{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:FLX7RFOKGHAR7XMNZDOHLEXPGI","short_pith_number":"pith:FLX7RFOK","schema_version":"1.0","canonical_sha256":"2aeff895ca31c11fdd8dc8dc7592ef323432514efb6f2c3e313c624e3c7884b8","source":{"kind":"arxiv","id":"1209.1458","version":1},"attestation_state":"computed","paper":{"title":"A weighted bilateral shift with cyclic square is supercyclic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Stanislav Shkarin","submitted_at":"2012-09-07T08:24:23Z","abstract_excerpt":"It is shown that for a bounded weighted bilateral shift $T$ acting on $\\ell_p(\\Z)$ for $1\\leq p\\leq 2$ supercyclicity of $T$, weak supercyclicity of $T$, cyclicity of $T\\oplus T$ and cyclicity of $T^2$ are equivalent. A new sufficient condition for cyclicity of a weighted bilateral shift is proved, which implies, in particular, that any compact weighted bilateral shift is cyclic."},"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":"1209.1458","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-07T08:24:23Z","cross_cats_sorted":[],"title_canon_sha256":"f58b81fe7ba24c216db47b1361ea8e5b4d843c167c956ecc1a71ce6e8a6019c9","abstract_canon_sha256":"3dd9db2407f99b2389ea2cb7f8861fa1ab33be598c4c3ca623746d34f16ae9e0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:04.737855Z","signature_b64":"0PzTHTdzC3HwPLtUrRpnSaXHesbs10Jzq9uzh/gTKxdbUCrTDvSQm6IW8JZYg9Ln0Tkst9hFr8qsVQgwGxrMBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2aeff895ca31c11fdd8dc8dc7592ef323432514efb6f2c3e313c624e3c7884b8","last_reissued_at":"2026-05-18T03:46:04.737141Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:04.737141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A weighted bilateral shift with cyclic square is supercyclic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Stanislav Shkarin","submitted_at":"2012-09-07T08:24:23Z","abstract_excerpt":"It is shown that for a bounded weighted bilateral shift $T$ acting on $\\ell_p(\\Z)$ for $1\\leq p\\leq 2$ supercyclicity of $T$, weak supercyclicity of $T$, cyclicity of $T\\oplus T$ and cyclicity of $T^2$ are equivalent. A new sufficient condition for cyclicity of a weighted bilateral shift is proved, which implies, in particular, that any compact weighted bilateral shift is cyclic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1458","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":"1209.1458","created_at":"2026-05-18T03:46:04.737273+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.1458v1","created_at":"2026-05-18T03:46:04.737273+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1458","created_at":"2026-05-18T03:46:04.737273+00:00"},{"alias_kind":"pith_short_12","alias_value":"FLX7RFOKGHAR","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"FLX7RFOKGHAR7XMN","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"FLX7RFOK","created_at":"2026-05-18T12:27:06.952714+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/FLX7RFOKGHAR7XMNZDOHLEXPGI","json":"https://pith.science/pith/FLX7RFOKGHAR7XMNZDOHLEXPGI.json","graph_json":"https://pith.science/api/pith-number/FLX7RFOKGHAR7XMNZDOHLEXPGI/graph.json","events_json":"https://pith.science/api/pith-number/FLX7RFOKGHAR7XMNZDOHLEXPGI/events.json","paper":"https://pith.science/paper/FLX7RFOK"},"agent_actions":{"view_html":"https://pith.science/pith/FLX7RFOKGHAR7XMNZDOHLEXPGI","download_json":"https://pith.science/pith/FLX7RFOKGHAR7XMNZDOHLEXPGI.json","view_paper":"https://pith.science/paper/FLX7RFOK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.1458&json=true","fetch_graph":"https://pith.science/api/pith-number/FLX7RFOKGHAR7XMNZDOHLEXPGI/graph.json","fetch_events":"https://pith.science/api/pith-number/FLX7RFOKGHAR7XMNZDOHLEXPGI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FLX7RFOKGHAR7XMNZDOHLEXPGI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FLX7RFOKGHAR7XMNZDOHLEXPGI/action/storage_attestation","attest_author":"https://pith.science/pith/FLX7RFOKGHAR7XMNZDOHLEXPGI/action/author_attestation","sign_citation":"https://pith.science/pith/FLX7RFOKGHAR7XMNZDOHLEXPGI/action/citation_signature","submit_replication":"https://pith.science/pith/FLX7RFOKGHAR7XMNZDOHLEXPGI/action/replication_record"}},"created_at":"2026-05-18T03:46:04.737273+00:00","updated_at":"2026-05-18T03:46:04.737273+00:00"}