{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:A3IOBJF7W3V2CO3TVQPTPGMQUW","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":"ef3a670edfc957c41633ba65ffa1d932326c15e78691f80f7e08f57205ce0110","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-03-18T22:55:46Z","title_canon_sha256":"e3315724ea8d4268ba51898ad18192de7e165059a653a9f1dd4cde7dd1746207"},"schema_version":"1.0","source":{"id":"1503.05606","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.05606","created_at":"2026-05-18T02:20:28Z"},{"alias_kind":"arxiv_version","alias_value":"1503.05606v2","created_at":"2026-05-18T02:20:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05606","created_at":"2026-05-18T02:20:28Z"},{"alias_kind":"pith_short_12","alias_value":"A3IOBJF7W3V2","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"A3IOBJF7W3V2CO3T","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"A3IOBJF7","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:cca7f7883f2399005ef75e0d02fb04c504787c2500c07c60d92c13e172e57f43","target":"graph","created_at":"2026-05-18T02:20:28Z","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":"A complex function $f(z)$ is called a Herglotz-Nevanlinna function if it is holomorphic in the upper half-plane ${\\mathbb C}_+$ and maps ${\\mathbb C}_+$ into itself. By a maximum principle a Herglotz-Nevanlinna function which takes a real value $a$ in a single point $z_0\\in {\\mathbb C}_+$ should be identically equal to $a$. In the present note we prove similar invariance results both for the point and the continuous spectra of an operator-valued Herglotz-Nevanlinna function with values in the set of bounded or unbounded linear operators (or relations) in a Hilbert space. The proof of this inva","authors_text":"Mark Malamud, Seppo Hassi, Vladimir Derkach","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-03-18T22:55:46Z","title":"Invariance theorems for Nevanlinna families"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05606","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":"sha256:87bf4b178b9505d0a1f032ebc76084ec487a675d4fe8a9f69db20817479300e4","target":"record","created_at":"2026-05-18T02:20:28Z","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":"ef3a670edfc957c41633ba65ffa1d932326c15e78691f80f7e08f57205ce0110","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-03-18T22:55:46Z","title_canon_sha256":"e3315724ea8d4268ba51898ad18192de7e165059a653a9f1dd4cde7dd1746207"},"schema_version":"1.0","source":{"id":"1503.05606","kind":"arxiv","version":2}},"canonical_sha256":"06d0e0a4bfb6eba13b73ac1f379990a58c92eaf919cc8cd4444ba6d176ff5162","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06d0e0a4bfb6eba13b73ac1f379990a58c92eaf919cc8cd4444ba6d176ff5162","first_computed_at":"2026-05-18T02:20:28.213201Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:28.213201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zZqAldjZ3i9SryTLFJo8GKUDbob6HWx/MHDVp5OV224dft/YxnGJbIMSWql+BFV0Wah1yadaKCDMjdEZR2mjDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:28.213827Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.05606","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87bf4b178b9505d0a1f032ebc76084ec487a675d4fe8a9f69db20817479300e4","sha256:cca7f7883f2399005ef75e0d02fb04c504787c2500c07c60d92c13e172e57f43"],"state_sha256":"2ce16b97b175fe37938d3d4d9063ee8ac374f7fc99f9b9fcd28e2f93bf9cf344"}