{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:GQ3LYWUDXATR7EEOAN5INRL7PM","short_pith_number":"pith:GQ3LYWUD","schema_version":"1.0","canonical_sha256":"3436bc5a83b8271f908e037a86c57f7b04afbb3fee217f62d1c82a8d06f758c0","source":{"kind":"arxiv","id":"1305.2325","version":1},"attestation_state":"computed","paper":{"title":"Difference sets and frequently hypercyclic weighted shifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Fr\\'ed\\'eric Bayart, Imre Ruzsa","submitted_at":"2013-05-10T12:18:32Z","abstract_excerpt":"We solve several problems on frequently hypercyclic operators. Firstly, we characterize frequently hypercyclic weighted shifts on $\\ell^p(\\mathbb Z)$, $p\\geq 1$. Our method uses properties of the difference set of a set with positive upper density. Secondly, we show that there exists an operator which is $\\mathcal U$-frequently hypercyclic, yet not frequently hypercyclic and that there exists an operator which is frequently hypercyclic, yet not distributionally chaotic. These (surprizing) counterexamples are given by weighted shifts on $c_0$. The construction of these shifts lies on the constr"},"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":"1305.2325","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-05-10T12:18:32Z","cross_cats_sorted":[],"title_canon_sha256":"c3530db9918c46f3db771fd81cc8e629c5c94904315f2304519e187a160302e5","abstract_canon_sha256":"7fee3cf9c0694d7a73b5b76de8039f2b78033d2490a8a3adc53422580d8fa586"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:17.527077Z","signature_b64":"izKToLYbjbBJaUE7Xs5mjFXL5k6wAYcXhylYvDAAFfuIf0J6DiztlSckHGms96SsN2/xlCH0/PmJPTf6MnhsAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3436bc5a83b8271f908e037a86c57f7b04afbb3fee217f62d1c82a8d06f758c0","last_reissued_at":"2026-05-17T23:53:17.526364Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:17.526364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Difference sets and frequently hypercyclic weighted shifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Fr\\'ed\\'eric Bayart, Imre Ruzsa","submitted_at":"2013-05-10T12:18:32Z","abstract_excerpt":"We solve several problems on frequently hypercyclic operators. Firstly, we characterize frequently hypercyclic weighted shifts on $\\ell^p(\\mathbb Z)$, $p\\geq 1$. Our method uses properties of the difference set of a set with positive upper density. Secondly, we show that there exists an operator which is $\\mathcal U$-frequently hypercyclic, yet not frequently hypercyclic and that there exists an operator which is frequently hypercyclic, yet not distributionally chaotic. These (surprizing) counterexamples are given by weighted shifts on $c_0$. The construction of these shifts lies on the constr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2325","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1305.2325","created_at":"2026-05-17T23:53:17.526477+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.2325v1","created_at":"2026-05-17T23:53:17.526477+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.2325","created_at":"2026-05-17T23:53:17.526477+00:00"},{"alias_kind":"pith_short_12","alias_value":"GQ3LYWUDXATR","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_16","alias_value":"GQ3LYWUDXATR7EEO","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_8","alias_value":"GQ3LYWUD","created_at":"2026-05-18T12:27:45.050594+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/GQ3LYWUDXATR7EEOAN5INRL7PM","json":"https://pith.science/pith/GQ3LYWUDXATR7EEOAN5INRL7PM.json","graph_json":"https://pith.science/api/pith-number/GQ3LYWUDXATR7EEOAN5INRL7PM/graph.json","events_json":"https://pith.science/api/pith-number/GQ3LYWUDXATR7EEOAN5INRL7PM/events.json","paper":"https://pith.science/paper/GQ3LYWUD"},"agent_actions":{"view_html":"https://pith.science/pith/GQ3LYWUDXATR7EEOAN5INRL7PM","download_json":"https://pith.science/pith/GQ3LYWUDXATR7EEOAN5INRL7PM.json","view_paper":"https://pith.science/paper/GQ3LYWUD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.2325&json=true","fetch_graph":"https://pith.science/api/pith-number/GQ3LYWUDXATR7EEOAN5INRL7PM/graph.json","fetch_events":"https://pith.science/api/pith-number/GQ3LYWUDXATR7EEOAN5INRL7PM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GQ3LYWUDXATR7EEOAN5INRL7PM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GQ3LYWUDXATR7EEOAN5INRL7PM/action/storage_attestation","attest_author":"https://pith.science/pith/GQ3LYWUDXATR7EEOAN5INRL7PM/action/author_attestation","sign_citation":"https://pith.science/pith/GQ3LYWUDXATR7EEOAN5INRL7PM/action/citation_signature","submit_replication":"https://pith.science/pith/GQ3LYWUDXATR7EEOAN5INRL7PM/action/replication_record"}},"created_at":"2026-05-17T23:53:17.526477+00:00","updated_at":"2026-05-17T23:53:17.526477+00:00"}