{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:63MLQEEYNSFJPXZGVJID5VMLUE","short_pith_number":"pith:63MLQEEY","canonical_record":{"source":{"id":"2002.09087","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2020-02-21T01:58:53Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"cd2e3add94fabc3fe67380ebe55bb88fd166f9bdce1b95070a0c23bf1a3de257","abstract_canon_sha256":"d9921ad46554eb7073ccd7e2efa9df9f4dd0b23a834649c53d83f7145480693b"},"schema_version":"1.0"},"canonical_sha256":"f6d8b810986c8a97df26aa503ed58ba12bf32da2996a827e4ca63e41570f7e79","source":{"kind":"arxiv","id":"2002.09087","version":8},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.09087","created_at":"2026-05-17T23:39:01Z"},{"alias_kind":"arxiv_version","alias_value":"2002.09087v8","created_at":"2026-05-17T23:39:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.09087","created_at":"2026-05-17T23:39:01Z"},{"alias_kind":"pith_short_12","alias_value":"63MLQEEYNSFJ","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"63MLQEEYNSFJPXZG","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"63MLQEEY","created_at":"2026-05-18T12:33:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:63MLQEEYNSFJPXZGVJID5VMLUE","target":"record","payload":{"canonical_record":{"source":{"id":"2002.09087","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2020-02-21T01:58:53Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"cd2e3add94fabc3fe67380ebe55bb88fd166f9bdce1b95070a0c23bf1a3de257","abstract_canon_sha256":"d9921ad46554eb7073ccd7e2efa9df9f4dd0b23a834649c53d83f7145480693b"},"schema_version":"1.0"},"canonical_sha256":"f6d8b810986c8a97df26aa503ed58ba12bf32da2996a827e4ca63e41570f7e79","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:01.958685Z","signature_b64":"fSepvric7lZV8hwVfouxVUcQsZ2X1UOUy5lveOPYEMpUUZWbf+I1muCWd4LJlDArDXPjySSk9i7AIRAtnbgXCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6d8b810986c8a97df26aa503ed58ba12bf32da2996a827e4ca63e41570f7e79","last_reissued_at":"2026-05-17T23:39:01.958044Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:01.958044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2002.09087","source_version":8,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:39:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E/qioPWRmOmoq54alKbYAkIRuR0imEM9Xvxtdsc8bxE0yRf8fg5vIhnQt5xbsaeyxJ88ynbPfOit1HqiHHLJBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T19:21:52.672310Z"},"content_sha256":"fc53099f07581bc9d753dd78147c6e53c529ce76bb67b049cf84ab09800054f6","schema_version":"1.0","event_id":"sha256:fc53099f07581bc9d753dd78147c6e53c529ce76bb67b049cf84ab09800054f6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:63MLQEEYNSFJPXZGVJID5VMLUE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On spectral inclusion and mapping theorems for scalar type spectral operators and semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.FA","authors_text":"Marat V. Markin","submitted_at":"2020-02-21T01:58:53Z","abstract_excerpt":"We establish spectral inclusion and mapping theorems for scalar type spectral operators, generalizing their counterparts for normal operators. Thereby, we extend a precise weak spectral mapping theorem, known to hold for $C_0$-semigroups of normal operators on complex Hilbert spaces, to the more general case of $C_0$-semigroups of scalar type spectral operators on complex Banach spaces. The finer spectrum structure is given itemized consideration."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.09087","kind":"arxiv","version":8},"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":"2026-05-17T23:39:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+G7Wn3WhNarraV/Bz+bvMojKKOyY8VvV4xhRRIY/AOR/mvL4lhGXxJjTuyGQCWvT8KLAXuP4GwQuOMrI5G9BAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T19:21:52.672969Z"},"content_sha256":"0828b5ba7c462c76afde35e8ff57c84decb8ae24420bbe40be8ca6b55725e37e","schema_version":"1.0","event_id":"sha256:0828b5ba7c462c76afde35e8ff57c84decb8ae24420bbe40be8ca6b55725e37e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/63MLQEEYNSFJPXZGVJID5VMLUE/bundle.json","state_url":"https://pith.science/pith/63MLQEEYNSFJPXZGVJID5VMLUE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/63MLQEEYNSFJPXZGVJID5VMLUE/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":"2026-06-05T19:21:52Z","links":{"resolver":"https://pith.science/pith/63MLQEEYNSFJPXZGVJID5VMLUE","bundle":"https://pith.science/pith/63MLQEEYNSFJPXZGVJID5VMLUE/bundle.json","state":"https://pith.science/pith/63MLQEEYNSFJPXZGVJID5VMLUE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/63MLQEEYNSFJPXZGVJID5VMLUE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:63MLQEEYNSFJPXZGVJID5VMLUE","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":"d9921ad46554eb7073ccd7e2efa9df9f4dd0b23a834649c53d83f7145480693b","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2020-02-21T01:58:53Z","title_canon_sha256":"cd2e3add94fabc3fe67380ebe55bb88fd166f9bdce1b95070a0c23bf1a3de257"},"schema_version":"1.0","source":{"id":"2002.09087","kind":"arxiv","version":8}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.09087","created_at":"2026-05-17T23:39:01Z"},{"alias_kind":"arxiv_version","alias_value":"2002.09087v8","created_at":"2026-05-17T23:39:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.09087","created_at":"2026-05-17T23:39:01Z"},{"alias_kind":"pith_short_12","alias_value":"63MLQEEYNSFJ","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"63MLQEEYNSFJPXZG","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"63MLQEEY","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:0828b5ba7c462c76afde35e8ff57c84decb8ae24420bbe40be8ca6b55725e37e","target":"graph","created_at":"2026-05-17T23:39:01Z","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 establish spectral inclusion and mapping theorems for scalar type spectral operators, generalizing their counterparts for normal operators. Thereby, we extend a precise weak spectral mapping theorem, known to hold for $C_0$-semigroups of normal operators on complex Hilbert spaces, to the more general case of $C_0$-semigroups of scalar type spectral operators on complex Banach spaces. The finer spectrum structure is given itemized consideration.","authors_text":"Marat V. Markin","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2020-02-21T01:58:53Z","title":"On spectral inclusion and mapping theorems for scalar type spectral operators and semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.09087","kind":"arxiv","version":8},"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:fc53099f07581bc9d753dd78147c6e53c529ce76bb67b049cf84ab09800054f6","target":"record","created_at":"2026-05-17T23:39:01Z","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":"d9921ad46554eb7073ccd7e2efa9df9f4dd0b23a834649c53d83f7145480693b","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2020-02-21T01:58:53Z","title_canon_sha256":"cd2e3add94fabc3fe67380ebe55bb88fd166f9bdce1b95070a0c23bf1a3de257"},"schema_version":"1.0","source":{"id":"2002.09087","kind":"arxiv","version":8}},"canonical_sha256":"f6d8b810986c8a97df26aa503ed58ba12bf32da2996a827e4ca63e41570f7e79","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6d8b810986c8a97df26aa503ed58ba12bf32da2996a827e4ca63e41570f7e79","first_computed_at":"2026-05-17T23:39:01.958044Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:01.958044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fSepvric7lZV8hwVfouxVUcQsZ2X1UOUy5lveOPYEMpUUZWbf+I1muCWd4LJlDArDXPjySSk9i7AIRAtnbgXCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:01.958685Z","signed_message":"canonical_sha256_bytes"},"source_id":"2002.09087","source_kind":"arxiv","source_version":8}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc53099f07581bc9d753dd78147c6e53c529ce76bb67b049cf84ab09800054f6","sha256:0828b5ba7c462c76afde35e8ff57c84decb8ae24420bbe40be8ca6b55725e37e"],"state_sha256":"4a7c7d706f12f575f55d33e211282b4cf145e883a60b4895fc2658de5ecdf2e6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KmP/E4/1EgTib28jH81HhDcPeLaKyPly1PpRSO7MIzCGHJ7iEMZgN0FeHUa6w9brjKi0tu1JfTTjU4P48ywnCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T19:21:52.676334Z","bundle_sha256":"394c28d48e66f1f3c72df0602a56006538e520f199d725f18c1f5d1daaf1e55b"}}