{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:UK24YFAGI2JMBA2MCUWZJ7MADK","short_pith_number":"pith:UK24YFAG","schema_version":"1.0","canonical_sha256":"a2b5cc14064692c0834c152d94fd801a8f73468f688a82d5bc4fdadf4d3b1f91","source":{"kind":"arxiv","id":"1403.5032","version":2},"attestation_state":"computed","paper":{"title":"Transitivity and bundle shifts","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Anjian Xu, Ronald G. Douglas","submitted_at":"2014-03-20T03:34:46Z","abstract_excerpt":"A subalgebra $A$ of the algebra $B(\\mathcal{H})$ of bounded linear operators on a separable Hilbert space $\\mathcal{H}$ is said to be catalytic if every transitive subalgebra $\\mathcal{T}\\subset B(\\mathcal{H})$ containing it is strongly dense. We show that for a hypo-Dirichlet or logmodular algebra, $A=H^{\\infty}(m)$ acting on a generalized Hardy space $H^{2}(m)$ for a representing measure $m$ that defines a reproducing kernel Hilbert space is catalytic. For the case of a nice finitely-connected domain, we show that the \"holomorphic functions\" of a bundle shift yields a catalytic algebra, thus"},"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":"1403.5032","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.FA","submitted_at":"2014-03-20T03:34:46Z","cross_cats_sorted":[],"title_canon_sha256":"9dfba6d7794ef3c0b6a4d60338a7cebde46ab471c781d8927a72ae978474e80f","abstract_canon_sha256":"e8285569e5e6eeb4a3f7d68070729e89b4e8264869577a0daa85b790160a57f9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:56.833109Z","signature_b64":"ZmzMFypitERA641pZf9AxiX4nxUddaCRphU6tTXffc31SsAWjuGXp/xtb+KI2sOjr+ykNWtk1zHhv9I3RfcFCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2b5cc14064692c0834c152d94fd801a8f73468f688a82d5bc4fdadf4d3b1f91","last_reissued_at":"2026-05-18T02:55:56.832534Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:56.832534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Transitivity and bundle shifts","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Anjian Xu, Ronald G. Douglas","submitted_at":"2014-03-20T03:34:46Z","abstract_excerpt":"A subalgebra $A$ of the algebra $B(\\mathcal{H})$ of bounded linear operators on a separable Hilbert space $\\mathcal{H}$ is said to be catalytic if every transitive subalgebra $\\mathcal{T}\\subset B(\\mathcal{H})$ containing it is strongly dense. We show that for a hypo-Dirichlet or logmodular algebra, $A=H^{\\infty}(m)$ acting on a generalized Hardy space $H^{2}(m)$ for a representing measure $m$ that defines a reproducing kernel Hilbert space is catalytic. For the case of a nice finitely-connected domain, we show that the \"holomorphic functions\" of a bundle shift yields a catalytic algebra, thus"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5032","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":"1403.5032","created_at":"2026-05-18T02:55:56.832620+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.5032v2","created_at":"2026-05-18T02:55:56.832620+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5032","created_at":"2026-05-18T02:55:56.832620+00:00"},{"alias_kind":"pith_short_12","alias_value":"UK24YFAGI2JM","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_16","alias_value":"UK24YFAGI2JMBA2M","created_at":"2026-05-18T12:28:52.271510+00:00"},{"alias_kind":"pith_short_8","alias_value":"UK24YFAG","created_at":"2026-05-18T12:28:52.271510+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/UK24YFAGI2JMBA2MCUWZJ7MADK","json":"https://pith.science/pith/UK24YFAGI2JMBA2MCUWZJ7MADK.json","graph_json":"https://pith.science/api/pith-number/UK24YFAGI2JMBA2MCUWZJ7MADK/graph.json","events_json":"https://pith.science/api/pith-number/UK24YFAGI2JMBA2MCUWZJ7MADK/events.json","paper":"https://pith.science/paper/UK24YFAG"},"agent_actions":{"view_html":"https://pith.science/pith/UK24YFAGI2JMBA2MCUWZJ7MADK","download_json":"https://pith.science/pith/UK24YFAGI2JMBA2MCUWZJ7MADK.json","view_paper":"https://pith.science/paper/UK24YFAG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.5032&json=true","fetch_graph":"https://pith.science/api/pith-number/UK24YFAGI2JMBA2MCUWZJ7MADK/graph.json","fetch_events":"https://pith.science/api/pith-number/UK24YFAGI2JMBA2MCUWZJ7MADK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UK24YFAGI2JMBA2MCUWZJ7MADK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UK24YFAGI2JMBA2MCUWZJ7MADK/action/storage_attestation","attest_author":"https://pith.science/pith/UK24YFAGI2JMBA2MCUWZJ7MADK/action/author_attestation","sign_citation":"https://pith.science/pith/UK24YFAGI2JMBA2MCUWZJ7MADK/action/citation_signature","submit_replication":"https://pith.science/pith/UK24YFAGI2JMBA2MCUWZJ7MADK/action/replication_record"}},"created_at":"2026-05-18T02:55:56.832620+00:00","updated_at":"2026-05-18T02:55:56.832620+00:00"}