{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:EIX3P3KM3N26YGAB5AQFRFCD55","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":"5f875ec8ee54d5f0bec16445a54634bcdede51737b5e9073e3e3569694b5ca60","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-06-08T14:05:03Z","title_canon_sha256":"3dfc49fb56d7fbf723a7573f37bfef3c0ea7dbf267af0be6090cbc9786a526e7"},"schema_version":"1.0","source":{"id":"1206.1762","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.1762","created_at":"2026-05-18T03:53:16Z"},{"alias_kind":"arxiv_version","alias_value":"1206.1762v2","created_at":"2026-05-18T03:53:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.1762","created_at":"2026-05-18T03:53:16Z"},{"alias_kind":"pith_short_12","alias_value":"EIX3P3KM3N26","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"EIX3P3KM3N26YGAB","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"EIX3P3KM","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:b64f1de0953acd2a272235013e8a5283e2c8e53cb3fe98f0fc2b0554133733e1","target":"graph","created_at":"2026-05-18T03:53:16Z","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":"Consider a matrix function f defined for Hermitian matrices. The purpose of this paper is two-fold. We derive new results for the absolute structured condition number of the matrix function and we derive new bounds for the perturbation ||f(A+E)-f(A)|| expressed in terms of eigenvalues of A and A+E. The results are general and under certain conditions hold for an arbitrary unitarily invariant matrix norm ||\\cdot||. We illustrate the use of the formulas with an application to the error analysis of calculations in electronic structure theory.","authors_text":"Elias Jarlebring, Emanuel H. Rubensson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-06-08T14:05:03Z","title":"On the condition number and perturbation of matrix functions for Hermitian matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1762","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":"sha256:0c554ae9d3c39a4dc2d464699e725dafe0876d72decd69c190d3500eb0263118","target":"record","created_at":"2026-05-18T03:53:16Z","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":"5f875ec8ee54d5f0bec16445a54634bcdede51737b5e9073e3e3569694b5ca60","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-06-08T14:05:03Z","title_canon_sha256":"3dfc49fb56d7fbf723a7573f37bfef3c0ea7dbf267af0be6090cbc9786a526e7"},"schema_version":"1.0","source":{"id":"1206.1762","kind":"arxiv","version":2}},"canonical_sha256":"222fb7ed4cdb75ec1801e820589443ef546d162b3e191f0551a20604c03fc99f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"222fb7ed4cdb75ec1801e820589443ef546d162b3e191f0551a20604c03fc99f","first_computed_at":"2026-05-18T03:53:16.920088Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:53:16.920088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x/HA9YADHUDJr/z9/llI1YivOzaCFk3k7T0y3bMyKNCkoswUPoYV3XBdil6K16S4SgvCcK0YSM8cslqJ5Sd5Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:53:16.920933Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.1762","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c554ae9d3c39a4dc2d464699e725dafe0876d72decd69c190d3500eb0263118","sha256:b64f1de0953acd2a272235013e8a5283e2c8e53cb3fe98f0fc2b0554133733e1"],"state_sha256":"1cb4cf555e73213b7998589073c487c9ec60dad5771f100dc559f8c62463e4b0"}