{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:DL6OPELBYO63VY4EIGMZ4GG2EK","short_pith_number":"pith:DL6OPELB","schema_version":"1.0","canonical_sha256":"1afce79161c3bdbae38441999e18da2287ac602ea279bd9487dfcff1e78734d6","source":{"kind":"arxiv","id":"1307.0174","version":1},"attestation_state":"computed","paper":{"title":"Geometric constructions of thin Blaschke products and reducing subspace problem","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Hansong Huang, Kunyu Guo","submitted_at":"2013-06-30T03:45:52Z","abstract_excerpt":"In this paper, we mainly study geometric constructions of thin Blaschke products $B$ and reducing subspace problem of multiplication operators induced by such symbols $B$ on the Bergman space. Considering such multiplication operators $M_B$, we present a representation of those operators commuting with both $M_B$ and $M_B^*$. It is shown that for \"most\" thin Blaschke products $B$, $M_B$ is irreducible, i.e. $M_B$ has no nontrivial reducing subspace; and such a thin Blaschke product $B$ is constructed.\n  As an application of the methods, it is proved that for \"most\" finite Blaschke products $\\p"},"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":"1307.0174","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.FA","submitted_at":"2013-06-30T03:45:52Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"d599675d2dab9b37a5594a0d800c4d6683ee0ae65ec0c3afd20f1dab34550112","abstract_canon_sha256":"37997997859aff8f6f3830b2b0a911505df87f3b0d38ef7e51cc61826b25a244"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:29.673272Z","signature_b64":"NAwjnV7EFRhzwhC/dyUno67uf+K4goVqYw14gYHd9tkujfXZ8fH0K85OdS3SZkxlvIxCxEzbgzhtafDJieGcCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1afce79161c3bdbae38441999e18da2287ac602ea279bd9487dfcff1e78734d6","last_reissued_at":"2026-05-18T00:44:29.672744Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:29.672744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometric constructions of thin Blaschke products and reducing subspace problem","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Hansong Huang, Kunyu Guo","submitted_at":"2013-06-30T03:45:52Z","abstract_excerpt":"In this paper, we mainly study geometric constructions of thin Blaschke products $B$ and reducing subspace problem of multiplication operators induced by such symbols $B$ on the Bergman space. Considering such multiplication operators $M_B$, we present a representation of those operators commuting with both $M_B$ and $M_B^*$. It is shown that for \"most\" thin Blaschke products $B$, $M_B$ is irreducible, i.e. $M_B$ has no nontrivial reducing subspace; and such a thin Blaschke product $B$ is constructed.\n  As an application of the methods, it is proved that for \"most\" finite Blaschke products $\\p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0174","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":"1307.0174","created_at":"2026-05-18T00:44:29.672815+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.0174v1","created_at":"2026-05-18T00:44:29.672815+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.0174","created_at":"2026-05-18T00:44:29.672815+00:00"},{"alias_kind":"pith_short_12","alias_value":"DL6OPELBYO63","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"DL6OPELBYO63VY4E","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"DL6OPELB","created_at":"2026-05-18T12:27:43.054852+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/DL6OPELBYO63VY4EIGMZ4GG2EK","json":"https://pith.science/pith/DL6OPELBYO63VY4EIGMZ4GG2EK.json","graph_json":"https://pith.science/api/pith-number/DL6OPELBYO63VY4EIGMZ4GG2EK/graph.json","events_json":"https://pith.science/api/pith-number/DL6OPELBYO63VY4EIGMZ4GG2EK/events.json","paper":"https://pith.science/paper/DL6OPELB"},"agent_actions":{"view_html":"https://pith.science/pith/DL6OPELBYO63VY4EIGMZ4GG2EK","download_json":"https://pith.science/pith/DL6OPELBYO63VY4EIGMZ4GG2EK.json","view_paper":"https://pith.science/paper/DL6OPELB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.0174&json=true","fetch_graph":"https://pith.science/api/pith-number/DL6OPELBYO63VY4EIGMZ4GG2EK/graph.json","fetch_events":"https://pith.science/api/pith-number/DL6OPELBYO63VY4EIGMZ4GG2EK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DL6OPELBYO63VY4EIGMZ4GG2EK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DL6OPELBYO63VY4EIGMZ4GG2EK/action/storage_attestation","attest_author":"https://pith.science/pith/DL6OPELBYO63VY4EIGMZ4GG2EK/action/author_attestation","sign_citation":"https://pith.science/pith/DL6OPELBYO63VY4EIGMZ4GG2EK/action/citation_signature","submit_replication":"https://pith.science/pith/DL6OPELBYO63VY4EIGMZ4GG2EK/action/replication_record"}},"created_at":"2026-05-18T00:44:29.672815+00:00","updated_at":"2026-05-18T00:44:29.672815+00:00"}