{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TD5N4P4CW3V6LAVLPDC2HF7HQS","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":"4d486bad780f4470fe492213c1603bb6a5456dbf9524e15c037d647ac5ad5c33","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-05-03T19:41:13Z","title_canon_sha256":"25e72de80dadba4d850790ed1f10265c1a70c43ed35a627b2b7095a8e561afdc"},"schema_version":"1.0","source":{"id":"1605.01041","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.01041","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"arxiv_version","alias_value":"1605.01041v1","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.01041","created_at":"2026-05-18T01:15:47Z"},{"alias_kind":"pith_short_12","alias_value":"TD5N4P4CW3V6","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TD5N4P4CW3V6LAVL","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TD5N4P4C","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:23781fd197d7c9f3b1469176472341f2883ce7837483da6ba36f478da06455d0","target":"graph","created_at":"2026-05-18T01:15:47Z","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 prove local convergence results for the spectra and pseudospectra of sequences of linear operators acting in different Hilbert spaces and converging in generalised strong resolvent sense to an operator with possibly non-empty essential spectrum. We establish local spectral exactness outside the limiting essential spectrum, local $\\varepsilon$-pseudospectral exactness outside the limiting essential $\\varepsilon$-near spectrum, and discuss properties of these two notions including perturbation results.","authors_text":"Sabine B\\\"ogli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-05-03T19:41:13Z","title":"Local convergence of spectra and pseudospectra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01041","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:be7e56c8fafaf002b7ea85564bd04d0ca07d763c5b2dad69f93b00893a4ee26b","target":"record","created_at":"2026-05-18T01:15:47Z","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":"4d486bad780f4470fe492213c1603bb6a5456dbf9524e15c037d647ac5ad5c33","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-05-03T19:41:13Z","title_canon_sha256":"25e72de80dadba4d850790ed1f10265c1a70c43ed35a627b2b7095a8e561afdc"},"schema_version":"1.0","source":{"id":"1605.01041","kind":"arxiv","version":1}},"canonical_sha256":"98fade3f82b6ebe582ab78c5a397e7848c57f62668f7c9b30aa30c2b387fd974","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98fade3f82b6ebe582ab78c5a397e7848c57f62668f7c9b30aa30c2b387fd974","first_computed_at":"2026-05-18T01:15:47.428723Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:47.428723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vuCiEhoPFq3edyL9/A5/oBrkg93pt3hbeikTx1nVxxYs2LLv9YNPvm5pBCIvv0s1ceurUDmwTkg19pP1RdABBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:47.429338Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.01041","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be7e56c8fafaf002b7ea85564bd04d0ca07d763c5b2dad69f93b00893a4ee26b","sha256:23781fd197d7c9f3b1469176472341f2883ce7837483da6ba36f478da06455d0"],"state_sha256":"ebe5664d5d729e5ea2c19a798172be53d8a53f34515d440863b2d7aea599b25e"}