{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QKEUTLDVBB3E62MTB4CW3PWK47","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":"d0452c5a5785e43532713c44e00eda1091563990f901f100c8654b8d06b74d84","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2013-08-20T10:16:16Z","title_canon_sha256":"4a48d8019404531ddf39ce81a50baff69187ca22837a38db7c2992132d712256"},"schema_version":"1.0","source":{"id":"1308.4275","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4275","created_at":"2026-05-18T02:45:49Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4275v2","created_at":"2026-05-18T02:45:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4275","created_at":"2026-05-18T02:45:49Z"},{"alias_kind":"pith_short_12","alias_value":"QKEUTLDVBB3E","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QKEUTLDVBB3E62MT","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QKEUTLDV","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:ef23caf911059bde7d3156c9fc23e4dd42dd98f153b67d014854b2f6e28c1045","target":"graph","created_at":"2026-05-18T02:45:49Z","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":"Estimating the number of eigenvalues located in a given interval of a large sparse Hermitian matrix is an important problem in certain applications and it is a prerequisite of eigensolvers based on a divide-and-conquer paradigm. Often an exact count is not necessary and methods based on stochastic estimates can be utilized to yield rough approximations. This paper examines a number of techniques tailored to this specific task. It reviews standard approaches and explores new ones based on polynomial and rational approximation filtering combined with a stochastic procedure.","authors_text":"(2) Dept. of Electrical, (3) Computer Science & Engineering, Computer Engineering, Edoardo Di Napoli (1), Eric Polizzi (2), Forshungszentrum J\\\"ulich, University of Massachusetts, University of Minnesota.), Yousef Saad (3) ((1) J\\\"ulich Supercomputing Centre","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2013-08-20T10:16:16Z","title":"Efficient estimation of eigenvalue counts in an interval"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4275","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:e202f4bccd1c6194cd398ef6881a302f43f189df30ee699a5e114ef7e26be2a5","target":"record","created_at":"2026-05-18T02:45:49Z","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":"d0452c5a5785e43532713c44e00eda1091563990f901f100c8654b8d06b74d84","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2013-08-20T10:16:16Z","title_canon_sha256":"4a48d8019404531ddf39ce81a50baff69187ca22837a38db7c2992132d712256"},"schema_version":"1.0","source":{"id":"1308.4275","kind":"arxiv","version":2}},"canonical_sha256":"828949ac7508764f69930f056dbecae7fcd47a7662646901a0548ff6425c6ea7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"828949ac7508764f69930f056dbecae7fcd47a7662646901a0548ff6425c6ea7","first_computed_at":"2026-05-18T02:45:49.745242Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:49.745242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"319UrU9YvZNWAN2wHN9ven4IKy322kJ9Ogya8garjsn2cg+0Mx84QTOv6qbpxbU16emRuB6kXlbwNbbOkuQOBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:49.745730Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.4275","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e202f4bccd1c6194cd398ef6881a302f43f189df30ee699a5e114ef7e26be2a5","sha256:ef23caf911059bde7d3156c9fc23e4dd42dd98f153b67d014854b2f6e28c1045"],"state_sha256":"14557d754333776812044abf294b83f63c9f55e7fe7e6f5fe9471ac560b01991"}