{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:TQQGTBQTGSWLVLIB76X6MN5YU3","short_pith_number":"pith:TQQGTBQT","canonical_record":{"source":{"id":"1310.5083","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-10-18T16:35:45Z","cross_cats_sorted":[],"title_canon_sha256":"659fba8f78409b8e99842b11f0bd230b77d621a5964d2ca7a5f9660c7a925407","abstract_canon_sha256":"fe689ae8b556bccfbaebb7ff3b55e72a51b42d87954f78a0aa9a63ce5b606819"},"schema_version":"1.0"},"canonical_sha256":"9c2069861334acbaad01ffafe637b8a6dba904955076ee5213d37dbdad00d822","source":{"kind":"arxiv","id":"1310.5083","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.5083","created_at":"2026-05-18T03:10:01Z"},{"alias_kind":"arxiv_version","alias_value":"1310.5083v1","created_at":"2026-05-18T03:10:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.5083","created_at":"2026-05-18T03:10:01Z"},{"alias_kind":"pith_short_12","alias_value":"TQQGTBQTGSWL","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TQQGTBQTGSWLVLIB","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TQQGTBQT","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:TQQGTBQTGSWLVLIB76X6MN5YU3","target":"record","payload":{"canonical_record":{"source":{"id":"1310.5083","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-10-18T16:35:45Z","cross_cats_sorted":[],"title_canon_sha256":"659fba8f78409b8e99842b11f0bd230b77d621a5964d2ca7a5f9660c7a925407","abstract_canon_sha256":"fe689ae8b556bccfbaebb7ff3b55e72a51b42d87954f78a0aa9a63ce5b606819"},"schema_version":"1.0"},"canonical_sha256":"9c2069861334acbaad01ffafe637b8a6dba904955076ee5213d37dbdad00d822","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:01.132476Z","signature_b64":"Qtqe0Z8mgvtqZczOSuelJgQSdXnZsqdYxEwZ70l95qinm9Y5BpJBfMGeAC1yuSxULynLUuggvh5UVVombzrCCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c2069861334acbaad01ffafe637b8a6dba904955076ee5213d37dbdad00d822","last_reissued_at":"2026-05-18T03:10:01.131756Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:01.131756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.5083","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":"2026-05-18T03:10:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pxW57XfNZ80do5tb6qobQmIuGzD2zb38nKhgREhj201avX180Q+CnkdA13wsglyo6Qhjcc6VhLLHDpeR8pZWDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T05:26:23.363346Z"},"content_sha256":"186a2e6832611e4c9142bb232a7267c76b14a1f29130adf40b64699a7bf63c61","schema_version":"1.0","event_id":"sha256:186a2e6832611e4c9142bb232a7267c76b14a1f29130adf40b64699a7bf63c61"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:TQQGTBQTGSWLVLIB76X6MN5YU3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mean ergodic properties of the continuous Ces\\`aro operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Angela A. Albanese, Jos\\'e Bonet, Werner J. Ricker","submitted_at":"2013-10-18T16:35:45Z","abstract_excerpt":"Various properties of the (continuous) Ces\\`aro operator $\\mathsf{C}$, acting on Banach and Fr\\'echet spaces of continuous functions and $L^p$-spaces, are investigated. For instance, the spectrum and point spectrum of $\\mathsf{C}$ are completely determined and a study of certain dynamics of $\\mathsf{C}$ is undertaken (eg. hyper- and supercyclicity, chaotic behaviour). In addition, the mean (and uniform mean) ergodic nature of $\\mathsf{C}$ acting in the various spaces is identified."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5083","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":"2026-05-18T03:10:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VUZcyJk8er4RGboxBPeZHmvnOuGDNPf/nJzLsPerORQFg/OQqITISohvnyabbypHbJ9VmXlI6U55RAjDva+CAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T05:26:23.363701Z"},"content_sha256":"705300c542d525a509e07b329d1517fdbdd9e2a625cde1760a3b7526213b966f","schema_version":"1.0","event_id":"sha256:705300c542d525a509e07b329d1517fdbdd9e2a625cde1760a3b7526213b966f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TQQGTBQTGSWLVLIB76X6MN5YU3/bundle.json","state_url":"https://pith.science/pith/TQQGTBQTGSWLVLIB76X6MN5YU3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TQQGTBQTGSWLVLIB76X6MN5YU3/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":"2026-06-23T05:26:23Z","links":{"resolver":"https://pith.science/pith/TQQGTBQTGSWLVLIB76X6MN5YU3","bundle":"https://pith.science/pith/TQQGTBQTGSWLVLIB76X6MN5YU3/bundle.json","state":"https://pith.science/pith/TQQGTBQTGSWLVLIB76X6MN5YU3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TQQGTBQTGSWLVLIB76X6MN5YU3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TQQGTBQTGSWLVLIB76X6MN5YU3","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":"fe689ae8b556bccfbaebb7ff3b55e72a51b42d87954f78a0aa9a63ce5b606819","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-10-18T16:35:45Z","title_canon_sha256":"659fba8f78409b8e99842b11f0bd230b77d621a5964d2ca7a5f9660c7a925407"},"schema_version":"1.0","source":{"id":"1310.5083","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.5083","created_at":"2026-05-18T03:10:01Z"},{"alias_kind":"arxiv_version","alias_value":"1310.5083v1","created_at":"2026-05-18T03:10:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.5083","created_at":"2026-05-18T03:10:01Z"},{"alias_kind":"pith_short_12","alias_value":"TQQGTBQTGSWL","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TQQGTBQTGSWLVLIB","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TQQGTBQT","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:705300c542d525a509e07b329d1517fdbdd9e2a625cde1760a3b7526213b966f","target":"graph","created_at":"2026-05-18T03:10:01Z","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":"Various properties of the (continuous) Ces\\`aro operator $\\mathsf{C}$, acting on Banach and Fr\\'echet spaces of continuous functions and $L^p$-spaces, are investigated. For instance, the spectrum and point spectrum of $\\mathsf{C}$ are completely determined and a study of certain dynamics of $\\mathsf{C}$ is undertaken (eg. hyper- and supercyclicity, chaotic behaviour). In addition, the mean (and uniform mean) ergodic nature of $\\mathsf{C}$ acting in the various spaces is identified.","authors_text":"Angela A. Albanese, Jos\\'e Bonet, Werner J. Ricker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-10-18T16:35:45Z","title":"Mean ergodic properties of the continuous Ces\\`aro operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5083","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":"sha256:186a2e6832611e4c9142bb232a7267c76b14a1f29130adf40b64699a7bf63c61","target":"record","created_at":"2026-05-18T03:10:01Z","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":"fe689ae8b556bccfbaebb7ff3b55e72a51b42d87954f78a0aa9a63ce5b606819","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-10-18T16:35:45Z","title_canon_sha256":"659fba8f78409b8e99842b11f0bd230b77d621a5964d2ca7a5f9660c7a925407"},"schema_version":"1.0","source":{"id":"1310.5083","kind":"arxiv","version":1}},"canonical_sha256":"9c2069861334acbaad01ffafe637b8a6dba904955076ee5213d37dbdad00d822","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c2069861334acbaad01ffafe637b8a6dba904955076ee5213d37dbdad00d822","first_computed_at":"2026-05-18T03:10:01.131756Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:01.131756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qtqe0Z8mgvtqZczOSuelJgQSdXnZsqdYxEwZ70l95qinm9Y5BpJBfMGeAC1yuSxULynLUuggvh5UVVombzrCCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:01.132476Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.5083","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:186a2e6832611e4c9142bb232a7267c76b14a1f29130adf40b64699a7bf63c61","sha256:705300c542d525a509e07b329d1517fdbdd9e2a625cde1760a3b7526213b966f"],"state_sha256":"7f3e3828d530bc6e9024dc5907b11dc8afdd17a19e7bced27d3f284cad753892"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HVelsHMRpsckNt////h7xPAYTdaodS59NtPEWeFLnvqGF9v+ZZM/Q4Sm1LR/7eCYyO7kkFOH0moZnrWpT9InAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T05:26:23.365690Z","bundle_sha256":"a1cf96a51f8c54b69ffa39e4abc3c5bfa21c506d19cd269e3c7619365c10a1dc"}}