{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:2DZYDS6377JUQMKAV5EXMKUQES","short_pith_number":"pith:2DZYDS63","schema_version":"1.0","canonical_sha256":"d0f381cbdbffd3483140af49762a90248b42a84d1349dda9bf01ac3e54d03be5","source":{"kind":"arxiv","id":"1008.4017","version":2},"attestation_state":"computed","paper":{"title":"Szemeredi's theorem, frequent hypercyclicity and multiple recurrence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.FA","authors_text":"George Costakis, Ioannis Parissis","submitted_at":"2010-08-24T11:50:07Z","abstract_excerpt":"Let T be a bounded linear operator acting on a complex Banach space X and (\\lambda_n) a sequence of complex numbers. Our main result is that if |\\lambda_n|/|\\lambda_{n+1}| \\to 1 and the sequence (\\lambda_n T^n) is frequently universal then T is topologically multiply recurrent. To achieve such a result one has to carefully apply Szemer\\'edi's theorem in arithmetic progressions. We show that the previous assumption on the sequence (\\lambda_n) is optimal among sequences such that |\\lambda_n|/|\\lambda_{n+1}| converges in [0,+\\infty]. In the case of bilateral weighted shifts and adjoints of multip"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1008.4017","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2010-08-24T11:50:07Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"f1418b8a2fb9157292d4b01d85d6949832225f3ec455002e5fa25973f64b60fe","abstract_canon_sha256":"29638a628ceb1f7a57cf9746032acbcb0552c46e97939c79912175e9b1a4844c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:46.176564Z","signature_b64":"UOt9VTyIBQD9iDrJRWZX6vFHXYzqYVd7BHvtPtW5mvf4CWVzYFpC+w2PYSuaq3ktRc1hS3Hc4+nJKMmc9KIuCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0f381cbdbffd3483140af49762a90248b42a84d1349dda9bf01ac3e54d03be5","last_reissued_at":"2026-05-18T03:10:46.175712Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:46.175712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Szemeredi's theorem, frequent hypercyclicity and multiple recurrence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.FA","authors_text":"George Costakis, Ioannis Parissis","submitted_at":"2010-08-24T11:50:07Z","abstract_excerpt":"Let T be a bounded linear operator acting on a complex Banach space X and (\\lambda_n) a sequence of complex numbers. Our main result is that if |\\lambda_n|/|\\lambda_{n+1}| \\to 1 and the sequence (\\lambda_n T^n) is frequently universal then T is topologically multiply recurrent. To achieve such a result one has to carefully apply Szemer\\'edi's theorem in arithmetic progressions. We show that the previous assumption on the sequence (\\lambda_n) is optimal among sequences such that |\\lambda_n|/|\\lambda_{n+1}| converges in [0,+\\infty]. In the case of bilateral weighted shifts and adjoints of multip"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4017","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1008.4017","created_at":"2026-05-18T03:10:46.175822+00:00"},{"alias_kind":"arxiv_version","alias_value":"1008.4017v2","created_at":"2026-05-18T03:10:46.175822+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.4017","created_at":"2026-05-18T03:10:46.175822+00:00"},{"alias_kind":"pith_short_12","alias_value":"2DZYDS6377JU","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_16","alias_value":"2DZYDS6377JUQMKA","created_at":"2026-05-18T12:26:03.138858+00:00"},{"alias_kind":"pith_short_8","alias_value":"2DZYDS63","created_at":"2026-05-18T12:26:03.138858+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2DZYDS6377JUQMKAV5EXMKUQES","json":"https://pith.science/pith/2DZYDS6377JUQMKAV5EXMKUQES.json","graph_json":"https://pith.science/api/pith-number/2DZYDS6377JUQMKAV5EXMKUQES/graph.json","events_json":"https://pith.science/api/pith-number/2DZYDS6377JUQMKAV5EXMKUQES/events.json","paper":"https://pith.science/paper/2DZYDS63"},"agent_actions":{"view_html":"https://pith.science/pith/2DZYDS6377JUQMKAV5EXMKUQES","download_json":"https://pith.science/pith/2DZYDS6377JUQMKAV5EXMKUQES.json","view_paper":"https://pith.science/paper/2DZYDS63","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1008.4017&json=true","fetch_graph":"https://pith.science/api/pith-number/2DZYDS6377JUQMKAV5EXMKUQES/graph.json","fetch_events":"https://pith.science/api/pith-number/2DZYDS6377JUQMKAV5EXMKUQES/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2DZYDS6377JUQMKAV5EXMKUQES/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2DZYDS6377JUQMKAV5EXMKUQES/action/storage_attestation","attest_author":"https://pith.science/pith/2DZYDS6377JUQMKAV5EXMKUQES/action/author_attestation","sign_citation":"https://pith.science/pith/2DZYDS6377JUQMKAV5EXMKUQES/action/citation_signature","submit_replication":"https://pith.science/pith/2DZYDS6377JUQMKAV5EXMKUQES/action/replication_record"}},"created_at":"2026-05-18T03:10:46.175822+00:00","updated_at":"2026-05-18T03:10:46.175822+00:00"}