{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:A3IOBJF7W3V2CO3TVQPTPGMQUW","short_pith_number":"pith:A3IOBJF7","canonical_record":{"source":{"id":"1503.05606","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-03-18T22:55:46Z","cross_cats_sorted":[],"title_canon_sha256":"e3315724ea8d4268ba51898ad18192de7e165059a653a9f1dd4cde7dd1746207","abstract_canon_sha256":"ef3a670edfc957c41633ba65ffa1d932326c15e78691f80f7e08f57205ce0110"},"schema_version":"1.0"},"canonical_sha256":"06d0e0a4bfb6eba13b73ac1f379990a58c92eaf919cc8cd4444ba6d176ff5162","source":{"kind":"arxiv","id":"1503.05606","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:A3IOBJF7W3V2CO3TVQPTPGMQUW","target":"record","payload":{"canonical_record":{"source":{"id":"1503.05606","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-03-18T22:55:46Z","cross_cats_sorted":[],"title_canon_sha256":"e3315724ea8d4268ba51898ad18192de7e165059a653a9f1dd4cde7dd1746207","abstract_canon_sha256":"ef3a670edfc957c41633ba65ffa1d932326c15e78691f80f7e08f57205ce0110"},"schema_version":"1.0"},"canonical_sha256":"06d0e0a4bfb6eba13b73ac1f379990a58c92eaf919cc8cd4444ba6d176ff5162","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:28.213827Z","signature_b64":"zZqAldjZ3i9SryTLFJo8GKUDbob6HWx/MHDVp5OV224dft/YxnGJbIMSWql+BFV0Wah1yadaKCDMjdEZR2mjDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06d0e0a4bfb6eba13b73ac1f379990a58c92eaf919cc8cd4444ba6d176ff5162","last_reissued_at":"2026-05-18T02:20:28.213201Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:28.213201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.05606","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:20:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9UG67bZyNVuVMYmRiiKC4qNQTE6yufw+kzMK7rGkjcCBdJ60WmKqQL3cIvrtcknXMzh7Pc2cCMAEWZ6rlOa+DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T11:21:15.364912Z"},"content_sha256":"87bf4b178b9505d0a1f032ebc76084ec487a675d4fe8a9f69db20817479300e4","schema_version":"1.0","event_id":"sha256:87bf4b178b9505d0a1f032ebc76084ec487a675d4fe8a9f69db20817479300e4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:A3IOBJF7W3V2CO3TVQPTPGMQUW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Invariance theorems for Nevanlinna families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mark Malamud, Seppo Hassi, Vladimir Derkach","submitted_at":"2015-03-18T22:55:46Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05606","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:20:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eON0vef4mXrTKnz5HblJqNsycuFioZR3WTsAZSMmN13gxoeuJPyv3U2xHCgegbD2IPYCtw3w7rZPaZnTowqLCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T11:21:15.365249Z"},"content_sha256":"cca7f7883f2399005ef75e0d02fb04c504787c2500c07c60d92c13e172e57f43","schema_version":"1.0","event_id":"sha256:cca7f7883f2399005ef75e0d02fb04c504787c2500c07c60d92c13e172e57f43"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A3IOBJF7W3V2CO3TVQPTPGMQUW/bundle.json","state_url":"https://pith.science/pith/A3IOBJF7W3V2CO3TVQPTPGMQUW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A3IOBJF7W3V2CO3TVQPTPGMQUW/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T11:21:15Z","links":{"resolver":"https://pith.science/pith/A3IOBJF7W3V2CO3TVQPTPGMQUW","bundle":"https://pith.science/pith/A3IOBJF7W3V2CO3TVQPTPGMQUW/bundle.json","state":"https://pith.science/pith/A3IOBJF7W3V2CO3TVQPTPGMQUW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A3IOBJF7W3V2CO3TVQPTPGMQUW/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qX3T7YPnBZLg/AUwOw3ehZnjAKfOWjBLQdEamyvNw/3h9TNvoUZN1vGCBqiMXMgXbRpdkAELcLPfH5EcVbQXBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T11:21:15.367120Z","bundle_sha256":"593821b0a54bcf3edc31c881d4902154d096ee7b2fd1511269ef455336b4c43c"}}