{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:IPE66T77EYZ7QL6KW3MOD6RZ5O","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":"d23a99cbe43625270f050e078256e83be3b0484d12b8d554197fd33a8951c9f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-01-29T08:45:46Z","title_canon_sha256":"a6a8431f70389167694691a84786778a3d8f3bb99d755c5f8ca375ad1503ef8a"},"schema_version":"1.0","source":{"id":"1501.07376","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.07376","created_at":"2026-05-18T02:28:22Z"},{"alias_kind":"arxiv_version","alias_value":"1501.07376v1","created_at":"2026-05-18T02:28:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.07376","created_at":"2026-05-18T02:28:22Z"},{"alias_kind":"pith_short_12","alias_value":"IPE66T77EYZ7","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IPE66T77EYZ7QL6K","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IPE66T77","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:267cd943ff3fe389bda8079811931fb86c66f12e7fd3f71656f8d0b1aa087b92","target":"graph","created_at":"2026-05-18T02:28:22Z","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":"We present decay bounds for a broad class of Hermitian matrix functions where the matrix argument is banded or a Kronecker sum of banded matrices. Besides being significantly tighter than previous estimates, the new bounds closely capture the actual (non-monotonic) decay behavior of the entries of functions of matrices with Kronecker sum structure. We also discuss extensions to more general sparse matrices.","authors_text":"Michele Benzi, Valeria Simoncini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-01-29T08:45:46Z","title":"Decay bounds for functions of matrices with banded or Kronecker structure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07376","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":"sha256:1c84ad4a97d91b03198b16b209c7e0e0daab6eb339653438658cbe77007bb3fe","target":"record","created_at":"2026-05-18T02:28:22Z","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":"d23a99cbe43625270f050e078256e83be3b0484d12b8d554197fd33a8951c9f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-01-29T08:45:46Z","title_canon_sha256":"a6a8431f70389167694691a84786778a3d8f3bb99d755c5f8ca375ad1503ef8a"},"schema_version":"1.0","source":{"id":"1501.07376","kind":"arxiv","version":1}},"canonical_sha256":"43c9ef4fff2633f82fcab6d8e1fa39eba6dec692f01d53eca74ae6276dee0f4f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43c9ef4fff2633f82fcab6d8e1fa39eba6dec692f01d53eca74ae6276dee0f4f","first_computed_at":"2026-05-18T02:28:22.113083Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:22.113083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JGkte3+KntJHScVqBwjMRGadA5bVoXEU/Tm2RjaQSGcNQLEBKRufhuOa3Ovaf9aCbEHn51robBthtlx4IcArAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:22.113620Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.07376","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c84ad4a97d91b03198b16b209c7e0e0daab6eb339653438658cbe77007bb3fe","sha256:267cd943ff3fe389bda8079811931fb86c66f12e7fd3f71656f8d0b1aa087b92"],"state_sha256":"cc1aacbb13300b137626be18bbcd8f2ba275bcec22e292376a17fa3630cd8fd4"}