version":"1.0","source":{"id":"1512.08135","kind":"arxiv","version":1}},"canonical_sha256":"920669a07e690407082fc7dcbc92c2151d55d9d9115848de06868741a730b78c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"920669a07e690407082fc7dcbc92c2151d55d9d9115848de06868741a730b78c","first_computed_at":"2026-05-18T01:23:43.143343Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:43.143343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+42+AVBMyBXPUAtDS2KZjZW9MOO6s6eNXzp3CDj0oAGseby0L00LBeVFHWrqAQg7Em5OvUvmvml9uE9gtmivCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:43.144149Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.08135","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81fb7bc8461e365e547714284edebf5ea5667db5f67cf41d44d50b5b9640d254","sha256:2d9512b91ddfdd7fdd0317823dc94467d4e66bd7b6dfc29d7c9e39438c297411"],"state_sha256":"8631de4510c36b3778ece480e910980b497eb2c03c1527d613d1f059a554a250"}