{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:HV6UNDH34SHWZRDVX4YOQUDBWE","short_pith_number":"pith:HV6UNDH3","canonical_record":{"source":{"id":"1502.01957","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-02-06T17:02:53Z","cross_cats_sorted":[],"title_canon_sha256":"d077ff36c5df7e5d1accd42c62c95f1c0c6477046285254213fc5f0d85f7a008","abstract_canon_sha256":"73b05402665d092e02d4d34e6cb487a8a5170fff08b80fd17087095b5db72080"},"schema_version":"1.0"},"canonical_sha256":"3d7d468cfbe48f6cc475bf30e85061b104ae5f919d103bf9e7142eedfa699554","source":{"kind":"arxiv","id":"1502.01957","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.01957","created_at":"2026-05-18T01:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"1502.01957v1","created_at":"2026-05-18T01:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.01957","created_at":"2026-05-18T01:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"HV6UNDH34SHW","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HV6UNDH34SHWZRDV","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HV6UNDH3","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:HV6UNDH34SHWZRDVX4YOQUDBWE","target":"record","payload":{"canonical_record":{"source":{"id":"1502.01957","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-02-06T17:02:53Z","cross_cats_sorted":[],"title_canon_sha256":"d077ff36c5df7e5d1accd42c62c95f1c0c6477046285254213fc5f0d85f7a008","abstract_canon_sha256":"73b05402665d092e02d4d34e6cb487a8a5170fff08b80fd17087095b5db72080"},"schema_version":"1.0"},"canonical_sha256":"3d7d468cfbe48f6cc475bf30e85061b104ae5f919d103bf9e7142eedfa699554","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:44.510090Z","signature_b64":"pUcgndX8WJZTkdmWzl4ByEhz7dFIqPFsFjJ+k1HMqOW5Gm7awEcDFQRloFWlF6XyNzveVBL6ZSFAOrgO2vOYDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d7d468cfbe48f6cc475bf30e85061b104ae5f919d103bf9e7142eedfa699554","last_reissued_at":"2026-05-18T01:03:44.509510Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:44.509510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.01957","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":"2026-05-18T01:03:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YEEqoJF0iJKgXoRD/BOadVuZ4m9MIWjF0T4cfAdDaIncjvkMvmlNi6RylM0xWYLTWdKsJzcgBlxjgsEqWbbrDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T14:00:22.206251Z"},"content_sha256":"ebe1e597e5420a22da43be6805c457fb5e7da76f2cb371b6a44cc49dd61e3979","schema_version":"1.0","event_id":"sha256:ebe1e597e5420a22da43be6805c457fb5e7da76f2cb371b6a44cc49dd61e3979"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:HV6UNDH34SHWZRDVX4YOQUDBWE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Functional calculus for $C_0$-semigroups using infinite-dimensional systems theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Felix Schwenninger, Hans Zwart","submitted_at":"2015-02-06T17:02:53Z","abstract_excerpt":"In this short note we use ideas from systems theory to define a functional calculus for infinitesimal generators of strongly continuous semigroups on a Hilbert space. Among others, we show how this leads to new proofs of (known) results in functional calculus."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01957","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":"2026-05-18T01:03:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OOL2Tu7iVjrmkiSk3O7WvKji/iJ0N4u9RZVPOkCapmjEfgpM160ZgX4f0OcxEDarNqilrs2IQX5/OFrcp6g0Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T14:00:22.206611Z"},"content_sha256":"5db4899613b630d7065303e4af2ce6a85c91c106d864fd348537bfa6d5141c2a","schema_version":"1.0","event_id":"sha256:5db4899613b630d7065303e4af2ce6a85c91c106d864fd348537bfa6d5141c2a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HV6UNDH34SHWZRDVX4YOQUDBWE/bundle.json","state_url":"https://pith.science/pith/HV6UNDH34SHWZRDVX4YOQUDBWE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HV6UNDH34SHWZRDVX4YOQUDBWE/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":"2026-06-21T14:00:22Z","links":{"resolver":"https://pith.science/pith/HV6UNDH34SHWZRDVX4YOQUDBWE","bundle":"https://pith.science/pith/HV6UNDH34SHWZRDVX4YOQUDBWE/bundle.json","state":"https://pith.science/pith/HV6UNDH34SHWZRDVX4YOQUDBWE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HV6UNDH34SHWZRDVX4YOQUDBWE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HV6UNDH34SHWZRDVX4YOQUDBWE","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":"73b05402665d092e02d4d34e6cb487a8a5170fff08b80fd17087095b5db72080","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-02-06T17:02:53Z","title_canon_sha256":"d077ff36c5df7e5d1accd42c62c95f1c0c6477046285254213fc5f0d85f7a008"},"schema_version":"1.0","source":{"id":"1502.01957","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.01957","created_at":"2026-05-18T01:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"1502.01957v1","created_at":"2026-05-18T01:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.01957","created_at":"2026-05-18T01:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"HV6UNDH34SHW","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HV6UNDH34SHWZRDV","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HV6UNDH3","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:5db4899613b630d7065303e4af2ce6a85c91c106d864fd348537bfa6d5141c2a","target":"graph","created_at":"2026-05-18T01:03:44Z","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 short note we use ideas from systems theory to define a functional calculus for infinitesimal generators of strongly continuous semigroups on a Hilbert space. Among others, we show how this leads to new proofs of (known) results in functional calculus.","authors_text":"Felix Schwenninger, Hans Zwart","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-02-06T17:02:53Z","title":"Functional calculus for $C_0$-semigroups using infinite-dimensional systems theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01957","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:ebe1e597e5420a22da43be6805c457fb5e7da76f2cb371b6a44cc49dd61e3979","target":"record","created_at":"2026-05-18T01:03:44Z","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":"73b05402665d092e02d4d34e6cb487a8a5170fff08b80fd17087095b5db72080","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-02-06T17:02:53Z","title_canon_sha256":"d077ff36c5df7e5d1accd42c62c95f1c0c6477046285254213fc5f0d85f7a008"},"schema_version":"1.0","source":{"id":"1502.01957","kind":"arxiv","version":1}},"canonical_sha256":"3d7d468cfbe48f6cc475bf30e85061b104ae5f919d103bf9e7142eedfa699554","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d7d468cfbe48f6cc475bf30e85061b104ae5f919d103bf9e7142eedfa699554","first_computed_at":"2026-05-18T01:03:44.509510Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:44.509510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pUcgndX8WJZTkdmWzl4ByEhz7dFIqPFsFjJ+k1HMqOW5Gm7awEcDFQRloFWlF6XyNzveVBL6ZSFAOrgO2vOYDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:44.510090Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.01957","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ebe1e597e5420a22da43be6805c457fb5e7da76f2cb371b6a44cc49dd61e3979","sha256:5db4899613b630d7065303e4af2ce6a85c91c106d864fd348537bfa6d5141c2a"],"state_sha256":"7e1690a837fd2b88574d8facb70763a9efb67dc6c4c1cc3b910910292f7982c8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xhJQcOyzrLjtdEI6tEgA9QNH2sGMp0R7ZyZzBgnoOujBZDqb//WXPOeZga2e4VaW189lwAXq5HfPQuzR2uScBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T14:00:22.208886Z","bundle_sha256":"788e09f43d39d31a79c1052897080a47809b46edc6bb3a130b99761c06555316"}}