{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:DYF7X7ME2BUN4LC5K7TKMSWABY","short_pith_number":"pith:DYF7X7ME","canonical_record":{"source":{"id":"1207.6229","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-07-26T10:28:25Z","cross_cats_sorted":[],"title_canon_sha256":"c037867b19ba8386c950e0aaecd523d82fe8ef4f7d45d2584a5b17140fc204ad","abstract_canon_sha256":"9375a6ea2b4d8be612f6c710800a8d7263539f69bb21234d9a885521b33bf04d"},"schema_version":"1.0"},"canonical_sha256":"1e0bfbfd84d068de2c5d57e6a64ac00e34aecb137aa0268c576eaa297dbc2859","source":{"kind":"arxiv","id":"1207.6229","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.6229","created_at":"2026-05-18T03:50:08Z"},{"alias_kind":"arxiv_version","alias_value":"1207.6229v1","created_at":"2026-05-18T03:50:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.6229","created_at":"2026-05-18T03:50:08Z"},{"alias_kind":"pith_short_12","alias_value":"DYF7X7ME2BUN","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DYF7X7ME2BUN4LC5","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DYF7X7ME","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:DYF7X7ME2BUN4LC5K7TKMSWABY","target":"record","payload":{"canonical_record":{"source":{"id":"1207.6229","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-07-26T10:28:25Z","cross_cats_sorted":[],"title_canon_sha256":"c037867b19ba8386c950e0aaecd523d82fe8ef4f7d45d2584a5b17140fc204ad","abstract_canon_sha256":"9375a6ea2b4d8be612f6c710800a8d7263539f69bb21234d9a885521b33bf04d"},"schema_version":"1.0"},"canonical_sha256":"1e0bfbfd84d068de2c5d57e6a64ac00e34aecb137aa0268c576eaa297dbc2859","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:08.409429Z","signature_b64":"zzrCkEuw1d9TScyaAXdHMXb2E680LbU22oUN37tqgyyZwp54aJfMipr96nMMP1XvqaV/2jdSxFvQegAGnlbfDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1e0bfbfd84d068de2c5d57e6a64ac00e34aecb137aa0268c576eaa297dbc2859","last_reissued_at":"2026-05-18T03:50:08.408647Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:08.408647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.6229","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":"2026-05-18T03:50:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WCsrTCiMbQnDBG7umi3EgI3vpeXOEu/xJEca1ziFturYJaOU92Y5xZWoiHPVNn+UAdx46u5dSZwvJvfCQj6dBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T14:46:37.261797Z"},"content_sha256":"6aa14b42f7c54334a8ac129076a37c4818e870944585226c1a35c182e3ab77bf","schema_version":"1.0","event_id":"sha256:6aa14b42f7c54334a8ac129076a37c4818e870944585226c1a35c182e3ab77bf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:DYF7X7ME2BUN4LC5K7TKMSWABY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weakly admissible $H^{\\infty}(\\C_{-})$-calculus on general Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Felix Schwenninger, Hans Zwart","submitted_at":"2012-07-26T10:28:25Z","abstract_excerpt":"We show that, given a Banach space and a generator of an exponentially stable $C_{0}$-semigroup, a weakly admissible operator $g(A)$ can be defined for any $g$ bounded, analytic function on the left half-plane. This yields an (unbounded) functional calculus. The construction uses a Toeplitz operator and is motivated by system theory. In separable Hilbert spaces, we even get admissibility. Furthermore, it is investigated when a bounded calculus can be guaranteed. For this we introduce the new notion of exact observability by direction. Finally, it is shown that the calculus coincides with one f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6229","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":"2026-05-18T03:50:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v6DgVKsPhgyfEBsC+4kDozG8UcmdVsq0ZbRhrTKq0/67nw2nsDDm+mLsNRXqPeK0yvaSQLdRUYGLaqyB5REzBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T14:46:37.262164Z"},"content_sha256":"d67103362f1f806e9943bcbbce556844e6371c186f9b674ff4d95ca9316632bb","schema_version":"1.0","event_id":"sha256:d67103362f1f806e9943bcbbce556844e6371c186f9b674ff4d95ca9316632bb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DYF7X7ME2BUN4LC5K7TKMSWABY/bundle.json","state_url":"https://pith.science/pith/DYF7X7ME2BUN4LC5K7TKMSWABY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DYF7X7ME2BUN4LC5K7TKMSWABY/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":"2026-06-21T14:46:37Z","links":{"resolver":"https://pith.science/pith/DYF7X7ME2BUN4LC5K7TKMSWABY","bundle":"https://pith.science/pith/DYF7X7ME2BUN4LC5K7TKMSWABY/bundle.json","state":"https://pith.science/pith/DYF7X7ME2BUN4LC5K7TKMSWABY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DYF7X7ME2BUN4LC5K7TKMSWABY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DYF7X7ME2BUN4LC5K7TKMSWABY","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":"9375a6ea2b4d8be612f6c710800a8d7263539f69bb21234d9a885521b33bf04d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-07-26T10:28:25Z","title_canon_sha256":"c037867b19ba8386c950e0aaecd523d82fe8ef4f7d45d2584a5b17140fc204ad"},"schema_version":"1.0","source":{"id":"1207.6229","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.6229","created_at":"2026-05-18T03:50:08Z"},{"alias_kind":"arxiv_version","alias_value":"1207.6229v1","created_at":"2026-05-18T03:50:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.6229","created_at":"2026-05-18T03:50:08Z"},{"alias_kind":"pith_short_12","alias_value":"DYF7X7ME2BUN","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DYF7X7ME2BUN4LC5","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DYF7X7ME","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:d67103362f1f806e9943bcbbce556844e6371c186f9b674ff4d95ca9316632bb","target":"graph","created_at":"2026-05-18T03:50:08Z","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 show that, given a Banach space and a generator of an exponentially stable $C_{0}$-semigroup, a weakly admissible operator $g(A)$ can be defined for any $g$ bounded, analytic function on the left half-plane. This yields an (unbounded) functional calculus. The construction uses a Toeplitz operator and is motivated by system theory. In separable Hilbert spaces, we even get admissibility. Furthermore, it is investigated when a bounded calculus can be guaranteed. For this we introduce the new notion of exact observability by direction. Finally, it is shown that the calculus coincides with one f","authors_text":"Felix Schwenninger, Hans Zwart","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-07-26T10:28:25Z","title":"Weakly admissible $H^{\\infty}(\\C_{-})$-calculus on general Banach spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6229","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":"sha256:6aa14b42f7c54334a8ac129076a37c4818e870944585226c1a35c182e3ab77bf","target":"record","created_at":"2026-05-18T03:50:08Z","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":"9375a6ea2b4d8be612f6c710800a8d7263539f69bb21234d9a885521b33bf04d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-07-26T10:28:25Z","title_canon_sha256":"c037867b19ba8386c950e0aaecd523d82fe8ef4f7d45d2584a5b17140fc204ad"},"schema_version":"1.0","source":{"id":"1207.6229","kind":"arxiv","version":1}},"canonical_sha256":"1e0bfbfd84d068de2c5d57e6a64ac00e34aecb137aa0268c576eaa297dbc2859","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e0bfbfd84d068de2c5d57e6a64ac00e34aecb137aa0268c576eaa297dbc2859","first_computed_at":"2026-05-18T03:50:08.408647Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:08.408647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zzrCkEuw1d9TScyaAXdHMXb2E680LbU22oUN37tqgyyZwp54aJfMipr96nMMP1XvqaV/2jdSxFvQegAGnlbfDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:08.409429Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.6229","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6aa14b42f7c54334a8ac129076a37c4818e870944585226c1a35c182e3ab77bf","sha256:d67103362f1f806e9943bcbbce556844e6371c186f9b674ff4d95ca9316632bb"],"state_sha256":"266fba796cea7f2987d3713945f4f4f3051ce23ad129848646a8e9271d089848"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5NdsyV4UA+kLhtde0QyLWoKEOtsJx4wVTlLZqKH4eSf+p0wk/4BpifN5LB18hH3m/DgoXJlXaPu69kAQw2fVAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T14:46:37.264129Z","bundle_sha256":"d7abe63626685ced1d60f7b9b6da25192bb8464f8e5c2f9b4a5e81d72f5449fc"}}