{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:RZNQHFIRERTUSRHUT7CKTHYTW3","short_pith_number":"pith:RZNQHFIR","canonical_record":{"source":{"id":"1306.5674","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-06-24T16:59:06Z","cross_cats_sorted":[],"title_canon_sha256":"dd9eeabcb17c73a2b44c372a384265366357995a04ce9ee58110fd861b383511","abstract_canon_sha256":"73f977f1ac7932a20757e7801ca0fbe9310c6eeb4874949865d0d3a486ec8192"},"schema_version":"1.0"},"canonical_sha256":"8e5b03951124674944f49fc4a99f13b6cf8325d643417bd5b44d0eecd953dea4","source":{"kind":"arxiv","id":"1306.5674","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.5674","created_at":"2026-05-18T02:38:26Z"},{"alias_kind":"arxiv_version","alias_value":"1306.5674v1","created_at":"2026-05-18T02:38:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.5674","created_at":"2026-05-18T02:38:26Z"},{"alias_kind":"pith_short_12","alias_value":"RZNQHFIRERTU","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RZNQHFIRERTUSRHU","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RZNQHFIR","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:RZNQHFIRERTUSRHUT7CKTHYTW3","target":"record","payload":{"canonical_record":{"source":{"id":"1306.5674","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-06-24T16:59:06Z","cross_cats_sorted":[],"title_canon_sha256":"dd9eeabcb17c73a2b44c372a384265366357995a04ce9ee58110fd861b383511","abstract_canon_sha256":"73f977f1ac7932a20757e7801ca0fbe9310c6eeb4874949865d0d3a486ec8192"},"schema_version":"1.0"},"canonical_sha256":"8e5b03951124674944f49fc4a99f13b6cf8325d643417bd5b44d0eecd953dea4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:26.663014Z","signature_b64":"kZlr84pCQVICgmH3nvwVpswVv2EQSG0WADDopK+qRzVAr3Al7H8fK2HNX5lyPqXGXqvRSf7Qzg1x5oJFROMkAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e5b03951124674944f49fc4a99f13b6cf8325d643417bd5b44d0eecd953dea4","last_reissued_at":"2026-05-18T02:38:26.662526Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:26.662526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.5674","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:38:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MoucQePPEWTxnwv59D/Zw6CTSN39lBUsLDfC79bDivj5FV9TYIuEtJDOs+ee1hmGWNGWlcgsO1RrlQ9w+FCqBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T18:54:42.913161Z"},"content_sha256":"eb65f691764ff524e92f759ba504287fcb7c02a18566d03bc4559397e429247e","schema_version":"1.0","event_id":"sha256:eb65f691764ff524e92f759ba504287fcb7c02a18566d03bc4559397e429247e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:RZNQHFIRERTUSRHUT7CKTHYTW3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Robustness of strong stability of semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Lassi Paunonen","submitted_at":"2013-06-24T16:59:06Z","abstract_excerpt":"In this paper we study the preservation of strong stability of strongly continuous semigroups on Hilbert spaces. In particular, we study a situation where the generator of the semigroup has a finite number of spectral points on the imaginary axis and the norm of its resolvent operator is polynomially bounded near these points. We characterize classes of finite rank perturbations preserving the strong stability of the semigroup. In addition, we improve recent results on preservation of polynomial stability of a semigroup under finite rank perturbations of its generator. Theoretic results are il"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5674","kind":"arxiv","version":1},"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":"2026-05-18T02:38:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CZR1gJNwqScxHpTxg3IhDErslF/B+vzocIHUReMfNdfSSzXVUiEfwrnebRwgVuqSRBZ1uO2+CIBWMZ1muXoFAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T18:54:42.913510Z"},"content_sha256":"e0831c11db3bc1093a499694b6ffe2ab9854ffb969d484e84e96ff5611371e11","schema_version":"1.0","event_id":"sha256:e0831c11db3bc1093a499694b6ffe2ab9854ffb969d484e84e96ff5611371e11"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RZNQHFIRERTUSRHUT7CKTHYTW3/bundle.json","state_url":"https://pith.science/pith/RZNQHFIRERTUSRHUT7CKTHYTW3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RZNQHFIRERTUSRHUT7CKTHYTW3/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":"2026-06-27T18:54:42Z","links":{"resolver":"https://pith.science/pith/RZNQHFIRERTUSRHUT7CKTHYTW3","bundle":"https://pith.science/pith/RZNQHFIRERTUSRHUT7CKTHYTW3/bundle.json","state":"https://pith.science/pith/RZNQHFIRERTUSRHUT7CKTHYTW3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RZNQHFIRERTUSRHUT7CKTHYTW3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RZNQHFIRERTUSRHUT7CKTHYTW3","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":"73f977f1ac7932a20757e7801ca0fbe9310c6eeb4874949865d0d3a486ec8192","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-06-24T16:59:06Z","title_canon_sha256":"dd9eeabcb17c73a2b44c372a384265366357995a04ce9ee58110fd861b383511"},"schema_version":"1.0","source":{"id":"1306.5674","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.5674","created_at":"2026-05-18T02:38:26Z"},{"alias_kind":"arxiv_version","alias_value":"1306.5674v1","created_at":"2026-05-18T02:38:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.5674","created_at":"2026-05-18T02:38:26Z"},{"alias_kind":"pith_short_12","alias_value":"RZNQHFIRERTU","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RZNQHFIRERTUSRHU","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RZNQHFIR","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:e0831c11db3bc1093a499694b6ffe2ab9854ffb969d484e84e96ff5611371e11","target":"graph","created_at":"2026-05-18T02:38:26Z","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":"In this paper we study the preservation of strong stability of strongly continuous semigroups on Hilbert spaces. In particular, we study a situation where the generator of the semigroup has a finite number of spectral points on the imaginary axis and the norm of its resolvent operator is polynomially bounded near these points. We characterize classes of finite rank perturbations preserving the strong stability of the semigroup. In addition, we improve recent results on preservation of polynomial stability of a semigroup under finite rank perturbations of its generator. Theoretic results are il","authors_text":"Lassi Paunonen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-06-24T16:59:06Z","title":"Robustness of strong stability of semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5674","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:eb65f691764ff524e92f759ba504287fcb7c02a18566d03bc4559397e429247e","target":"record","created_at":"2026-05-18T02:38:26Z","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":"73f977f1ac7932a20757e7801ca0fbe9310c6eeb4874949865d0d3a486ec8192","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-06-24T16:59:06Z","title_canon_sha256":"dd9eeabcb17c73a2b44c372a384265366357995a04ce9ee58110fd861b383511"},"schema_version":"1.0","source":{"id":"1306.5674","kind":"arxiv","version":1}},"canonical_sha256":"8e5b03951124674944f49fc4a99f13b6cf8325d643417bd5b44d0eecd953dea4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e5b03951124674944f49fc4a99f13b6cf8325d643417bd5b44d0eecd953dea4","first_computed_at":"2026-05-18T02:38:26.662526Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:26.662526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kZlr84pCQVICgmH3nvwVpswVv2EQSG0WADDopK+qRzVAr3Al7H8fK2HNX5lyPqXGXqvRSf7Qzg1x5oJFROMkAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:26.663014Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.5674","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb65f691764ff524e92f759ba504287fcb7c02a18566d03bc4559397e429247e","sha256:e0831c11db3bc1093a499694b6ffe2ab9854ffb969d484e84e96ff5611371e11"],"state_sha256":"86f2349aceb09a7885bfbb7777a74ed8e32da6f2f50e0b0ba2c59172f010d8ef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+GKISnXxOlUFl6A0e8e4ph0eJkn/oZ/3Z4q7mwYCkK+z7clcMAlh6GNfap1fRtf13GKX+h2ZrNH2ctHNAMyPDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T18:54:42.915354Z","bundle_sha256":"8f86638439b42440ec4110943d6916493537572b36681bf6f3b01dd2f1ce7793"}}