{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:ROOSG4ETYARYJGAAGZYTZ2KDM2","short_pith_number":"pith:ROOSG4ET","schema_version":"1.0","canonical_sha256":"8b9d237093c02384980036713ce94366a1ecb3b2294fc35f1f1864ebefef5b31","source":{"kind":"arxiv","id":"2411.14609","version":1},"attestation_state":"computed","paper":{"title":"Hypercyclic algebras for weighted shifts on trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.FA","authors_text":"Arafat Abbar, Fernando Costa Jr","submitted_at":"2024-11-21T22:16:42Z","abstract_excerpt":"We study the existence of algebras of hypercyclic vectors for weighted backward shifts on sequence spaces of directed trees with the coordinatewise product. When $V$ is a rooted directed tree, we show the set of hypercyclic vectors of any backward weighted shift operator on the space $c_0(V)$ or $\\ell^1(V)$ is algebrable whenever it is not empty. We provide necessary and sufficient conditions for the existence of these structures on $\\ell^p(V), 1<p<+\\infty$. Examples of hypercyclic operators not having a hypercyclic algebra are found. We also study the existence of mixing and non-mixing backwa"},"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":"2411.14609","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2024-11-21T22:16:42Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"71c0df60e122c40e446a32282514a75325782c82b3d74a9e381a5be909815e7b","abstract_canon_sha256":"b2a46ec820a282bca867b5fcde1ce810cbb3dbeaf4ed3a173a86567dcaef2df1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:38:53.913050Z","signature_b64":"JLzTKOLe2TU1UGugNN82YvcvwiyL9P44qyuy7nSVXFRG2vs8aSol9zwexGxLkCog0M49uxAFTjNY5xTf4FFfAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b9d237093c02384980036713ce94366a1ecb3b2294fc35f1f1864ebefef5b31","last_reissued_at":"2026-07-05T09:38:53.912642Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:38:53.912642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hypercyclic algebras for weighted shifts on trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.FA","authors_text":"Arafat Abbar, Fernando Costa Jr","submitted_at":"2024-11-21T22:16:42Z","abstract_excerpt":"We study the existence of algebras of hypercyclic vectors for weighted backward shifts on sequence spaces of directed trees with the coordinatewise product. When $V$ is a rooted directed tree, we show the set of hypercyclic vectors of any backward weighted shift operator on the space $c_0(V)$ or $\\ell^1(V)$ is algebrable whenever it is not empty. We provide necessary and sufficient conditions for the existence of these structures on $\\ell^p(V), 1<p<+\\infty$. Examples of hypercyclic operators not having a hypercyclic algebra are found. We also study the existence of mixing and non-mixing backwa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.14609","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.14609/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2411.14609","created_at":"2026-07-05T09:38:53.912699+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.14609v1","created_at":"2026-07-05T09:38:53.912699+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.14609","created_at":"2026-07-05T09:38:53.912699+00:00"},{"alias_kind":"pith_short_12","alias_value":"ROOSG4ETYARY","created_at":"2026-07-05T09:38:53.912699+00:00"},{"alias_kind":"pith_short_16","alias_value":"ROOSG4ETYARYJGAA","created_at":"2026-07-05T09:38:53.912699+00:00"},{"alias_kind":"pith_short_8","alias_value":"ROOSG4ET","created_at":"2026-07-05T09:38:53.912699+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/ROOSG4ETYARYJGAAGZYTZ2KDM2","json":"https://pith.science/pith/ROOSG4ETYARYJGAAGZYTZ2KDM2.json","graph_json":"https://pith.science/api/pith-number/ROOSG4ETYARYJGAAGZYTZ2KDM2/graph.json","events_json":"https://pith.science/api/pith-number/ROOSG4ETYARYJGAAGZYTZ2KDM2/events.json","paper":"https://pith.science/paper/ROOSG4ET"},"agent_actions":{"view_html":"https://pith.science/pith/ROOSG4ETYARYJGAAGZYTZ2KDM2","download_json":"https://pith.science/pith/ROOSG4ETYARYJGAAGZYTZ2KDM2.json","view_paper":"https://pith.science/paper/ROOSG4ET","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.14609&json=true","fetch_graph":"https://pith.science/api/pith-number/ROOSG4ETYARYJGAAGZYTZ2KDM2/graph.json","fetch_events":"https://pith.science/api/pith-number/ROOSG4ETYARYJGAAGZYTZ2KDM2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ROOSG4ETYARYJGAAGZYTZ2KDM2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ROOSG4ETYARYJGAAGZYTZ2KDM2/action/storage_attestation","attest_author":"https://pith.science/pith/ROOSG4ETYARYJGAAGZYTZ2KDM2/action/author_attestation","sign_citation":"https://pith.science/pith/ROOSG4ETYARYJGAAGZYTZ2KDM2/action/citation_signature","submit_replication":"https://pith.science/pith/ROOSG4ETYARYJGAAGZYTZ2KDM2/action/replication_record"}},"created_at":"2026-07-05T09:38:53.912699+00:00","updated_at":"2026-07-05T09:38:53.912699+00:00"}