{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:XWUDA5E6FQYIS6SBVSBVBGVLHX","short_pith_number":"pith:XWUDA5E6","schema_version":"1.0","canonical_sha256":"bda830749e2c30897a41ac83509aab3dee54288e8dc0ff78ad8e7123821d215f","source":{"kind":"arxiv","id":"1312.7498","version":2},"attestation_state":"computed","paper":{"title":"Cowen's class and Thomson's class","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Hansong Huang, Kunyu Guo","submitted_at":"2013-12-29T04:00:59Z","abstract_excerpt":"In studying commutants of analytic Toeplitz operators, Thomson proved a remarkable theorem which states that under a mild condition, the commutant of an analytic Toeplitz operator is equal to that of Toeplitz operator defined by a finite Blaschke product. Cowen gave an significant improvement of Thosom's result. In this paper, we will present examples in Cowen's class which does not lie in Thomson's class."},"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":"1312.7498","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.CV","submitted_at":"2013-12-29T04:00:59Z","cross_cats_sorted":[],"title_canon_sha256":"8c4852ab5f91c1ab1c45a399d91009f642fa317bd19584ad176a8e70c10c7f8e","abstract_canon_sha256":"c1d8401e68aae1536f3c67cd9182fb4c7a8a87112dab3f6e6e0f264b0c6824f5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:20.039351Z","signature_b64":"o5CybwLs0w6FzIhOpKXVDqo+TeXRS57VDy2L8eX/jB+VTUzph15oMPFJZX811brZhZ6wFw+B7i0jHwxgPzU8Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bda830749e2c30897a41ac83509aab3dee54288e8dc0ff78ad8e7123821d215f","last_reissued_at":"2026-05-18T03:02:20.038463Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:20.038463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cowen's class and Thomson's class","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Hansong Huang, Kunyu Guo","submitted_at":"2013-12-29T04:00:59Z","abstract_excerpt":"In studying commutants of analytic Toeplitz operators, Thomson proved a remarkable theorem which states that under a mild condition, the commutant of an analytic Toeplitz operator is equal to that of Toeplitz operator defined by a finite Blaschke product. Cowen gave an significant improvement of Thosom's result. In this paper, we will present examples in Cowen's class which does not lie in Thomson's class."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7498","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":"1312.7498","created_at":"2026-05-18T03:02:20.038614+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.7498v2","created_at":"2026-05-18T03:02:20.038614+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.7498","created_at":"2026-05-18T03:02:20.038614+00:00"},{"alias_kind":"pith_short_12","alias_value":"XWUDA5E6FQYI","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"XWUDA5E6FQYIS6SB","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"XWUDA5E6","created_at":"2026-05-18T12:28:06.772260+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/XWUDA5E6FQYIS6SBVSBVBGVLHX","json":"https://pith.science/pith/XWUDA5E6FQYIS6SBVSBVBGVLHX.json","graph_json":"https://pith.science/api/pith-number/XWUDA5E6FQYIS6SBVSBVBGVLHX/graph.json","events_json":"https://pith.science/api/pith-number/XWUDA5E6FQYIS6SBVSBVBGVLHX/events.json","paper":"https://pith.science/paper/XWUDA5E6"},"agent_actions":{"view_html":"https://pith.science/pith/XWUDA5E6FQYIS6SBVSBVBGVLHX","download_json":"https://pith.science/pith/XWUDA5E6FQYIS6SBVSBVBGVLHX.json","view_paper":"https://pith.science/paper/XWUDA5E6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.7498&json=true","fetch_graph":"https://pith.science/api/pith-number/XWUDA5E6FQYIS6SBVSBVBGVLHX/graph.json","fetch_events":"https://pith.science/api/pith-number/XWUDA5E6FQYIS6SBVSBVBGVLHX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XWUDA5E6FQYIS6SBVSBVBGVLHX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XWUDA5E6FQYIS6SBVSBVBGVLHX/action/storage_attestation","attest_author":"https://pith.science/pith/XWUDA5E6FQYIS6SBVSBVBGVLHX/action/author_attestation","sign_citation":"https://pith.science/pith/XWUDA5E6FQYIS6SBVSBVBGVLHX/action/citation_signature","submit_replication":"https://pith.science/pith/XWUDA5E6FQYIS6SBVSBVBGVLHX/action/replication_record"}},"created_at":"2026-05-18T03:02:20.038614+00:00","updated_at":"2026-05-18T03:02:20.038614+00:00"}