{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:MNZ36556HD2LFQ5TUUXNJRO5GB","short_pith_number":"pith:MNZ36556","canonical_record":{"source":{"id":"1301.1812","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-01-09T11:07:46Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"1fc9165af2ced9a2a1084bf7d62f643e48f359a72a38dc6be55bba85ea3d1216","abstract_canon_sha256":"c334e9a1cfdc1616fdff6edeab92fd97c175be02e5828ed0bb705cc23ffa5a13"},"schema_version":"1.0"},"canonical_sha256":"6373bf77be38f4b2c3b3a52ed4c5dd307edba593d031bcffa2bcaa644b97b086","source":{"kind":"arxiv","id":"1301.1812","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1812","created_at":"2026-05-18T01:34:36Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1812v2","created_at":"2026-05-18T01:34:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1812","created_at":"2026-05-18T01:34:36Z"},{"alias_kind":"pith_short_12","alias_value":"MNZ36556HD2L","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MNZ36556HD2LFQ5T","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MNZ36556","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:MNZ36556HD2LFQ5TUUXNJRO5GB","target":"record","payload":{"canonical_record":{"source":{"id":"1301.1812","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-01-09T11:07:46Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"1fc9165af2ced9a2a1084bf7d62f643e48f359a72a38dc6be55bba85ea3d1216","abstract_canon_sha256":"c334e9a1cfdc1616fdff6edeab92fd97c175be02e5828ed0bb705cc23ffa5a13"},"schema_version":"1.0"},"canonical_sha256":"6373bf77be38f4b2c3b3a52ed4c5dd307edba593d031bcffa2bcaa644b97b086","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:36.069548Z","signature_b64":"DKhhEPYpue3EHtngAzgt1EABmH2xbUwqUzDvo4IzpJkltxrAi1fR1ahBveaPn0c/k2XUzC45P2/cv7JYde7eDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6373bf77be38f4b2c3b3a52ed4c5dd307edba593d031bcffa2bcaa644b97b086","last_reissued_at":"2026-05-18T01:34:36.068836Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:36.068836Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.1812","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:34:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9WyqtAR5ByjzhZMh7uBFtmtg53/HKQMPNhdAQSObdBmA307ovi3XkegwPhW3GqpbqcHdi2kAB6Kk1UorsQdYCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T05:29:18.816138Z"},"content_sha256":"1d50a8b15413458b16922b7be3210bbe27034ddab02f11299ef3194d5fd54d22","schema_version":"1.0","event_id":"sha256:1d50a8b15413458b16922b7be3210bbe27034ddab02f11299ef3194d5fd54d22"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:MNZ36556HD2LFQ5TUUXNJRO5GB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Recurrent Linear Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.FA","authors_text":"Antonios Manoussos, George Costakis, Ioannis Parissis","submitted_at":"2013-01-09T11:07:46Z","abstract_excerpt":"We study the notion of recurrence and some of its variations for linear operators acting on Banach spaces. We characterize recurrence for several classes of linear operators such as weighted shifts, composition operators and multiplication operators on classical Banach spaces. We show that on separable complex Hilbert spaces the study of recurrent operators reduces, in many cases, to the study of unitary operators. Finally, we study the notion of product recurrence and state some relevant open questions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1812","kind":"arxiv","version":2},"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":"2026-05-18T01:34:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6jGSKd7XzuqlzXl43C4YR8gc6oQ3UETLbMoWPjBEP3e3rJJX/FaPvVJm+2lw3FnI1u7+qqspksHfeptyby2lBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T05:29:18.816506Z"},"content_sha256":"2fb3ddbca87f6a36bf8d569b002679b4f56619574b2381630cd17b86bec78108","schema_version":"1.0","event_id":"sha256:2fb3ddbca87f6a36bf8d569b002679b4f56619574b2381630cd17b86bec78108"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MNZ36556HD2LFQ5TUUXNJRO5GB/bundle.json","state_url":"https://pith.science/pith/MNZ36556HD2LFQ5TUUXNJRO5GB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MNZ36556HD2LFQ5TUUXNJRO5GB/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":"2026-05-28T05:29:18Z","links":{"resolver":"https://pith.science/pith/MNZ36556HD2LFQ5TUUXNJRO5GB","bundle":"https://pith.science/pith/MNZ36556HD2LFQ5TUUXNJRO5GB/bundle.json","state":"https://pith.science/pith/MNZ36556HD2LFQ5TUUXNJRO5GB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MNZ36556HD2LFQ5TUUXNJRO5GB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MNZ36556HD2LFQ5TUUXNJRO5GB","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":"c334e9a1cfdc1616fdff6edeab92fd97c175be02e5828ed0bb705cc23ffa5a13","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-01-09T11:07:46Z","title_canon_sha256":"1fc9165af2ced9a2a1084bf7d62f643e48f359a72a38dc6be55bba85ea3d1216"},"schema_version":"1.0","source":{"id":"1301.1812","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1812","created_at":"2026-05-18T01:34:36Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1812v2","created_at":"2026-05-18T01:34:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1812","created_at":"2026-05-18T01:34:36Z"},{"alias_kind":"pith_short_12","alias_value":"MNZ36556HD2L","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MNZ36556HD2LFQ5T","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MNZ36556","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:2fb3ddbca87f6a36bf8d569b002679b4f56619574b2381630cd17b86bec78108","target":"graph","created_at":"2026-05-18T01:34:36Z","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 study the notion of recurrence and some of its variations for linear operators acting on Banach spaces. We characterize recurrence for several classes of linear operators such as weighted shifts, composition operators and multiplication operators on classical Banach spaces. We show that on separable complex Hilbert spaces the study of recurrent operators reduces, in many cases, to the study of unitary operators. Finally, we study the notion of product recurrence and state some relevant open questions.","authors_text":"Antonios Manoussos, George Costakis, Ioannis Parissis","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-01-09T11:07:46Z","title":"Recurrent Linear Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1812","kind":"arxiv","version":2},"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":"sha256:1d50a8b15413458b16922b7be3210bbe27034ddab02f11299ef3194d5fd54d22","target":"record","created_at":"2026-05-18T01:34:36Z","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":"c334e9a1cfdc1616fdff6edeab92fd97c175be02e5828ed0bb705cc23ffa5a13","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-01-09T11:07:46Z","title_canon_sha256":"1fc9165af2ced9a2a1084bf7d62f643e48f359a72a38dc6be55bba85ea3d1216"},"schema_version":"1.0","source":{"id":"1301.1812","kind":"arxiv","version":2}},"canonical_sha256":"6373bf77be38f4b2c3b3a52ed4c5dd307edba593d031bcffa2bcaa644b97b086","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6373bf77be38f4b2c3b3a52ed4c5dd307edba593d031bcffa2bcaa644b97b086","first_computed_at":"2026-05-18T01:34:36.068836Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:36.068836Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DKhhEPYpue3EHtngAzgt1EABmH2xbUwqUzDvo4IzpJkltxrAi1fR1ahBveaPn0c/k2XUzC45P2/cv7JYde7eDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:36.069548Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.1812","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d50a8b15413458b16922b7be3210bbe27034ddab02f11299ef3194d5fd54d22","sha256:2fb3ddbca87f6a36bf8d569b002679b4f56619574b2381630cd17b86bec78108"],"state_sha256":"5f3b47cd8aca563a84723c40bfe0099b9936b82700ae8f928768e0bcbeeba6ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6Fm4CdDUSV1HvFT3tKmSkrYo3jMoV+MB6PVQegEQCWIajlq8NbMKk5y7gMvni4JYXW/yyyKs++zivh+hxgo+CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T05:29:18.818419Z","bundle_sha256":"936c056750e9a342d8f46a8ff5e5e7bb646565b4788cbdc3fb00feab6810990c"}}